Research Article Fault Line Selection Method of Small...
Transcript of Research Article Fault Line Selection Method of Small...
Research ArticleFault Line Selection Method of Small Current toGround System Based on Atomic Sparse Decomposition andExtreme Learning Machine
Xiaowei Wang1 Yanfang Wei1 Zhihui Zeng1 Yaxiao Hou2 Jie Gao1 and Xiangxiang Wei1
1School of Electrical Engineering and Automation Henan Polytechnic University Jiaozuo 454000 China2School of Electrical Engineering and Automation Harbin Institute of Technology Harbin 150001 China
Correspondence should be addressed to Xiaowei Wang proceedings126com
Received 13 October 2014 Accepted 28 November 2014
Academic Editor Sergiu Dan Stan
Copyright copy 2015 Xiaowei Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
This paper proposed a fault line voting selection method based on atomic sparse decomposition (ASD) and extreme learningmachine (ELM) Firstly it adopted ASD algorithm to decompose zero sequence current of every feeder line at first two cycles andselected the first four atoms to construct main component atom library fundamental atom library and transient characteristicatom libraries 1 and 2 respectively And it used information entropy theory to calculate the atom libraries the measure values ofinformation entropy are got It constructed four ELM networks to train and test atom sample and then obtained every networkaccuracy At last it combined the ELM network output and confidence degree to vote and then compared the vote number toachieve fault line selection (FLS) Simulation experiment illustrated that the method accuracy is 100 it is not affected by faultdistance and transition resistance and it has strong ability of antinoise interference
1 Introduction
For small current to ground system FLS study focus is faultline identified when single phase to ground fault occurredat this moment the fault current is weaker and Petersencoil to ground mode also has the features Therefore theconventional method with using current amplitude size andphase information is difficult to obtain satisfactory results
In recent years modern signal processing technologyused FLS to get fault characteristic information such aswavelet transform [1] 119878 transform [2] mathematical mor-phology [3] Hilbert-Huang transform (HHT) [4] Pronyalgorithm [5] and Hough transform [6] Besides the com-mon method of FLS criterion had artificial neural networks[7] support vector machines [8] and Bayesian classification[9]
Zero sequence current was decomposed by wavelet trans-form and calculated wavelet modulus maxima to determinearrival time of traveling waversquos head and then compared the
amplitude and polarity of every feeder line at this time toachieve FLS [1] It used 119878 transform to get modulus value andphase angle of every frequency range and comparedmodulusvalue and phase angle to obtain characteristic frequency andvoting mechanism respectively the experiments indicatedthat the method could not only judge the fault line accuratelybut also obtain the FLS confidence degree [2] Paper [10]used 119878 transform to get transient fault feature and based onthe frequency point of transient maximum energy it chosecharacteristic frequency sequence therefore the criterionwith relative entropy values of multiple combination modesdetermined the fault section Paper [3] proposed a novelmethod which was based on mathematical morphology themethod included two aspects one used morphological filtersto preprocess the data and removed the noise impact forFLS at the maximum extent and the other adopted morpho-logical operators to detect the denoised signal with mutantaspect to judge the fault line Paper [4] calculated transient
Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 678120 19 pageshttpdxdoiorg1011552015678120
2 Journal of Sensors
instantaneous power by Hilbert-Huang transform (HHT)and got fault direction well the method took advantage oftransient high-frequency component at lower sampling rateIt tried to divide the zero sequence current signal into severalsegments to ensure good continuity and smaller mutationat every subsegment and Prony algorithm was appliedto choose transient dominant component with maximumenergy principle and then calculated the relative entropy andvoted by preliminary vote and 119896 values check to judge thefault line [5] Hough transform was adopted to constructwhole mutant direction angle which indicated overall trendof zero sequence current at initial stage and FLSwas achievedby distinguishing the direction angle [6] Paper [7] replacedordinary neurons with rough neurons and fuzzy neuronsto identify 10 kinds of fault type the method improvedthe training speed and reduced training samples and faultidentification accuracy was enhanced It used correlationcoefficient of zero sequence voltage and charge as charac-teristic input to construct FLS process which was based ontransient zero sequence 119876-119880 features the method adoptedsupport vector machine algorithm with small sample [8]For incomplete information of fault diagnosis [9] adoptedevidence uncertainty reasoning and compared abnormalevents to reduce computation amount
This paper proposed a novel FLS method which wasbased on combination of ASD and ELM Firstly it usedatomic sparse algorithm to decompose zero sequence currentof every feeder line and extracted the first four atomsto construct fault sample library respectively besides itcalculated information entropy measure of every libraryThen it trained the ELM network to improve network outputaccuracy At last fault votingwas adopted to vote every feederline and compared the values and then the fault line wasjudged Simulation results showed that the accuracy rate ofproposed method is 100 and had strong ability of antinoiseinterference
The remaining of this paper is organized as follows InSection 2 we analyzed the physical characteristics of zerosequence current In Sections 3 and 4 the theory of time-frequency atom decomposition and ELM work principle arepresented respectively In Section 5 test signals analysis isgiven in the paper In Section 6 we chose the characteristicatoms of zero sequence current In Section 7 the FLS meth-ods are proposed In Section 8 example analysis is appliedto verify the proposed method In Section 9 we discussedthe applicability of the method In Section 10 the paper iscompleted with conclusions and future directions
2 Physical Characteristics Analysis
Transient zero sequence circuit of single phase to ground faultis shown in Figure 1 where 119862
0and 119871
0are zero sequence
capacitance and inductance respectively 119877119892is transition
resistance of grounding point 119877119901and 119871
119901are equivalent
resistance and inductance of arc suppression coil and 119890(119905) iszero sequence voltage
When the fault occurred in compensation networkFigure 1 the transient zero sequence current flows through
i0t Rg
e(t)i0Lt
Lp
Rp
L0
i0Ct
C0
Figure 1 Transient zero sequence equivalent circuit of single phaseto ground
fault location [11 12] the calculation is shown in the followingformula
1198940119905= 1198940119871119905
+ 1198940119862119905
= 119868119871119898
cos120593119890minus119905120591119871 + 119868119862119898
times (120596119891
120596sin120593 sin120596119905 minus cos120593 cos120596
119891119905) 119890minus120575119905
(1)
where 1198940119871119905
and 1198940119862119905
are inductance component and capaci-tance component of transient zero sequence current 119868
119871119898and
119868119862119898
are initial value of inductance current and capacitancecurrent respectively 120596 is angular frequency 120596
119891and 120575
are oscillation angle frequency and attenuation coefficientof transient zero sequence current capacitance componentrespectively 120591
119871is decay time constant of inductance current
and 120593 is initial phase of fault line120596119891and 120575 calculations are shown in the following formula
respectively
120596119891= radic
1003816100381610038161003816100381610038161003816100381610038161003816
1
11987101198620
minus (119877119892
21198710
)
21003816100381610038161003816100381610038161003816100381610038161003816
(2)
120575 =119877119892
21198710
(3)
Transient zero sequence current is comprised of sinu-soidal function from formula (1) and its waveform has atten-uation characteristics It can be seen from formula (2) and (3)that oscillation angle frequency 120596
119891is influenced by 119871
0 1198620
and 119877119892 attenuation coefficient 120575 is also influenced by 119871
0and
119877119892 when transition resistance 119877
119892increased 120596
119891decreased
and 120575 increased it reflected that wave oscillation trend ofzero sequence current becomes slow and the attenuation timebecome fast and then transient processwill end soon and intosteady state Therefore if it could extract accurately transientcomponent to achieve FLS exactly at the large resistanceto ground fault it will be an important index to test theapplicability of the FLS methods
Figure 2 is zero sequence current of actual distributionnetworkwhen overhead line 1 caused fault it can be seen fromFigure 2 that whether the overhead line cable line or hybridline its zero sequence current has oscillation attenuationcharacteristics
Journal of Sensors 3
300
200
100
0
minus100
minus2000 0005 001 0015 002
i 0t
(A)
t (s)
(a) Overhead line 1
20
10
0
minus10
minus200 0005 001 0015 002
i 0t
(A)
t (s)
(b) Overhead line 2
100
50
0
minus50
minus1000 0005 001 0015 002
i 0t
(A)
t (s)
(c) Hybrid line
200
100
0
minus100
minus2000 0005 001 0015 002
i 0t
(A)
t (s)
(d) Cable line
Figure 2 Transient zero sequence current
3 Time-Frequency AtomDecomposition Theory
31 Decomposition Methods For continuous signal 119891(119905) isin
119867 119867 is Hilbert space and transformed 119891(119905) into 119891(119899) itsprocess is discretization [13ndash15]Defined atomdictionary119863 =
(119892119903)119903isinΓ
Γ is group of parameters 119903 119892119903= 1 Choose the atoms
to match the signal 119891(119899) from atom dictionary119863 that is themaximum inner product between119891(119899) and all atoms 119892
(1199030)(119899)
meet the following formula10038161003816100381610038161003816⟨119891 (119899) 119892(1199030)
(119899)⟩10038161003816100381610038161003816= sup120574isinΓ
1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (4)
The signal could be decomposed by the best matchingatom 119892
(1199030)(119899) component and the residual signal 119877119891(119899) and
the calculation expression is shown in the following formula
119891 (119899) = ⟨119891 (119899) 119892(1199030)(119899)⟩ 119892(1199030)
(119899) + 119877119891 (119899) (5)
In (5) 119877119891(119899) approached along 119892(1199030)
(119899) direction Obvi-ously 119892
(1199030)(119899) and 119877119891(119899) were orthogonal therefore the
following formula was got1003817100381710038171003817119891(119899)
1003817100381710038171003817
2=10038161003816100381610038161003816⟨119891(119899) 119892
(1199030)(119899)⟩
10038161003816100381610038161003816
2
+1003817100381710038171003817119877119891(119899)
1003817100381710038171003817
2 (6)
Because atom dictionaries are over completeness theoptimal solution could be turned to suboptimal solution thatis choose the approximation atom to a certain extent Thecalculation is shown in
10038161003816100381610038161003816⟨119891 (119899) 119892
(1199030)(119899)⟩
10038161003816100381610038161003816= 120572 sup120574isinΓ
1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (7)
In formula (7) 0 le 120572 le 1 decompose 119877119891(119899) andchose the best matching atom 119892
(1199031)(119899) from atom dictionary
make 1198770119891(119899) = 119891(119899) iterative 119896 times the 119896 time residualcomponent 119877119896119891(119899) could be expressed as
119877119896119891 (119899) = ⟨119877
119896119891 (119899) 119892(119903119896)
(119899)⟩ 119892(119903119896)(119899) + 119877
119896+1119891 (119899) (8)
The signal 119891(119899) decomposed 119898 times and its expressionis shown in
119891 (119899) =
119898minus1
sum
119896=0
⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩ 119892
(119903119896)(119899) + 119877
119898119891 (119899) (9)
Therefore signal energy 119891(119899)2 could be expressed in
1003817100381710038171003817119891(119899)1003817100381710038171003817
2=
119898minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891(119899) 119892
(119903119896)(119899)⟩ 119892
(119903119896)(119899)
10038161003816100381610038161003816
2
+1003817100381710038171003817119877119898119891(119899)
1003817100381710038171003817
2
(10)
4 Journal of Sensors
02
015
01
005
0
minus005
minus01
minus015
minus02
Am
plitu
de
Sampling point50 100 150 200
(a) Time-frequency diagram
04
035
03
025
02
015
01
Am
plitu
de
Sampling point50 100 150 200
(b) Wigner-Ville distribution
Figure 3 Gabor atoms time-frequency diagram and Wigner-Ville distribution 119904 = 26 119906 = 128 120585 = 1205872
In (10) 119892(119903119896)
(119899)meet the formula
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩
10038161003816100381610038161003816= 120572 sup120574isinΓ
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
119903⟩10038161003816100381610038161003816 (11)
If it decomposed 119898 times to meet the accuracythen stop the decomposition Because the residualcomponent 119877119898119891(119899) tends to 0 119891(119899) could be expressed bychosen atoms It was shown in
119891 (119899) =
119898minus1
sum
119896=0
⟨119877119896119891 (119899) 119892(119903119896)
(119899)⟩ 119892(119903119896)(119899) (12)
The similarity degree119862119898between original signal119891(119899) and
constructed signal 119891119898(119899) is shown in
119862119898=
⟨119891 (119899) 119891119898(119899)⟩
1003817100381710038171003817119891 (119899)1003817100381710038171003817 sdot1003817100381710038171003817119891119898 (119899)
1003817100381710038171003817
(13)
Because 119892119903 = 1 calculated Wigner-Ville distribution of
formula (12) it could get
119882119891(119899 119897)
=
119872minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
119903119896(119899)⟩
10038161003816100381610038161003816
2
119882119892119903119896(119899 119897)
+
119872minus1
sum
119896=0
119872minus1
sum
119898=0119898 =119896
⟨119877119896119891 (119899) 119892
119903119896(119899)⟩ ⟨119877119898119891 (119899) 119892
119903119898(119899)⟩
sdot 119882 [119892119903119896(119899) 119892
119903119898(119899)] (119899 119897)
(14)
In (14) 119882119892119903119896(119899 119897) is Wigner-Ville distribution of atom
119892119903119896(119899) and 119897 is discretization frequency variable The last item
in (14) is cross terms of every atom Mallat eliminated thecross terms and got the energy distribution in
119864119891 (119899 119897) =
119872minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩
10038161003816100381610038161003816
2
119882119892(119903119896)
(119899 119897) (15)
In (15) |⟨119877119896119891(119899) 119892(119903119896)
(119899)⟩|2 is energy intensity and 119864119891(119899 119897) is
density function of 119891(119899) energy distribution
32 Gabor Atoms Gabor atoms are constructed by Gaussenergy function with telescopic translation and modulationtransform and its expression is shown in the followingformula
119892119903(119905) =
1
radic119904119892 (
119905 minus 119906
119904) 119890119895120585119905 (16)
The expression of corresponding real Gabor atom isshown in the following formula
119892(119903120601)
(119905) =1
radic119904119892 (
119905 minus 119906
119904) cos (120585119905 + 120601) (17)
In (17) 119892(119905) is standard Gauss signal and is equalto 214119890minus1205871199052
119904 is scale parameter 1radic119904 is atom normalizationparameter and 119906 120585 and 120601 are parameters of time shiftfrequency modulation and phase
Parameter 119903 is equal to (119904 119906 120585) and its discretizationtreatment is 119903 = (119886
119895 119901119886119895Δ119906 119896119886
minus119895Δ120585) where 0 lt 119895 le log
2119873
0 le 119901 le 1198732minus119895+1 0 le 119896 le 2
119895+1 and 119873 is sampling pointswhere 119886 = 2Δ119906 = 05 andΔ120585 = 120587 120601 is discrete as120601 = Vsdot1205876where 0 le V le 12 V is integer
Single atom time-frequency diagram and Wigner-Villedistribution of Gabor atom are shown in Figure 3
It can be known that Gabor atom has the best time-frequency aggregation in Figure 3 and utilized sparse signalrepresentation to fully reveal signal time-frequency charac-teristicsThe deficiency of Gabor atom is that atom frequency
Journal of Sensors 5
Gabor atoms
Original signal
Normalization
Obtain the best atom bymatching pursuit
Residual signal
Does it meet the termination
End
Delayelement
Atoms index
Identificationprocess
Storage unit
Optimization process byNewton downhill method
conditionNo
Yes
Figure 4 Atomic sparse decomposition process
is not changed with time and the division way of time-frequency plane belongs to lattice segmentation CompareFigures 2 and 3 it is known that the similarity degree betweenGabor atom waveforms and zero sequence currents is higherand therefore adoptsmatching pursuitway tomatch it couldnot only accurately extract the fault feature components butalso save a large number of calculation time Hence it usedGabor atoms to extract the fault features in the paper
4 ELM Work Principle
Extreme learning machine is a novel feed-forward neuralnetwork [16ndash18] which is assumed to have119873 training sample(x119896 119905119896)119873
119896=1 its expression is shown in (16)
119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)
In (18) xk b and 119900119896 are input vector hidden layer bias andnetwork output respectivelyWin is input weight linked inputnode and hidden layer node120596 is output weight linked hiddenlayer node and output node 119891 is hidden layer activationfunction and its form is Sigmoid function generally and 119873
is sample numberAt the beginning of training Win and b randomly
generated and remain unchanged it only needs to trainoutput weight 120596 Assume that feed-forward neural networkapproached training samplewith zero error that issum119873
119896=1119900119896minus
119905119896 = 0 ThereforeWin b and 120596meet the formula
120596119879119891 (Winxk + b) = 119905
119896 119896 = 1 2 119873 (19)
Formula (19) is written to matrix form that is H120596 = Twhere
H =[[
[
119891(Winx1 + b1) sdot sdot sdot 119891(Winx1 + b
119898)
d
119891(Winx119873 + b1) sdot sdot sdot 119891(Winx119873 + b
119898)
]]
]119873times119898
(20)
In (20) H and 119898 are output matrix and node number ofhidden layer respectively andT is expected output vector and
it could be expressed as T = [1199051 1199052 119905
119873]119879 If the activation
function of hidden layer is infinitely differentiable and thenumber of hidden layer node met the relationship 119898 le 119873 itcould approach training sample with small training error 120596value is calculated by pseudoinverse algorithm generally [19]
The training process of single-hidden layer feed-forwardneural network (SLFN) is equivalent to calculating leastsquares solution of linear system it is shown in
H minus T = min120596
H120596 minus T (21)
In (21) is least squares solution ofminimumnorm ofH120596 =T H+ is generalized inverse of hidden layer output matrixH For feed-forward neural network smaller weights havestronger generalization ability For all least squares solutionof equation H120596 = T has the smallest norm number thatis = H+T le 120596 where
forall120596 isin 120596 | H120596 minus T le Hz minus T forallz isin 119877119873times119898 (22)
From (22) not only can ELM achieve the minimum trainingerror but it also has stronger generalization ability than thetraditional gradient descent algorithm There is only one H+for the generalized inverse H+of matrix H so the value isunique
5 Test Signal Analysis
Given the test signal there are three frequency componentswhich have different time scale intervals the calculation is asfollows
119904 (119905) =
9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s
38119890minus119905 sin (100120587119905)
+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s
(23)
We added 20 db Gauss white noise to the signal and veri-fied anti-interference ability of atom decomposition methodFor original signal it should be normalized the signal isdivided by its Euclid norm [20] The decomposition processwas shown in Figure 4
6 Journal of Sensors
01
0
minus0150 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Gabor atom 1st iteration
t (ms)
(a)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 2nd iteration
t (ms)
(b)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 3rd iteration
t (ms)
(c)
Figure 5 The first second and third atoms
005
0
minus005
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Original signalConstructed signal
Figure 6 Comparison of original signal and constructed signal by20 iterations
Identification method frequency center 119865 is equaled to1198911199041205852120587 119891
119904is sampling frequency start time is 119879
119904= 119906 minus 1199042
end time is119879119890= 119906+1199042 120601 is phase angle and the amplitude is
equaled to atom normalization amplitude to multiply actualenergy value which is Euclid norm
Set 119891119904= 1 kHz simulation time and sampling points
areequaled to 05 s and 500 respectively Before the decom-position the normalization equation is shown in
119904119892 (119899) =
119904 (119899)
119904 (119899) (24)
In (24) 119904(119899) is discrete signal of 119904(119905) 119904119892(119899) is normalization
expression of 119904(119899) 119904(119899) is Euclid norm and its value is927915
Set iteration number as 20 and decompose 119904119892(119899) by
atomic algorithm Figure 5 shows atom 1 atom 2 and atom 3generated by iteration respectively and all atoms in Figure 5are normalized results Comparison of original signal andconstructed signal is shown in Figure 6 it indicated that thedifference of two signals is smaller by 20 iteration numbersThe residual component amplitude is only 10minus3 in Figure 7and further shows that the accuracy is satisfied atomicdecomposition requirement
001
0005
0
minus0005
minus001
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Residues
t (ms)
Figure 7 Residual component decomposed by 20 iterations
The parameters of atom 1 atom 2 and atom 3 areshown in Table 1 Notably every atom decomposed by atomicalgorithm does not have physical meaning it just indicateddistribution characteristics of time scales Hence the atomicparameters in Table 1 are needed for identification processingand we transformed it to indicate local features of originalsignal it is shown in Table 2
We observed the amplitude frequency and phase valueof atoms in Table 2 it could know that the atoms 12 and 3 represent 9119890minus119905 sin(150120587119905) 38119890minus119905 sin(100120587119905) and28119890minus05119905 sin(70120587119905) of original signal respectively by identi-
fication processing For atom 1 because the actual end time is200ms and the calculated end time is 1877268ms deviationis 122732ms But for atoms 2 and 3 comparing the calculatedstart time with actual start time the deviations are 14297msand 78642ms respectively the difference is smaller
Time-frequency analysis by 20 iteration number decom-position is shown in Figure 8 we can see that the atoms couldindicate local characteristics of nonstationary test signalsaccurately including frequency segment time interval andfrequency components energy compared to the traditionalFFT spectrum cross interference and noise interference canbe suppressed effectively and the calculation accuracy is alsohigher than FFT
Journal of Sensors 7
Table 1 Characteristic parameters of every atom
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 2276520 729008 04709 minus20125 009032 3083047 3527226 03150 minus22285 003803 3168729 3663006 02200 minus18173 00281
Table 2 Local characteristic parameters of test signal
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 90112 749841 minus20125 mdash 18672682 37921 501592 minus22285 1985703 mdash3 28041 350319 minus18173 2078642 mdash
500
450
400
350
300
250
200
150
100
50
f(H
z)
90
75
60
45
30
15
Time-frequency distribution based on matching pursuit
5
0
minus5
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Figure 8 Time-frequency representation of test signal
006004002
0minus002minus004minus006
0005 001 0015 002 0025 003 0035 004
Original signalConstructed signal
t (s)
Am
plitu
de (p
u)
Figure 9 Fitting waveform of overhead line 1198782
6 Choose Characteristic Atom of ZeroSequence Current
To verify ASD algorithm extracting fault feature componentsability in distribution network it gives the feeder fault asexample by ASD set the iteration number as 4 hence the
zero sequence current fitting waveform of overhead line isshown in Figure 9
The similarity between constructed signal and originaloverhead line 119878
2signal is higher by 4 iterations and the
fitting accuracy meets the requirements The first four atomsrsquowaveform and specific parameters are shown in Figure 10 andTables 3 and 4 respectively
Combined with Figure 10 and Table 4 atom 1 waveformshows oscillation attenuation trend both waveform andenergy value have higher similarity with original signal andit indicated major information of original signal thereforeatom 1 is defined asmain components atom and its frequencyvalue is equal to 4729299Hz Atom 2 is defined as funda-mental atom and its frequency value is 509554Hz Atom 3and atom 4 all show oscillation attenuation trend but theirfrequency values are different from atom 1 they are equal to17786624Hz and 11767516Hz respectively and all the highfrequency components therefore it is defined as transientcharacteristic atoms 1 and 2 respectively
Zero sequence current fitting waveform of cable line1198784is shown in Figure 11 the first four atoms are shown
in Figure 12 and the parameters of every atom are shownin Tables 5 and 6 Combining Figure 12 and Table 6 it isknown that atom 1 of cable line is main components atomand its frequency is equal to 4729299Hz Therefore thefrequencies of fundamental atom and transient characteristicatoms 1 and 2 are equal to 493631Hz 11751592Hz and23662420Hz respectively Comparing Figures 10 and 12 itgot different characteristic of transient characteristic atomsbetween overhead line and cable line
Comparing Figures 10(c) 10(d) and Figures 12(c) 12(d)respectively for cable line oscillation attenuation trend oftransient characteristic atoms is more obvious its oscillationprocess is shorter than overhead line Because the capacitanceto ground value of cable line is larger than overhead line inactual distribution network it got different oscillation processof fault current
7 Fault Line Selection Methods
71 Atom Dictionary Measure Based on Information EntropyIndex Information entropy canmeasure uncertain degree ofevent the information entropy value is larger it indicated that
8 Journal of Sensors
004002
0
minus004minus002
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(b) Atom 2
001
0
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
0010
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(d) Atom 4
Figure 10 Zero sequence current characteristic atom of overhead line 1198782
Table 3 Every atom characteristic parameters of overhead line 1198782
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135
004002
0minus002
minus006minus004
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
Original signalConstructed signal
Figure 11 Fitting waveform of cable line 1198784
uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows
Firstly calculate the ratio of atom library and atom librarysum it is shown in
120582 (119896) =119871 (119896)
sum119873
119896=0119871 (119896)
(25)
In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin
119867 = minus
119873
sum
119896=0
120582 (119896) ln 120582 (119896) (26)
In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher
Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows
Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867
1max 1198672max 1198673maxand 119867
4max compared the four values and determined themaximum entropy value119867max
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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DistributedSensor Networks
International Journal of
2 Journal of Sensors
instantaneous power by Hilbert-Huang transform (HHT)and got fault direction well the method took advantage oftransient high-frequency component at lower sampling rateIt tried to divide the zero sequence current signal into severalsegments to ensure good continuity and smaller mutationat every subsegment and Prony algorithm was appliedto choose transient dominant component with maximumenergy principle and then calculated the relative entropy andvoted by preliminary vote and 119896 values check to judge thefault line [5] Hough transform was adopted to constructwhole mutant direction angle which indicated overall trendof zero sequence current at initial stage and FLSwas achievedby distinguishing the direction angle [6] Paper [7] replacedordinary neurons with rough neurons and fuzzy neuronsto identify 10 kinds of fault type the method improvedthe training speed and reduced training samples and faultidentification accuracy was enhanced It used correlationcoefficient of zero sequence voltage and charge as charac-teristic input to construct FLS process which was based ontransient zero sequence 119876-119880 features the method adoptedsupport vector machine algorithm with small sample [8]For incomplete information of fault diagnosis [9] adoptedevidence uncertainty reasoning and compared abnormalevents to reduce computation amount
This paper proposed a novel FLS method which wasbased on combination of ASD and ELM Firstly it usedatomic sparse algorithm to decompose zero sequence currentof every feeder line and extracted the first four atomsto construct fault sample library respectively besides itcalculated information entropy measure of every libraryThen it trained the ELM network to improve network outputaccuracy At last fault votingwas adopted to vote every feederline and compared the values and then the fault line wasjudged Simulation results showed that the accuracy rate ofproposed method is 100 and had strong ability of antinoiseinterference
The remaining of this paper is organized as follows InSection 2 we analyzed the physical characteristics of zerosequence current In Sections 3 and 4 the theory of time-frequency atom decomposition and ELM work principle arepresented respectively In Section 5 test signals analysis isgiven in the paper In Section 6 we chose the characteristicatoms of zero sequence current In Section 7 the FLS meth-ods are proposed In Section 8 example analysis is appliedto verify the proposed method In Section 9 we discussedthe applicability of the method In Section 10 the paper iscompleted with conclusions and future directions
2 Physical Characteristics Analysis
Transient zero sequence circuit of single phase to ground faultis shown in Figure 1 where 119862
0and 119871
0are zero sequence
capacitance and inductance respectively 119877119892is transition
resistance of grounding point 119877119901and 119871
119901are equivalent
resistance and inductance of arc suppression coil and 119890(119905) iszero sequence voltage
When the fault occurred in compensation networkFigure 1 the transient zero sequence current flows through
i0t Rg
e(t)i0Lt
Lp
Rp
L0
i0Ct
C0
Figure 1 Transient zero sequence equivalent circuit of single phaseto ground
fault location [11 12] the calculation is shown in the followingformula
1198940119905= 1198940119871119905
+ 1198940119862119905
= 119868119871119898
cos120593119890minus119905120591119871 + 119868119862119898
times (120596119891
120596sin120593 sin120596119905 minus cos120593 cos120596
119891119905) 119890minus120575119905
(1)
where 1198940119871119905
and 1198940119862119905
are inductance component and capaci-tance component of transient zero sequence current 119868
119871119898and
119868119862119898
are initial value of inductance current and capacitancecurrent respectively 120596 is angular frequency 120596
119891and 120575
are oscillation angle frequency and attenuation coefficientof transient zero sequence current capacitance componentrespectively 120591
119871is decay time constant of inductance current
and 120593 is initial phase of fault line120596119891and 120575 calculations are shown in the following formula
respectively
120596119891= radic
1003816100381610038161003816100381610038161003816100381610038161003816
1
11987101198620
minus (119877119892
21198710
)
21003816100381610038161003816100381610038161003816100381610038161003816
(2)
120575 =119877119892
21198710
(3)
Transient zero sequence current is comprised of sinu-soidal function from formula (1) and its waveform has atten-uation characteristics It can be seen from formula (2) and (3)that oscillation angle frequency 120596
119891is influenced by 119871
0 1198620
and 119877119892 attenuation coefficient 120575 is also influenced by 119871
0and
119877119892 when transition resistance 119877
119892increased 120596
119891decreased
and 120575 increased it reflected that wave oscillation trend ofzero sequence current becomes slow and the attenuation timebecome fast and then transient processwill end soon and intosteady state Therefore if it could extract accurately transientcomponent to achieve FLS exactly at the large resistanceto ground fault it will be an important index to test theapplicability of the FLS methods
Figure 2 is zero sequence current of actual distributionnetworkwhen overhead line 1 caused fault it can be seen fromFigure 2 that whether the overhead line cable line or hybridline its zero sequence current has oscillation attenuationcharacteristics
Journal of Sensors 3
300
200
100
0
minus100
minus2000 0005 001 0015 002
i 0t
(A)
t (s)
(a) Overhead line 1
20
10
0
minus10
minus200 0005 001 0015 002
i 0t
(A)
t (s)
(b) Overhead line 2
100
50
0
minus50
minus1000 0005 001 0015 002
i 0t
(A)
t (s)
(c) Hybrid line
200
100
0
minus100
minus2000 0005 001 0015 002
i 0t
(A)
t (s)
(d) Cable line
Figure 2 Transient zero sequence current
3 Time-Frequency AtomDecomposition Theory
31 Decomposition Methods For continuous signal 119891(119905) isin
119867 119867 is Hilbert space and transformed 119891(119905) into 119891(119899) itsprocess is discretization [13ndash15]Defined atomdictionary119863 =
(119892119903)119903isinΓ
Γ is group of parameters 119903 119892119903= 1 Choose the atoms
to match the signal 119891(119899) from atom dictionary119863 that is themaximum inner product between119891(119899) and all atoms 119892
(1199030)(119899)
meet the following formula10038161003816100381610038161003816⟨119891 (119899) 119892(1199030)
(119899)⟩10038161003816100381610038161003816= sup120574isinΓ
1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (4)
The signal could be decomposed by the best matchingatom 119892
(1199030)(119899) component and the residual signal 119877119891(119899) and
the calculation expression is shown in the following formula
119891 (119899) = ⟨119891 (119899) 119892(1199030)(119899)⟩ 119892(1199030)
(119899) + 119877119891 (119899) (5)
In (5) 119877119891(119899) approached along 119892(1199030)
(119899) direction Obvi-ously 119892
(1199030)(119899) and 119877119891(119899) were orthogonal therefore the
following formula was got1003817100381710038171003817119891(119899)
1003817100381710038171003817
2=10038161003816100381610038161003816⟨119891(119899) 119892
(1199030)(119899)⟩
10038161003816100381610038161003816
2
+1003817100381710038171003817119877119891(119899)
1003817100381710038171003817
2 (6)
Because atom dictionaries are over completeness theoptimal solution could be turned to suboptimal solution thatis choose the approximation atom to a certain extent Thecalculation is shown in
10038161003816100381610038161003816⟨119891 (119899) 119892
(1199030)(119899)⟩
10038161003816100381610038161003816= 120572 sup120574isinΓ
1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (7)
In formula (7) 0 le 120572 le 1 decompose 119877119891(119899) andchose the best matching atom 119892
(1199031)(119899) from atom dictionary
make 1198770119891(119899) = 119891(119899) iterative 119896 times the 119896 time residualcomponent 119877119896119891(119899) could be expressed as
119877119896119891 (119899) = ⟨119877
119896119891 (119899) 119892(119903119896)
(119899)⟩ 119892(119903119896)(119899) + 119877
119896+1119891 (119899) (8)
The signal 119891(119899) decomposed 119898 times and its expressionis shown in
119891 (119899) =
119898minus1
sum
119896=0
⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩ 119892
(119903119896)(119899) + 119877
119898119891 (119899) (9)
Therefore signal energy 119891(119899)2 could be expressed in
1003817100381710038171003817119891(119899)1003817100381710038171003817
2=
119898minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891(119899) 119892
(119903119896)(119899)⟩ 119892
(119903119896)(119899)
10038161003816100381610038161003816
2
+1003817100381710038171003817119877119898119891(119899)
1003817100381710038171003817
2
(10)
4 Journal of Sensors
02
015
01
005
0
minus005
minus01
minus015
minus02
Am
plitu
de
Sampling point50 100 150 200
(a) Time-frequency diagram
04
035
03
025
02
015
01
Am
plitu
de
Sampling point50 100 150 200
(b) Wigner-Ville distribution
Figure 3 Gabor atoms time-frequency diagram and Wigner-Ville distribution 119904 = 26 119906 = 128 120585 = 1205872
In (10) 119892(119903119896)
(119899)meet the formula
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩
10038161003816100381610038161003816= 120572 sup120574isinΓ
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
119903⟩10038161003816100381610038161003816 (11)
If it decomposed 119898 times to meet the accuracythen stop the decomposition Because the residualcomponent 119877119898119891(119899) tends to 0 119891(119899) could be expressed bychosen atoms It was shown in
119891 (119899) =
119898minus1
sum
119896=0
⟨119877119896119891 (119899) 119892(119903119896)
(119899)⟩ 119892(119903119896)(119899) (12)
The similarity degree119862119898between original signal119891(119899) and
constructed signal 119891119898(119899) is shown in
119862119898=
⟨119891 (119899) 119891119898(119899)⟩
1003817100381710038171003817119891 (119899)1003817100381710038171003817 sdot1003817100381710038171003817119891119898 (119899)
1003817100381710038171003817
(13)
Because 119892119903 = 1 calculated Wigner-Ville distribution of
formula (12) it could get
119882119891(119899 119897)
=
119872minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
119903119896(119899)⟩
10038161003816100381610038161003816
2
119882119892119903119896(119899 119897)
+
119872minus1
sum
119896=0
119872minus1
sum
119898=0119898 =119896
⟨119877119896119891 (119899) 119892
119903119896(119899)⟩ ⟨119877119898119891 (119899) 119892
119903119898(119899)⟩
sdot 119882 [119892119903119896(119899) 119892
119903119898(119899)] (119899 119897)
(14)
In (14) 119882119892119903119896(119899 119897) is Wigner-Ville distribution of atom
119892119903119896(119899) and 119897 is discretization frequency variable The last item
in (14) is cross terms of every atom Mallat eliminated thecross terms and got the energy distribution in
119864119891 (119899 119897) =
119872minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩
10038161003816100381610038161003816
2
119882119892(119903119896)
(119899 119897) (15)
In (15) |⟨119877119896119891(119899) 119892(119903119896)
(119899)⟩|2 is energy intensity and 119864119891(119899 119897) is
density function of 119891(119899) energy distribution
32 Gabor Atoms Gabor atoms are constructed by Gaussenergy function with telescopic translation and modulationtransform and its expression is shown in the followingformula
119892119903(119905) =
1
radic119904119892 (
119905 minus 119906
119904) 119890119895120585119905 (16)
The expression of corresponding real Gabor atom isshown in the following formula
119892(119903120601)
(119905) =1
radic119904119892 (
119905 minus 119906
119904) cos (120585119905 + 120601) (17)
In (17) 119892(119905) is standard Gauss signal and is equalto 214119890minus1205871199052
119904 is scale parameter 1radic119904 is atom normalizationparameter and 119906 120585 and 120601 are parameters of time shiftfrequency modulation and phase
Parameter 119903 is equal to (119904 119906 120585) and its discretizationtreatment is 119903 = (119886
119895 119901119886119895Δ119906 119896119886
minus119895Δ120585) where 0 lt 119895 le log
2119873
0 le 119901 le 1198732minus119895+1 0 le 119896 le 2
119895+1 and 119873 is sampling pointswhere 119886 = 2Δ119906 = 05 andΔ120585 = 120587 120601 is discrete as120601 = Vsdot1205876where 0 le V le 12 V is integer
Single atom time-frequency diagram and Wigner-Villedistribution of Gabor atom are shown in Figure 3
It can be known that Gabor atom has the best time-frequency aggregation in Figure 3 and utilized sparse signalrepresentation to fully reveal signal time-frequency charac-teristicsThe deficiency of Gabor atom is that atom frequency
Journal of Sensors 5
Gabor atoms
Original signal
Normalization
Obtain the best atom bymatching pursuit
Residual signal
Does it meet the termination
End
Delayelement
Atoms index
Identificationprocess
Storage unit
Optimization process byNewton downhill method
conditionNo
Yes
Figure 4 Atomic sparse decomposition process
is not changed with time and the division way of time-frequency plane belongs to lattice segmentation CompareFigures 2 and 3 it is known that the similarity degree betweenGabor atom waveforms and zero sequence currents is higherand therefore adoptsmatching pursuitway tomatch it couldnot only accurately extract the fault feature components butalso save a large number of calculation time Hence it usedGabor atoms to extract the fault features in the paper
4 ELM Work Principle
Extreme learning machine is a novel feed-forward neuralnetwork [16ndash18] which is assumed to have119873 training sample(x119896 119905119896)119873
119896=1 its expression is shown in (16)
119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)
In (18) xk b and 119900119896 are input vector hidden layer bias andnetwork output respectivelyWin is input weight linked inputnode and hidden layer node120596 is output weight linked hiddenlayer node and output node 119891 is hidden layer activationfunction and its form is Sigmoid function generally and 119873
is sample numberAt the beginning of training Win and b randomly
generated and remain unchanged it only needs to trainoutput weight 120596 Assume that feed-forward neural networkapproached training samplewith zero error that issum119873
119896=1119900119896minus
119905119896 = 0 ThereforeWin b and 120596meet the formula
120596119879119891 (Winxk + b) = 119905
119896 119896 = 1 2 119873 (19)
Formula (19) is written to matrix form that is H120596 = Twhere
H =[[
[
119891(Winx1 + b1) sdot sdot sdot 119891(Winx1 + b
119898)
d
119891(Winx119873 + b1) sdot sdot sdot 119891(Winx119873 + b
119898)
]]
]119873times119898
(20)
In (20) H and 119898 are output matrix and node number ofhidden layer respectively andT is expected output vector and
it could be expressed as T = [1199051 1199052 119905
119873]119879 If the activation
function of hidden layer is infinitely differentiable and thenumber of hidden layer node met the relationship 119898 le 119873 itcould approach training sample with small training error 120596value is calculated by pseudoinverse algorithm generally [19]
The training process of single-hidden layer feed-forwardneural network (SLFN) is equivalent to calculating leastsquares solution of linear system it is shown in
H minus T = min120596
H120596 minus T (21)
In (21) is least squares solution ofminimumnorm ofH120596 =T H+ is generalized inverse of hidden layer output matrixH For feed-forward neural network smaller weights havestronger generalization ability For all least squares solutionof equation H120596 = T has the smallest norm number thatis = H+T le 120596 where
forall120596 isin 120596 | H120596 minus T le Hz minus T forallz isin 119877119873times119898 (22)
From (22) not only can ELM achieve the minimum trainingerror but it also has stronger generalization ability than thetraditional gradient descent algorithm There is only one H+for the generalized inverse H+of matrix H so the value isunique
5 Test Signal Analysis
Given the test signal there are three frequency componentswhich have different time scale intervals the calculation is asfollows
119904 (119905) =
9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s
38119890minus119905 sin (100120587119905)
+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s
(23)
We added 20 db Gauss white noise to the signal and veri-fied anti-interference ability of atom decomposition methodFor original signal it should be normalized the signal isdivided by its Euclid norm [20] The decomposition processwas shown in Figure 4
6 Journal of Sensors
01
0
minus0150 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Gabor atom 1st iteration
t (ms)
(a)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 2nd iteration
t (ms)
(b)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 3rd iteration
t (ms)
(c)
Figure 5 The first second and third atoms
005
0
minus005
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Original signalConstructed signal
Figure 6 Comparison of original signal and constructed signal by20 iterations
Identification method frequency center 119865 is equaled to1198911199041205852120587 119891
119904is sampling frequency start time is 119879
119904= 119906 minus 1199042
end time is119879119890= 119906+1199042 120601 is phase angle and the amplitude is
equaled to atom normalization amplitude to multiply actualenergy value which is Euclid norm
Set 119891119904= 1 kHz simulation time and sampling points
areequaled to 05 s and 500 respectively Before the decom-position the normalization equation is shown in
119904119892 (119899) =
119904 (119899)
119904 (119899) (24)
In (24) 119904(119899) is discrete signal of 119904(119905) 119904119892(119899) is normalization
expression of 119904(119899) 119904(119899) is Euclid norm and its value is927915
Set iteration number as 20 and decompose 119904119892(119899) by
atomic algorithm Figure 5 shows atom 1 atom 2 and atom 3generated by iteration respectively and all atoms in Figure 5are normalized results Comparison of original signal andconstructed signal is shown in Figure 6 it indicated that thedifference of two signals is smaller by 20 iteration numbersThe residual component amplitude is only 10minus3 in Figure 7and further shows that the accuracy is satisfied atomicdecomposition requirement
001
0005
0
minus0005
minus001
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Residues
t (ms)
Figure 7 Residual component decomposed by 20 iterations
The parameters of atom 1 atom 2 and atom 3 areshown in Table 1 Notably every atom decomposed by atomicalgorithm does not have physical meaning it just indicateddistribution characteristics of time scales Hence the atomicparameters in Table 1 are needed for identification processingand we transformed it to indicate local features of originalsignal it is shown in Table 2
We observed the amplitude frequency and phase valueof atoms in Table 2 it could know that the atoms 12 and 3 represent 9119890minus119905 sin(150120587119905) 38119890minus119905 sin(100120587119905) and28119890minus05119905 sin(70120587119905) of original signal respectively by identi-
fication processing For atom 1 because the actual end time is200ms and the calculated end time is 1877268ms deviationis 122732ms But for atoms 2 and 3 comparing the calculatedstart time with actual start time the deviations are 14297msand 78642ms respectively the difference is smaller
Time-frequency analysis by 20 iteration number decom-position is shown in Figure 8 we can see that the atoms couldindicate local characteristics of nonstationary test signalsaccurately including frequency segment time interval andfrequency components energy compared to the traditionalFFT spectrum cross interference and noise interference canbe suppressed effectively and the calculation accuracy is alsohigher than FFT
Journal of Sensors 7
Table 1 Characteristic parameters of every atom
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 2276520 729008 04709 minus20125 009032 3083047 3527226 03150 minus22285 003803 3168729 3663006 02200 minus18173 00281
Table 2 Local characteristic parameters of test signal
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 90112 749841 minus20125 mdash 18672682 37921 501592 minus22285 1985703 mdash3 28041 350319 minus18173 2078642 mdash
500
450
400
350
300
250
200
150
100
50
f(H
z)
90
75
60
45
30
15
Time-frequency distribution based on matching pursuit
5
0
minus5
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Figure 8 Time-frequency representation of test signal
006004002
0minus002minus004minus006
0005 001 0015 002 0025 003 0035 004
Original signalConstructed signal
t (s)
Am
plitu
de (p
u)
Figure 9 Fitting waveform of overhead line 1198782
6 Choose Characteristic Atom of ZeroSequence Current
To verify ASD algorithm extracting fault feature componentsability in distribution network it gives the feeder fault asexample by ASD set the iteration number as 4 hence the
zero sequence current fitting waveform of overhead line isshown in Figure 9
The similarity between constructed signal and originaloverhead line 119878
2signal is higher by 4 iterations and the
fitting accuracy meets the requirements The first four atomsrsquowaveform and specific parameters are shown in Figure 10 andTables 3 and 4 respectively
Combined with Figure 10 and Table 4 atom 1 waveformshows oscillation attenuation trend both waveform andenergy value have higher similarity with original signal andit indicated major information of original signal thereforeatom 1 is defined asmain components atom and its frequencyvalue is equal to 4729299Hz Atom 2 is defined as funda-mental atom and its frequency value is 509554Hz Atom 3and atom 4 all show oscillation attenuation trend but theirfrequency values are different from atom 1 they are equal to17786624Hz and 11767516Hz respectively and all the highfrequency components therefore it is defined as transientcharacteristic atoms 1 and 2 respectively
Zero sequence current fitting waveform of cable line1198784is shown in Figure 11 the first four atoms are shown
in Figure 12 and the parameters of every atom are shownin Tables 5 and 6 Combining Figure 12 and Table 6 it isknown that atom 1 of cable line is main components atomand its frequency is equal to 4729299Hz Therefore thefrequencies of fundamental atom and transient characteristicatoms 1 and 2 are equal to 493631Hz 11751592Hz and23662420Hz respectively Comparing Figures 10 and 12 itgot different characteristic of transient characteristic atomsbetween overhead line and cable line
Comparing Figures 10(c) 10(d) and Figures 12(c) 12(d)respectively for cable line oscillation attenuation trend oftransient characteristic atoms is more obvious its oscillationprocess is shorter than overhead line Because the capacitanceto ground value of cable line is larger than overhead line inactual distribution network it got different oscillation processof fault current
7 Fault Line Selection Methods
71 Atom Dictionary Measure Based on Information EntropyIndex Information entropy canmeasure uncertain degree ofevent the information entropy value is larger it indicated that
8 Journal of Sensors
004002
0
minus004minus002
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(b) Atom 2
001
0
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
0010
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(d) Atom 4
Figure 10 Zero sequence current characteristic atom of overhead line 1198782
Table 3 Every atom characteristic parameters of overhead line 1198782
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135
004002
0minus002
minus006minus004
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
Original signalConstructed signal
Figure 11 Fitting waveform of cable line 1198784
uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows
Firstly calculate the ratio of atom library and atom librarysum it is shown in
120582 (119896) =119871 (119896)
sum119873
119896=0119871 (119896)
(25)
In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin
119867 = minus
119873
sum
119896=0
120582 (119896) ln 120582 (119896) (26)
In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher
Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows
Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867
1max 1198672max 1198673maxand 119867
4max compared the four values and determined themaximum entropy value119867max
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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DistributedSensor Networks
International Journal of
Journal of Sensors 3
300
200
100
0
minus100
minus2000 0005 001 0015 002
i 0t
(A)
t (s)
(a) Overhead line 1
20
10
0
minus10
minus200 0005 001 0015 002
i 0t
(A)
t (s)
(b) Overhead line 2
100
50
0
minus50
minus1000 0005 001 0015 002
i 0t
(A)
t (s)
(c) Hybrid line
200
100
0
minus100
minus2000 0005 001 0015 002
i 0t
(A)
t (s)
(d) Cable line
Figure 2 Transient zero sequence current
3 Time-Frequency AtomDecomposition Theory
31 Decomposition Methods For continuous signal 119891(119905) isin
119867 119867 is Hilbert space and transformed 119891(119905) into 119891(119899) itsprocess is discretization [13ndash15]Defined atomdictionary119863 =
(119892119903)119903isinΓ
Γ is group of parameters 119903 119892119903= 1 Choose the atoms
to match the signal 119891(119899) from atom dictionary119863 that is themaximum inner product between119891(119899) and all atoms 119892
(1199030)(119899)
meet the following formula10038161003816100381610038161003816⟨119891 (119899) 119892(1199030)
(119899)⟩10038161003816100381610038161003816= sup120574isinΓ
1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (4)
The signal could be decomposed by the best matchingatom 119892
(1199030)(119899) component and the residual signal 119877119891(119899) and
the calculation expression is shown in the following formula
119891 (119899) = ⟨119891 (119899) 119892(1199030)(119899)⟩ 119892(1199030)
(119899) + 119877119891 (119899) (5)
In (5) 119877119891(119899) approached along 119892(1199030)
(119899) direction Obvi-ously 119892
(1199030)(119899) and 119877119891(119899) were orthogonal therefore the
following formula was got1003817100381710038171003817119891(119899)
1003817100381710038171003817
2=10038161003816100381610038161003816⟨119891(119899) 119892
(1199030)(119899)⟩
10038161003816100381610038161003816
2
+1003817100381710038171003817119877119891(119899)
1003817100381710038171003817
2 (6)
Because atom dictionaries are over completeness theoptimal solution could be turned to suboptimal solution thatis choose the approximation atom to a certain extent Thecalculation is shown in
10038161003816100381610038161003816⟨119891 (119899) 119892
(1199030)(119899)⟩
10038161003816100381610038161003816= 120572 sup120574isinΓ
1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (7)
In formula (7) 0 le 120572 le 1 decompose 119877119891(119899) andchose the best matching atom 119892
(1199031)(119899) from atom dictionary
make 1198770119891(119899) = 119891(119899) iterative 119896 times the 119896 time residualcomponent 119877119896119891(119899) could be expressed as
119877119896119891 (119899) = ⟨119877
119896119891 (119899) 119892(119903119896)
(119899)⟩ 119892(119903119896)(119899) + 119877
119896+1119891 (119899) (8)
The signal 119891(119899) decomposed 119898 times and its expressionis shown in
119891 (119899) =
119898minus1
sum
119896=0
⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩ 119892
(119903119896)(119899) + 119877
119898119891 (119899) (9)
Therefore signal energy 119891(119899)2 could be expressed in
1003817100381710038171003817119891(119899)1003817100381710038171003817
2=
119898minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891(119899) 119892
(119903119896)(119899)⟩ 119892
(119903119896)(119899)
10038161003816100381610038161003816
2
+1003817100381710038171003817119877119898119891(119899)
1003817100381710038171003817
2
(10)
4 Journal of Sensors
02
015
01
005
0
minus005
minus01
minus015
minus02
Am
plitu
de
Sampling point50 100 150 200
(a) Time-frequency diagram
04
035
03
025
02
015
01
Am
plitu
de
Sampling point50 100 150 200
(b) Wigner-Ville distribution
Figure 3 Gabor atoms time-frequency diagram and Wigner-Ville distribution 119904 = 26 119906 = 128 120585 = 1205872
In (10) 119892(119903119896)
(119899)meet the formula
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩
10038161003816100381610038161003816= 120572 sup120574isinΓ
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
119903⟩10038161003816100381610038161003816 (11)
If it decomposed 119898 times to meet the accuracythen stop the decomposition Because the residualcomponent 119877119898119891(119899) tends to 0 119891(119899) could be expressed bychosen atoms It was shown in
119891 (119899) =
119898minus1
sum
119896=0
⟨119877119896119891 (119899) 119892(119903119896)
(119899)⟩ 119892(119903119896)(119899) (12)
The similarity degree119862119898between original signal119891(119899) and
constructed signal 119891119898(119899) is shown in
119862119898=
⟨119891 (119899) 119891119898(119899)⟩
1003817100381710038171003817119891 (119899)1003817100381710038171003817 sdot1003817100381710038171003817119891119898 (119899)
1003817100381710038171003817
(13)
Because 119892119903 = 1 calculated Wigner-Ville distribution of
formula (12) it could get
119882119891(119899 119897)
=
119872minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
119903119896(119899)⟩
10038161003816100381610038161003816
2
119882119892119903119896(119899 119897)
+
119872minus1
sum
119896=0
119872minus1
sum
119898=0119898 =119896
⟨119877119896119891 (119899) 119892
119903119896(119899)⟩ ⟨119877119898119891 (119899) 119892
119903119898(119899)⟩
sdot 119882 [119892119903119896(119899) 119892
119903119898(119899)] (119899 119897)
(14)
In (14) 119882119892119903119896(119899 119897) is Wigner-Ville distribution of atom
119892119903119896(119899) and 119897 is discretization frequency variable The last item
in (14) is cross terms of every atom Mallat eliminated thecross terms and got the energy distribution in
119864119891 (119899 119897) =
119872minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩
10038161003816100381610038161003816
2
119882119892(119903119896)
(119899 119897) (15)
In (15) |⟨119877119896119891(119899) 119892(119903119896)
(119899)⟩|2 is energy intensity and 119864119891(119899 119897) is
density function of 119891(119899) energy distribution
32 Gabor Atoms Gabor atoms are constructed by Gaussenergy function with telescopic translation and modulationtransform and its expression is shown in the followingformula
119892119903(119905) =
1
radic119904119892 (
119905 minus 119906
119904) 119890119895120585119905 (16)
The expression of corresponding real Gabor atom isshown in the following formula
119892(119903120601)
(119905) =1
radic119904119892 (
119905 minus 119906
119904) cos (120585119905 + 120601) (17)
In (17) 119892(119905) is standard Gauss signal and is equalto 214119890minus1205871199052
119904 is scale parameter 1radic119904 is atom normalizationparameter and 119906 120585 and 120601 are parameters of time shiftfrequency modulation and phase
Parameter 119903 is equal to (119904 119906 120585) and its discretizationtreatment is 119903 = (119886
119895 119901119886119895Δ119906 119896119886
minus119895Δ120585) where 0 lt 119895 le log
2119873
0 le 119901 le 1198732minus119895+1 0 le 119896 le 2
119895+1 and 119873 is sampling pointswhere 119886 = 2Δ119906 = 05 andΔ120585 = 120587 120601 is discrete as120601 = Vsdot1205876where 0 le V le 12 V is integer
Single atom time-frequency diagram and Wigner-Villedistribution of Gabor atom are shown in Figure 3
It can be known that Gabor atom has the best time-frequency aggregation in Figure 3 and utilized sparse signalrepresentation to fully reveal signal time-frequency charac-teristicsThe deficiency of Gabor atom is that atom frequency
Journal of Sensors 5
Gabor atoms
Original signal
Normalization
Obtain the best atom bymatching pursuit
Residual signal
Does it meet the termination
End
Delayelement
Atoms index
Identificationprocess
Storage unit
Optimization process byNewton downhill method
conditionNo
Yes
Figure 4 Atomic sparse decomposition process
is not changed with time and the division way of time-frequency plane belongs to lattice segmentation CompareFigures 2 and 3 it is known that the similarity degree betweenGabor atom waveforms and zero sequence currents is higherand therefore adoptsmatching pursuitway tomatch it couldnot only accurately extract the fault feature components butalso save a large number of calculation time Hence it usedGabor atoms to extract the fault features in the paper
4 ELM Work Principle
Extreme learning machine is a novel feed-forward neuralnetwork [16ndash18] which is assumed to have119873 training sample(x119896 119905119896)119873
119896=1 its expression is shown in (16)
119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)
In (18) xk b and 119900119896 are input vector hidden layer bias andnetwork output respectivelyWin is input weight linked inputnode and hidden layer node120596 is output weight linked hiddenlayer node and output node 119891 is hidden layer activationfunction and its form is Sigmoid function generally and 119873
is sample numberAt the beginning of training Win and b randomly
generated and remain unchanged it only needs to trainoutput weight 120596 Assume that feed-forward neural networkapproached training samplewith zero error that issum119873
119896=1119900119896minus
119905119896 = 0 ThereforeWin b and 120596meet the formula
120596119879119891 (Winxk + b) = 119905
119896 119896 = 1 2 119873 (19)
Formula (19) is written to matrix form that is H120596 = Twhere
H =[[
[
119891(Winx1 + b1) sdot sdot sdot 119891(Winx1 + b
119898)
d
119891(Winx119873 + b1) sdot sdot sdot 119891(Winx119873 + b
119898)
]]
]119873times119898
(20)
In (20) H and 119898 are output matrix and node number ofhidden layer respectively andT is expected output vector and
it could be expressed as T = [1199051 1199052 119905
119873]119879 If the activation
function of hidden layer is infinitely differentiable and thenumber of hidden layer node met the relationship 119898 le 119873 itcould approach training sample with small training error 120596value is calculated by pseudoinverse algorithm generally [19]
The training process of single-hidden layer feed-forwardneural network (SLFN) is equivalent to calculating leastsquares solution of linear system it is shown in
H minus T = min120596
H120596 minus T (21)
In (21) is least squares solution ofminimumnorm ofH120596 =T H+ is generalized inverse of hidden layer output matrixH For feed-forward neural network smaller weights havestronger generalization ability For all least squares solutionof equation H120596 = T has the smallest norm number thatis = H+T le 120596 where
forall120596 isin 120596 | H120596 minus T le Hz minus T forallz isin 119877119873times119898 (22)
From (22) not only can ELM achieve the minimum trainingerror but it also has stronger generalization ability than thetraditional gradient descent algorithm There is only one H+for the generalized inverse H+of matrix H so the value isunique
5 Test Signal Analysis
Given the test signal there are three frequency componentswhich have different time scale intervals the calculation is asfollows
119904 (119905) =
9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s
38119890minus119905 sin (100120587119905)
+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s
(23)
We added 20 db Gauss white noise to the signal and veri-fied anti-interference ability of atom decomposition methodFor original signal it should be normalized the signal isdivided by its Euclid norm [20] The decomposition processwas shown in Figure 4
6 Journal of Sensors
01
0
minus0150 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Gabor atom 1st iteration
t (ms)
(a)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 2nd iteration
t (ms)
(b)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 3rd iteration
t (ms)
(c)
Figure 5 The first second and third atoms
005
0
minus005
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Original signalConstructed signal
Figure 6 Comparison of original signal and constructed signal by20 iterations
Identification method frequency center 119865 is equaled to1198911199041205852120587 119891
119904is sampling frequency start time is 119879
119904= 119906 minus 1199042
end time is119879119890= 119906+1199042 120601 is phase angle and the amplitude is
equaled to atom normalization amplitude to multiply actualenergy value which is Euclid norm
Set 119891119904= 1 kHz simulation time and sampling points
areequaled to 05 s and 500 respectively Before the decom-position the normalization equation is shown in
119904119892 (119899) =
119904 (119899)
119904 (119899) (24)
In (24) 119904(119899) is discrete signal of 119904(119905) 119904119892(119899) is normalization
expression of 119904(119899) 119904(119899) is Euclid norm and its value is927915
Set iteration number as 20 and decompose 119904119892(119899) by
atomic algorithm Figure 5 shows atom 1 atom 2 and atom 3generated by iteration respectively and all atoms in Figure 5are normalized results Comparison of original signal andconstructed signal is shown in Figure 6 it indicated that thedifference of two signals is smaller by 20 iteration numbersThe residual component amplitude is only 10minus3 in Figure 7and further shows that the accuracy is satisfied atomicdecomposition requirement
001
0005
0
minus0005
minus001
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Residues
t (ms)
Figure 7 Residual component decomposed by 20 iterations
The parameters of atom 1 atom 2 and atom 3 areshown in Table 1 Notably every atom decomposed by atomicalgorithm does not have physical meaning it just indicateddistribution characteristics of time scales Hence the atomicparameters in Table 1 are needed for identification processingand we transformed it to indicate local features of originalsignal it is shown in Table 2
We observed the amplitude frequency and phase valueof atoms in Table 2 it could know that the atoms 12 and 3 represent 9119890minus119905 sin(150120587119905) 38119890minus119905 sin(100120587119905) and28119890minus05119905 sin(70120587119905) of original signal respectively by identi-
fication processing For atom 1 because the actual end time is200ms and the calculated end time is 1877268ms deviationis 122732ms But for atoms 2 and 3 comparing the calculatedstart time with actual start time the deviations are 14297msand 78642ms respectively the difference is smaller
Time-frequency analysis by 20 iteration number decom-position is shown in Figure 8 we can see that the atoms couldindicate local characteristics of nonstationary test signalsaccurately including frequency segment time interval andfrequency components energy compared to the traditionalFFT spectrum cross interference and noise interference canbe suppressed effectively and the calculation accuracy is alsohigher than FFT
Journal of Sensors 7
Table 1 Characteristic parameters of every atom
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 2276520 729008 04709 minus20125 009032 3083047 3527226 03150 minus22285 003803 3168729 3663006 02200 minus18173 00281
Table 2 Local characteristic parameters of test signal
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 90112 749841 minus20125 mdash 18672682 37921 501592 minus22285 1985703 mdash3 28041 350319 minus18173 2078642 mdash
500
450
400
350
300
250
200
150
100
50
f(H
z)
90
75
60
45
30
15
Time-frequency distribution based on matching pursuit
5
0
minus5
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Figure 8 Time-frequency representation of test signal
006004002
0minus002minus004minus006
0005 001 0015 002 0025 003 0035 004
Original signalConstructed signal
t (s)
Am
plitu
de (p
u)
Figure 9 Fitting waveform of overhead line 1198782
6 Choose Characteristic Atom of ZeroSequence Current
To verify ASD algorithm extracting fault feature componentsability in distribution network it gives the feeder fault asexample by ASD set the iteration number as 4 hence the
zero sequence current fitting waveform of overhead line isshown in Figure 9
The similarity between constructed signal and originaloverhead line 119878
2signal is higher by 4 iterations and the
fitting accuracy meets the requirements The first four atomsrsquowaveform and specific parameters are shown in Figure 10 andTables 3 and 4 respectively
Combined with Figure 10 and Table 4 atom 1 waveformshows oscillation attenuation trend both waveform andenergy value have higher similarity with original signal andit indicated major information of original signal thereforeatom 1 is defined asmain components atom and its frequencyvalue is equal to 4729299Hz Atom 2 is defined as funda-mental atom and its frequency value is 509554Hz Atom 3and atom 4 all show oscillation attenuation trend but theirfrequency values are different from atom 1 they are equal to17786624Hz and 11767516Hz respectively and all the highfrequency components therefore it is defined as transientcharacteristic atoms 1 and 2 respectively
Zero sequence current fitting waveform of cable line1198784is shown in Figure 11 the first four atoms are shown
in Figure 12 and the parameters of every atom are shownin Tables 5 and 6 Combining Figure 12 and Table 6 it isknown that atom 1 of cable line is main components atomand its frequency is equal to 4729299Hz Therefore thefrequencies of fundamental atom and transient characteristicatoms 1 and 2 are equal to 493631Hz 11751592Hz and23662420Hz respectively Comparing Figures 10 and 12 itgot different characteristic of transient characteristic atomsbetween overhead line and cable line
Comparing Figures 10(c) 10(d) and Figures 12(c) 12(d)respectively for cable line oscillation attenuation trend oftransient characteristic atoms is more obvious its oscillationprocess is shorter than overhead line Because the capacitanceto ground value of cable line is larger than overhead line inactual distribution network it got different oscillation processof fault current
7 Fault Line Selection Methods
71 Atom Dictionary Measure Based on Information EntropyIndex Information entropy canmeasure uncertain degree ofevent the information entropy value is larger it indicated that
8 Journal of Sensors
004002
0
minus004minus002
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(b) Atom 2
001
0
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
0010
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(d) Atom 4
Figure 10 Zero sequence current characteristic atom of overhead line 1198782
Table 3 Every atom characteristic parameters of overhead line 1198782
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135
004002
0minus002
minus006minus004
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
Original signalConstructed signal
Figure 11 Fitting waveform of cable line 1198784
uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows
Firstly calculate the ratio of atom library and atom librarysum it is shown in
120582 (119896) =119871 (119896)
sum119873
119896=0119871 (119896)
(25)
In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin
119867 = minus
119873
sum
119896=0
120582 (119896) ln 120582 (119896) (26)
In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher
Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows
Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867
1max 1198672max 1198673maxand 119867
4max compared the four values and determined themaximum entropy value119867max
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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DistributedSensor Networks
International Journal of
4 Journal of Sensors
02
015
01
005
0
minus005
minus01
minus015
minus02
Am
plitu
de
Sampling point50 100 150 200
(a) Time-frequency diagram
04
035
03
025
02
015
01
Am
plitu
de
Sampling point50 100 150 200
(b) Wigner-Ville distribution
Figure 3 Gabor atoms time-frequency diagram and Wigner-Ville distribution 119904 = 26 119906 = 128 120585 = 1205872
In (10) 119892(119903119896)
(119899)meet the formula
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩
10038161003816100381610038161003816= 120572 sup120574isinΓ
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
119903⟩10038161003816100381610038161003816 (11)
If it decomposed 119898 times to meet the accuracythen stop the decomposition Because the residualcomponent 119877119898119891(119899) tends to 0 119891(119899) could be expressed bychosen atoms It was shown in
119891 (119899) =
119898minus1
sum
119896=0
⟨119877119896119891 (119899) 119892(119903119896)
(119899)⟩ 119892(119903119896)(119899) (12)
The similarity degree119862119898between original signal119891(119899) and
constructed signal 119891119898(119899) is shown in
119862119898=
⟨119891 (119899) 119891119898(119899)⟩
1003817100381710038171003817119891 (119899)1003817100381710038171003817 sdot1003817100381710038171003817119891119898 (119899)
1003817100381710038171003817
(13)
Because 119892119903 = 1 calculated Wigner-Ville distribution of
formula (12) it could get
119882119891(119899 119897)
=
119872minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
119903119896(119899)⟩
10038161003816100381610038161003816
2
119882119892119903119896(119899 119897)
+
119872minus1
sum
119896=0
119872minus1
sum
119898=0119898 =119896
⟨119877119896119891 (119899) 119892
119903119896(119899)⟩ ⟨119877119898119891 (119899) 119892
119903119898(119899)⟩
sdot 119882 [119892119903119896(119899) 119892
119903119898(119899)] (119899 119897)
(14)
In (14) 119882119892119903119896(119899 119897) is Wigner-Ville distribution of atom
119892119903119896(119899) and 119897 is discretization frequency variable The last item
in (14) is cross terms of every atom Mallat eliminated thecross terms and got the energy distribution in
119864119891 (119899 119897) =
119872minus1
sum
119896=0
10038161003816100381610038161003816⟨119877119896119891 (119899) 119892
(119903119896)(119899)⟩
10038161003816100381610038161003816
2
119882119892(119903119896)
(119899 119897) (15)
In (15) |⟨119877119896119891(119899) 119892(119903119896)
(119899)⟩|2 is energy intensity and 119864119891(119899 119897) is
density function of 119891(119899) energy distribution
32 Gabor Atoms Gabor atoms are constructed by Gaussenergy function with telescopic translation and modulationtransform and its expression is shown in the followingformula
119892119903(119905) =
1
radic119904119892 (
119905 minus 119906
119904) 119890119895120585119905 (16)
The expression of corresponding real Gabor atom isshown in the following formula
119892(119903120601)
(119905) =1
radic119904119892 (
119905 minus 119906
119904) cos (120585119905 + 120601) (17)
In (17) 119892(119905) is standard Gauss signal and is equalto 214119890minus1205871199052
119904 is scale parameter 1radic119904 is atom normalizationparameter and 119906 120585 and 120601 are parameters of time shiftfrequency modulation and phase
Parameter 119903 is equal to (119904 119906 120585) and its discretizationtreatment is 119903 = (119886
119895 119901119886119895Δ119906 119896119886
minus119895Δ120585) where 0 lt 119895 le log
2119873
0 le 119901 le 1198732minus119895+1 0 le 119896 le 2
119895+1 and 119873 is sampling pointswhere 119886 = 2Δ119906 = 05 andΔ120585 = 120587 120601 is discrete as120601 = Vsdot1205876where 0 le V le 12 V is integer
Single atom time-frequency diagram and Wigner-Villedistribution of Gabor atom are shown in Figure 3
It can be known that Gabor atom has the best time-frequency aggregation in Figure 3 and utilized sparse signalrepresentation to fully reveal signal time-frequency charac-teristicsThe deficiency of Gabor atom is that atom frequency
Journal of Sensors 5
Gabor atoms
Original signal
Normalization
Obtain the best atom bymatching pursuit
Residual signal
Does it meet the termination
End
Delayelement
Atoms index
Identificationprocess
Storage unit
Optimization process byNewton downhill method
conditionNo
Yes
Figure 4 Atomic sparse decomposition process
is not changed with time and the division way of time-frequency plane belongs to lattice segmentation CompareFigures 2 and 3 it is known that the similarity degree betweenGabor atom waveforms and zero sequence currents is higherand therefore adoptsmatching pursuitway tomatch it couldnot only accurately extract the fault feature components butalso save a large number of calculation time Hence it usedGabor atoms to extract the fault features in the paper
4 ELM Work Principle
Extreme learning machine is a novel feed-forward neuralnetwork [16ndash18] which is assumed to have119873 training sample(x119896 119905119896)119873
119896=1 its expression is shown in (16)
119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)
In (18) xk b and 119900119896 are input vector hidden layer bias andnetwork output respectivelyWin is input weight linked inputnode and hidden layer node120596 is output weight linked hiddenlayer node and output node 119891 is hidden layer activationfunction and its form is Sigmoid function generally and 119873
is sample numberAt the beginning of training Win and b randomly
generated and remain unchanged it only needs to trainoutput weight 120596 Assume that feed-forward neural networkapproached training samplewith zero error that issum119873
119896=1119900119896minus
119905119896 = 0 ThereforeWin b and 120596meet the formula
120596119879119891 (Winxk + b) = 119905
119896 119896 = 1 2 119873 (19)
Formula (19) is written to matrix form that is H120596 = Twhere
H =[[
[
119891(Winx1 + b1) sdot sdot sdot 119891(Winx1 + b
119898)
d
119891(Winx119873 + b1) sdot sdot sdot 119891(Winx119873 + b
119898)
]]
]119873times119898
(20)
In (20) H and 119898 are output matrix and node number ofhidden layer respectively andT is expected output vector and
it could be expressed as T = [1199051 1199052 119905
119873]119879 If the activation
function of hidden layer is infinitely differentiable and thenumber of hidden layer node met the relationship 119898 le 119873 itcould approach training sample with small training error 120596value is calculated by pseudoinverse algorithm generally [19]
The training process of single-hidden layer feed-forwardneural network (SLFN) is equivalent to calculating leastsquares solution of linear system it is shown in
H minus T = min120596
H120596 minus T (21)
In (21) is least squares solution ofminimumnorm ofH120596 =T H+ is generalized inverse of hidden layer output matrixH For feed-forward neural network smaller weights havestronger generalization ability For all least squares solutionof equation H120596 = T has the smallest norm number thatis = H+T le 120596 where
forall120596 isin 120596 | H120596 minus T le Hz minus T forallz isin 119877119873times119898 (22)
From (22) not only can ELM achieve the minimum trainingerror but it also has stronger generalization ability than thetraditional gradient descent algorithm There is only one H+for the generalized inverse H+of matrix H so the value isunique
5 Test Signal Analysis
Given the test signal there are three frequency componentswhich have different time scale intervals the calculation is asfollows
119904 (119905) =
9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s
38119890minus119905 sin (100120587119905)
+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s
(23)
We added 20 db Gauss white noise to the signal and veri-fied anti-interference ability of atom decomposition methodFor original signal it should be normalized the signal isdivided by its Euclid norm [20] The decomposition processwas shown in Figure 4
6 Journal of Sensors
01
0
minus0150 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Gabor atom 1st iteration
t (ms)
(a)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 2nd iteration
t (ms)
(b)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 3rd iteration
t (ms)
(c)
Figure 5 The first second and third atoms
005
0
minus005
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Original signalConstructed signal
Figure 6 Comparison of original signal and constructed signal by20 iterations
Identification method frequency center 119865 is equaled to1198911199041205852120587 119891
119904is sampling frequency start time is 119879
119904= 119906 minus 1199042
end time is119879119890= 119906+1199042 120601 is phase angle and the amplitude is
equaled to atom normalization amplitude to multiply actualenergy value which is Euclid norm
Set 119891119904= 1 kHz simulation time and sampling points
areequaled to 05 s and 500 respectively Before the decom-position the normalization equation is shown in
119904119892 (119899) =
119904 (119899)
119904 (119899) (24)
In (24) 119904(119899) is discrete signal of 119904(119905) 119904119892(119899) is normalization
expression of 119904(119899) 119904(119899) is Euclid norm and its value is927915
Set iteration number as 20 and decompose 119904119892(119899) by
atomic algorithm Figure 5 shows atom 1 atom 2 and atom 3generated by iteration respectively and all atoms in Figure 5are normalized results Comparison of original signal andconstructed signal is shown in Figure 6 it indicated that thedifference of two signals is smaller by 20 iteration numbersThe residual component amplitude is only 10minus3 in Figure 7and further shows that the accuracy is satisfied atomicdecomposition requirement
001
0005
0
minus0005
minus001
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Residues
t (ms)
Figure 7 Residual component decomposed by 20 iterations
The parameters of atom 1 atom 2 and atom 3 areshown in Table 1 Notably every atom decomposed by atomicalgorithm does not have physical meaning it just indicateddistribution characteristics of time scales Hence the atomicparameters in Table 1 are needed for identification processingand we transformed it to indicate local features of originalsignal it is shown in Table 2
We observed the amplitude frequency and phase valueof atoms in Table 2 it could know that the atoms 12 and 3 represent 9119890minus119905 sin(150120587119905) 38119890minus119905 sin(100120587119905) and28119890minus05119905 sin(70120587119905) of original signal respectively by identi-
fication processing For atom 1 because the actual end time is200ms and the calculated end time is 1877268ms deviationis 122732ms But for atoms 2 and 3 comparing the calculatedstart time with actual start time the deviations are 14297msand 78642ms respectively the difference is smaller
Time-frequency analysis by 20 iteration number decom-position is shown in Figure 8 we can see that the atoms couldindicate local characteristics of nonstationary test signalsaccurately including frequency segment time interval andfrequency components energy compared to the traditionalFFT spectrum cross interference and noise interference canbe suppressed effectively and the calculation accuracy is alsohigher than FFT
Journal of Sensors 7
Table 1 Characteristic parameters of every atom
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 2276520 729008 04709 minus20125 009032 3083047 3527226 03150 minus22285 003803 3168729 3663006 02200 minus18173 00281
Table 2 Local characteristic parameters of test signal
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 90112 749841 minus20125 mdash 18672682 37921 501592 minus22285 1985703 mdash3 28041 350319 minus18173 2078642 mdash
500
450
400
350
300
250
200
150
100
50
f(H
z)
90
75
60
45
30
15
Time-frequency distribution based on matching pursuit
5
0
minus5
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Figure 8 Time-frequency representation of test signal
006004002
0minus002minus004minus006
0005 001 0015 002 0025 003 0035 004
Original signalConstructed signal
t (s)
Am
plitu
de (p
u)
Figure 9 Fitting waveform of overhead line 1198782
6 Choose Characteristic Atom of ZeroSequence Current
To verify ASD algorithm extracting fault feature componentsability in distribution network it gives the feeder fault asexample by ASD set the iteration number as 4 hence the
zero sequence current fitting waveform of overhead line isshown in Figure 9
The similarity between constructed signal and originaloverhead line 119878
2signal is higher by 4 iterations and the
fitting accuracy meets the requirements The first four atomsrsquowaveform and specific parameters are shown in Figure 10 andTables 3 and 4 respectively
Combined with Figure 10 and Table 4 atom 1 waveformshows oscillation attenuation trend both waveform andenergy value have higher similarity with original signal andit indicated major information of original signal thereforeatom 1 is defined asmain components atom and its frequencyvalue is equal to 4729299Hz Atom 2 is defined as funda-mental atom and its frequency value is 509554Hz Atom 3and atom 4 all show oscillation attenuation trend but theirfrequency values are different from atom 1 they are equal to17786624Hz and 11767516Hz respectively and all the highfrequency components therefore it is defined as transientcharacteristic atoms 1 and 2 respectively
Zero sequence current fitting waveform of cable line1198784is shown in Figure 11 the first four atoms are shown
in Figure 12 and the parameters of every atom are shownin Tables 5 and 6 Combining Figure 12 and Table 6 it isknown that atom 1 of cable line is main components atomand its frequency is equal to 4729299Hz Therefore thefrequencies of fundamental atom and transient characteristicatoms 1 and 2 are equal to 493631Hz 11751592Hz and23662420Hz respectively Comparing Figures 10 and 12 itgot different characteristic of transient characteristic atomsbetween overhead line and cable line
Comparing Figures 10(c) 10(d) and Figures 12(c) 12(d)respectively for cable line oscillation attenuation trend oftransient characteristic atoms is more obvious its oscillationprocess is shorter than overhead line Because the capacitanceto ground value of cable line is larger than overhead line inactual distribution network it got different oscillation processof fault current
7 Fault Line Selection Methods
71 Atom Dictionary Measure Based on Information EntropyIndex Information entropy canmeasure uncertain degree ofevent the information entropy value is larger it indicated that
8 Journal of Sensors
004002
0
minus004minus002
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(b) Atom 2
001
0
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
0010
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(d) Atom 4
Figure 10 Zero sequence current characteristic atom of overhead line 1198782
Table 3 Every atom characteristic parameters of overhead line 1198782
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135
004002
0minus002
minus006minus004
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
Original signalConstructed signal
Figure 11 Fitting waveform of cable line 1198784
uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows
Firstly calculate the ratio of atom library and atom librarysum it is shown in
120582 (119896) =119871 (119896)
sum119873
119896=0119871 (119896)
(25)
In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin
119867 = minus
119873
sum
119896=0
120582 (119896) ln 120582 (119896) (26)
In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher
Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows
Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867
1max 1198672max 1198673maxand 119867
4max compared the four values and determined themaximum entropy value119867max
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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Navigation and Observation
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DistributedSensor Networks
International Journal of
Journal of Sensors 5
Gabor atoms
Original signal
Normalization
Obtain the best atom bymatching pursuit
Residual signal
Does it meet the termination
End
Delayelement
Atoms index
Identificationprocess
Storage unit
Optimization process byNewton downhill method
conditionNo
Yes
Figure 4 Atomic sparse decomposition process
is not changed with time and the division way of time-frequency plane belongs to lattice segmentation CompareFigures 2 and 3 it is known that the similarity degree betweenGabor atom waveforms and zero sequence currents is higherand therefore adoptsmatching pursuitway tomatch it couldnot only accurately extract the fault feature components butalso save a large number of calculation time Hence it usedGabor atoms to extract the fault features in the paper
4 ELM Work Principle
Extreme learning machine is a novel feed-forward neuralnetwork [16ndash18] which is assumed to have119873 training sample(x119896 119905119896)119873
119896=1 its expression is shown in (16)
119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)
In (18) xk b and 119900119896 are input vector hidden layer bias andnetwork output respectivelyWin is input weight linked inputnode and hidden layer node120596 is output weight linked hiddenlayer node and output node 119891 is hidden layer activationfunction and its form is Sigmoid function generally and 119873
is sample numberAt the beginning of training Win and b randomly
generated and remain unchanged it only needs to trainoutput weight 120596 Assume that feed-forward neural networkapproached training samplewith zero error that issum119873
119896=1119900119896minus
119905119896 = 0 ThereforeWin b and 120596meet the formula
120596119879119891 (Winxk + b) = 119905
119896 119896 = 1 2 119873 (19)
Formula (19) is written to matrix form that is H120596 = Twhere
H =[[
[
119891(Winx1 + b1) sdot sdot sdot 119891(Winx1 + b
119898)
d
119891(Winx119873 + b1) sdot sdot sdot 119891(Winx119873 + b
119898)
]]
]119873times119898
(20)
In (20) H and 119898 are output matrix and node number ofhidden layer respectively andT is expected output vector and
it could be expressed as T = [1199051 1199052 119905
119873]119879 If the activation
function of hidden layer is infinitely differentiable and thenumber of hidden layer node met the relationship 119898 le 119873 itcould approach training sample with small training error 120596value is calculated by pseudoinverse algorithm generally [19]
The training process of single-hidden layer feed-forwardneural network (SLFN) is equivalent to calculating leastsquares solution of linear system it is shown in
H minus T = min120596
H120596 minus T (21)
In (21) is least squares solution ofminimumnorm ofH120596 =T H+ is generalized inverse of hidden layer output matrixH For feed-forward neural network smaller weights havestronger generalization ability For all least squares solutionof equation H120596 = T has the smallest norm number thatis = H+T le 120596 where
forall120596 isin 120596 | H120596 minus T le Hz minus T forallz isin 119877119873times119898 (22)
From (22) not only can ELM achieve the minimum trainingerror but it also has stronger generalization ability than thetraditional gradient descent algorithm There is only one H+for the generalized inverse H+of matrix H so the value isunique
5 Test Signal Analysis
Given the test signal there are three frequency componentswhich have different time scale intervals the calculation is asfollows
119904 (119905) =
9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s
38119890minus119905 sin (100120587119905)
+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s
(23)
We added 20 db Gauss white noise to the signal and veri-fied anti-interference ability of atom decomposition methodFor original signal it should be normalized the signal isdivided by its Euclid norm [20] The decomposition processwas shown in Figure 4
6 Journal of Sensors
01
0
minus0150 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Gabor atom 1st iteration
t (ms)
(a)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 2nd iteration
t (ms)
(b)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 3rd iteration
t (ms)
(c)
Figure 5 The first second and third atoms
005
0
minus005
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Original signalConstructed signal
Figure 6 Comparison of original signal and constructed signal by20 iterations
Identification method frequency center 119865 is equaled to1198911199041205852120587 119891
119904is sampling frequency start time is 119879
119904= 119906 minus 1199042
end time is119879119890= 119906+1199042 120601 is phase angle and the amplitude is
equaled to atom normalization amplitude to multiply actualenergy value which is Euclid norm
Set 119891119904= 1 kHz simulation time and sampling points
areequaled to 05 s and 500 respectively Before the decom-position the normalization equation is shown in
119904119892 (119899) =
119904 (119899)
119904 (119899) (24)
In (24) 119904(119899) is discrete signal of 119904(119905) 119904119892(119899) is normalization
expression of 119904(119899) 119904(119899) is Euclid norm and its value is927915
Set iteration number as 20 and decompose 119904119892(119899) by
atomic algorithm Figure 5 shows atom 1 atom 2 and atom 3generated by iteration respectively and all atoms in Figure 5are normalized results Comparison of original signal andconstructed signal is shown in Figure 6 it indicated that thedifference of two signals is smaller by 20 iteration numbersThe residual component amplitude is only 10minus3 in Figure 7and further shows that the accuracy is satisfied atomicdecomposition requirement
001
0005
0
minus0005
minus001
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Residues
t (ms)
Figure 7 Residual component decomposed by 20 iterations
The parameters of atom 1 atom 2 and atom 3 areshown in Table 1 Notably every atom decomposed by atomicalgorithm does not have physical meaning it just indicateddistribution characteristics of time scales Hence the atomicparameters in Table 1 are needed for identification processingand we transformed it to indicate local features of originalsignal it is shown in Table 2
We observed the amplitude frequency and phase valueof atoms in Table 2 it could know that the atoms 12 and 3 represent 9119890minus119905 sin(150120587119905) 38119890minus119905 sin(100120587119905) and28119890minus05119905 sin(70120587119905) of original signal respectively by identi-
fication processing For atom 1 because the actual end time is200ms and the calculated end time is 1877268ms deviationis 122732ms But for atoms 2 and 3 comparing the calculatedstart time with actual start time the deviations are 14297msand 78642ms respectively the difference is smaller
Time-frequency analysis by 20 iteration number decom-position is shown in Figure 8 we can see that the atoms couldindicate local characteristics of nonstationary test signalsaccurately including frequency segment time interval andfrequency components energy compared to the traditionalFFT spectrum cross interference and noise interference canbe suppressed effectively and the calculation accuracy is alsohigher than FFT
Journal of Sensors 7
Table 1 Characteristic parameters of every atom
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 2276520 729008 04709 minus20125 009032 3083047 3527226 03150 minus22285 003803 3168729 3663006 02200 minus18173 00281
Table 2 Local characteristic parameters of test signal
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 90112 749841 minus20125 mdash 18672682 37921 501592 minus22285 1985703 mdash3 28041 350319 minus18173 2078642 mdash
500
450
400
350
300
250
200
150
100
50
f(H
z)
90
75
60
45
30
15
Time-frequency distribution based on matching pursuit
5
0
minus5
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Figure 8 Time-frequency representation of test signal
006004002
0minus002minus004minus006
0005 001 0015 002 0025 003 0035 004
Original signalConstructed signal
t (s)
Am
plitu
de (p
u)
Figure 9 Fitting waveform of overhead line 1198782
6 Choose Characteristic Atom of ZeroSequence Current
To verify ASD algorithm extracting fault feature componentsability in distribution network it gives the feeder fault asexample by ASD set the iteration number as 4 hence the
zero sequence current fitting waveform of overhead line isshown in Figure 9
The similarity between constructed signal and originaloverhead line 119878
2signal is higher by 4 iterations and the
fitting accuracy meets the requirements The first four atomsrsquowaveform and specific parameters are shown in Figure 10 andTables 3 and 4 respectively
Combined with Figure 10 and Table 4 atom 1 waveformshows oscillation attenuation trend both waveform andenergy value have higher similarity with original signal andit indicated major information of original signal thereforeatom 1 is defined asmain components atom and its frequencyvalue is equal to 4729299Hz Atom 2 is defined as funda-mental atom and its frequency value is 509554Hz Atom 3and atom 4 all show oscillation attenuation trend but theirfrequency values are different from atom 1 they are equal to17786624Hz and 11767516Hz respectively and all the highfrequency components therefore it is defined as transientcharacteristic atoms 1 and 2 respectively
Zero sequence current fitting waveform of cable line1198784is shown in Figure 11 the first four atoms are shown
in Figure 12 and the parameters of every atom are shownin Tables 5 and 6 Combining Figure 12 and Table 6 it isknown that atom 1 of cable line is main components atomand its frequency is equal to 4729299Hz Therefore thefrequencies of fundamental atom and transient characteristicatoms 1 and 2 are equal to 493631Hz 11751592Hz and23662420Hz respectively Comparing Figures 10 and 12 itgot different characteristic of transient characteristic atomsbetween overhead line and cable line
Comparing Figures 10(c) 10(d) and Figures 12(c) 12(d)respectively for cable line oscillation attenuation trend oftransient characteristic atoms is more obvious its oscillationprocess is shorter than overhead line Because the capacitanceto ground value of cable line is larger than overhead line inactual distribution network it got different oscillation processof fault current
7 Fault Line Selection Methods
71 Atom Dictionary Measure Based on Information EntropyIndex Information entropy canmeasure uncertain degree ofevent the information entropy value is larger it indicated that
8 Journal of Sensors
004002
0
minus004minus002
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(b) Atom 2
001
0
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
0010
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(d) Atom 4
Figure 10 Zero sequence current characteristic atom of overhead line 1198782
Table 3 Every atom characteristic parameters of overhead line 1198782
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135
004002
0minus002
minus006minus004
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
Original signalConstructed signal
Figure 11 Fitting waveform of cable line 1198784
uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows
Firstly calculate the ratio of atom library and atom librarysum it is shown in
120582 (119896) =119871 (119896)
sum119873
119896=0119871 (119896)
(25)
In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin
119867 = minus
119873
sum
119896=0
120582 (119896) ln 120582 (119896) (26)
In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher
Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows
Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867
1max 1198672max 1198673maxand 119867
4max compared the four values and determined themaximum entropy value119867max
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
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DistributedSensor Networks
International Journal of
6 Journal of Sensors
01
0
minus0150 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Gabor atom 1st iteration
t (ms)
(a)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 2nd iteration
t (ms)
(b)
002
0
minus002
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u) Gabor atom 3rd iteration
t (ms)
(c)
Figure 5 The first second and third atoms
005
0
minus005
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Original signalConstructed signal
Figure 6 Comparison of original signal and constructed signal by20 iterations
Identification method frequency center 119865 is equaled to1198911199041205852120587 119891
119904is sampling frequency start time is 119879
119904= 119906 minus 1199042
end time is119879119890= 119906+1199042 120601 is phase angle and the amplitude is
equaled to atom normalization amplitude to multiply actualenergy value which is Euclid norm
Set 119891119904= 1 kHz simulation time and sampling points
areequaled to 05 s and 500 respectively Before the decom-position the normalization equation is shown in
119904119892 (119899) =
119904 (119899)
119904 (119899) (24)
In (24) 119904(119899) is discrete signal of 119904(119905) 119904119892(119899) is normalization
expression of 119904(119899) 119904(119899) is Euclid norm and its value is927915
Set iteration number as 20 and decompose 119904119892(119899) by
atomic algorithm Figure 5 shows atom 1 atom 2 and atom 3generated by iteration respectively and all atoms in Figure 5are normalized results Comparison of original signal andconstructed signal is shown in Figure 6 it indicated that thedifference of two signals is smaller by 20 iteration numbersThe residual component amplitude is only 10minus3 in Figure 7and further shows that the accuracy is satisfied atomicdecomposition requirement
001
0005
0
minus0005
minus001
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)Residues
t (ms)
Figure 7 Residual component decomposed by 20 iterations
The parameters of atom 1 atom 2 and atom 3 areshown in Table 1 Notably every atom decomposed by atomicalgorithm does not have physical meaning it just indicateddistribution characteristics of time scales Hence the atomicparameters in Table 1 are needed for identification processingand we transformed it to indicate local features of originalsignal it is shown in Table 2
We observed the amplitude frequency and phase valueof atoms in Table 2 it could know that the atoms 12 and 3 represent 9119890minus119905 sin(150120587119905) 38119890minus119905 sin(100120587119905) and28119890minus05119905 sin(70120587119905) of original signal respectively by identi-
fication processing For atom 1 because the actual end time is200ms and the calculated end time is 1877268ms deviationis 122732ms But for atoms 2 and 3 comparing the calculatedstart time with actual start time the deviations are 14297msand 78642ms respectively the difference is smaller
Time-frequency analysis by 20 iteration number decom-position is shown in Figure 8 we can see that the atoms couldindicate local characteristics of nonstationary test signalsaccurately including frequency segment time interval andfrequency components energy compared to the traditionalFFT spectrum cross interference and noise interference canbe suppressed effectively and the calculation accuracy is alsohigher than FFT
Journal of Sensors 7
Table 1 Characteristic parameters of every atom
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 2276520 729008 04709 minus20125 009032 3083047 3527226 03150 minus22285 003803 3168729 3663006 02200 minus18173 00281
Table 2 Local characteristic parameters of test signal
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 90112 749841 minus20125 mdash 18672682 37921 501592 minus22285 1985703 mdash3 28041 350319 minus18173 2078642 mdash
500
450
400
350
300
250
200
150
100
50
f(H
z)
90
75
60
45
30
15
Time-frequency distribution based on matching pursuit
5
0
minus5
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Figure 8 Time-frequency representation of test signal
006004002
0minus002minus004minus006
0005 001 0015 002 0025 003 0035 004
Original signalConstructed signal
t (s)
Am
plitu
de (p
u)
Figure 9 Fitting waveform of overhead line 1198782
6 Choose Characteristic Atom of ZeroSequence Current
To verify ASD algorithm extracting fault feature componentsability in distribution network it gives the feeder fault asexample by ASD set the iteration number as 4 hence the
zero sequence current fitting waveform of overhead line isshown in Figure 9
The similarity between constructed signal and originaloverhead line 119878
2signal is higher by 4 iterations and the
fitting accuracy meets the requirements The first four atomsrsquowaveform and specific parameters are shown in Figure 10 andTables 3 and 4 respectively
Combined with Figure 10 and Table 4 atom 1 waveformshows oscillation attenuation trend both waveform andenergy value have higher similarity with original signal andit indicated major information of original signal thereforeatom 1 is defined asmain components atom and its frequencyvalue is equal to 4729299Hz Atom 2 is defined as funda-mental atom and its frequency value is 509554Hz Atom 3and atom 4 all show oscillation attenuation trend but theirfrequency values are different from atom 1 they are equal to17786624Hz and 11767516Hz respectively and all the highfrequency components therefore it is defined as transientcharacteristic atoms 1 and 2 respectively
Zero sequence current fitting waveform of cable line1198784is shown in Figure 11 the first four atoms are shown
in Figure 12 and the parameters of every atom are shownin Tables 5 and 6 Combining Figure 12 and Table 6 it isknown that atom 1 of cable line is main components atomand its frequency is equal to 4729299Hz Therefore thefrequencies of fundamental atom and transient characteristicatoms 1 and 2 are equal to 493631Hz 11751592Hz and23662420Hz respectively Comparing Figures 10 and 12 itgot different characteristic of transient characteristic atomsbetween overhead line and cable line
Comparing Figures 10(c) 10(d) and Figures 12(c) 12(d)respectively for cable line oscillation attenuation trend oftransient characteristic atoms is more obvious its oscillationprocess is shorter than overhead line Because the capacitanceto ground value of cable line is larger than overhead line inactual distribution network it got different oscillation processof fault current
7 Fault Line Selection Methods
71 Atom Dictionary Measure Based on Information EntropyIndex Information entropy canmeasure uncertain degree ofevent the information entropy value is larger it indicated that
8 Journal of Sensors
004002
0
minus004minus002
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(b) Atom 2
001
0
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
0010
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(d) Atom 4
Figure 10 Zero sequence current characteristic atom of overhead line 1198782
Table 3 Every atom characteristic parameters of overhead line 1198782
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135
004002
0minus002
minus006minus004
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
Original signalConstructed signal
Figure 11 Fitting waveform of cable line 1198784
uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows
Firstly calculate the ratio of atom library and atom librarysum it is shown in
120582 (119896) =119871 (119896)
sum119873
119896=0119871 (119896)
(25)
In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin
119867 = minus
119873
sum
119896=0
120582 (119896) ln 120582 (119896) (26)
In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher
Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows
Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867
1max 1198672max 1198673maxand 119867
4max compared the four values and determined themaximum entropy value119867max
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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DistributedSensor Networks
International Journal of
Journal of Sensors 7
Table 1 Characteristic parameters of every atom
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 2276520 729008 04709 minus20125 009032 3083047 3527226 03150 minus22285 003803 3168729 3663006 02200 minus18173 00281
Table 2 Local characteristic parameters of test signal
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 90112 749841 minus20125 mdash 18672682 37921 501592 minus22285 1985703 mdash3 28041 350319 minus18173 2078642 mdash
500
450
400
350
300
250
200
150
100
50
f(H
z)
90
75
60
45
30
15
Time-frequency distribution based on matching pursuit
5
0
minus5
50 100 150 200 250 300 350 400 450 500
Am
plitu
de (p
u)
t (ms)
Figure 8 Time-frequency representation of test signal
006004002
0minus002minus004minus006
0005 001 0015 002 0025 003 0035 004
Original signalConstructed signal
t (s)
Am
plitu
de (p
u)
Figure 9 Fitting waveform of overhead line 1198782
6 Choose Characteristic Atom of ZeroSequence Current
To verify ASD algorithm extracting fault feature componentsability in distribution network it gives the feeder fault asexample by ASD set the iteration number as 4 hence the
zero sequence current fitting waveform of overhead line isshown in Figure 9
The similarity between constructed signal and originaloverhead line 119878
2signal is higher by 4 iterations and the
fitting accuracy meets the requirements The first four atomsrsquowaveform and specific parameters are shown in Figure 10 andTables 3 and 4 respectively
Combined with Figure 10 and Table 4 atom 1 waveformshows oscillation attenuation trend both waveform andenergy value have higher similarity with original signal andit indicated major information of original signal thereforeatom 1 is defined asmain components atom and its frequencyvalue is equal to 4729299Hz Atom 2 is defined as funda-mental atom and its frequency value is 509554Hz Atom 3and atom 4 all show oscillation attenuation trend but theirfrequency values are different from atom 1 they are equal to17786624Hz and 11767516Hz respectively and all the highfrequency components therefore it is defined as transientcharacteristic atoms 1 and 2 respectively
Zero sequence current fitting waveform of cable line1198784is shown in Figure 11 the first four atoms are shown
in Figure 12 and the parameters of every atom are shownin Tables 5 and 6 Combining Figure 12 and Table 6 it isknown that atom 1 of cable line is main components atomand its frequency is equal to 4729299Hz Therefore thefrequencies of fundamental atom and transient characteristicatoms 1 and 2 are equal to 493631Hz 11751592Hz and23662420Hz respectively Comparing Figures 10 and 12 itgot different characteristic of transient characteristic atomsbetween overhead line and cable line
Comparing Figures 10(c) 10(d) and Figures 12(c) 12(d)respectively for cable line oscillation attenuation trend oftransient characteristic atoms is more obvious its oscillationprocess is shorter than overhead line Because the capacitanceto ground value of cable line is larger than overhead line inactual distribution network it got different oscillation processof fault current
7 Fault Line Selection Methods
71 Atom Dictionary Measure Based on Information EntropyIndex Information entropy canmeasure uncertain degree ofevent the information entropy value is larger it indicated that
8 Journal of Sensors
004002
0
minus004minus002
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(b) Atom 2
001
0
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
0010
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(d) Atom 4
Figure 10 Zero sequence current characteristic atom of overhead line 1198782
Table 3 Every atom characteristic parameters of overhead line 1198782
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135
004002
0minus002
minus006minus004
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
Original signalConstructed signal
Figure 11 Fitting waveform of cable line 1198784
uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows
Firstly calculate the ratio of atom library and atom librarysum it is shown in
120582 (119896) =119871 (119896)
sum119873
119896=0119871 (119896)
(25)
In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin
119867 = minus
119873
sum
119896=0
120582 (119896) ln 120582 (119896) (26)
In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher
Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows
Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867
1max 1198672max 1198673maxand 119867
4max compared the four values and determined themaximum entropy value119867max
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
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Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
8 Journal of Sensors
004002
0
minus004minus002
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004Am
plitu
de (p
u)
t (s)
(b) Atom 2
001
0
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
0010
minus001
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(d) Atom 4
Figure 10 Zero sequence current characteristic atom of overhead line 1198782
Table 3 Every atom characteristic parameters of overhead line 1198782
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135
004002
0minus002
minus006minus004
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
Original signalConstructed signal
Figure 11 Fitting waveform of cable line 1198784
uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows
Firstly calculate the ratio of atom library and atom librarysum it is shown in
120582 (119896) =119871 (119896)
sum119873
119896=0119871 (119896)
(25)
In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin
119867 = minus
119873
sum
119896=0
120582 (119896) ln 120582 (119896) (26)
In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher
Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows
Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867
1max 1198672max 1198673maxand 119867
4max compared the four values and determined themaximum entropy value119867max
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
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Active and Passive Electronic Components
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
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Electrical and Computer Engineering
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Volume 2014
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SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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International Journal of
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Sensors 9
005
0
minus0050005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(a) Atom 1
50
minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(b) Atom 2
510
0minus5
times10minus3
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
(c) Atom 3
20
minus2
0005 001 0015 002 0025 003 0035 004
t (s)
Am
plitu
de (p
u)
times10minus3
(d) Atom 4
Figure 12 Zero sequence current characteristic atom of cable line 1198784
2
1
0
minus1
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(a)
2
1
0
minus1
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(b)
4
2
0
minus2
times105
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(c)
1
0
minus1
minus2
times106
Entro
py v
alue
0 20 40 60 80 100 120
Sample number
(d)
Figure 13 Information entropy value of every atom library
Input layerHidden layer1205961 1205731 S1
S2S3
Sn120573Hn
T
Snminus11205964H
Figure 14 ELM network topology structure
Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)
Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library
The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower
72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages
(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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Active and Passive Electronic Components
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Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Electrical and Computer Engineering
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Volume 2014
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
10 Journal of Sensors
Zero sequencecurrent signal
Atomic sparsedecomposition
Main componentatoms
Fundamental waveatoms
Number 1 of characteristic atoms
Calculating measure values ofatoms information entropy
Training ELM1network
Training ELM2network
Training ELM3network
Training ELM4network
The trained ELM1model
The trained ELM2model
The trained ELM3model
The trained ELM4model
Calculating correct rateof every ELM network
Faultvote
transient
Number 2 of characteristic atoms
transient
Fault lineselection
results
Fault line selectioncredibility
Figure 15 Basic framework of fault voting
Table 4 Zero sequence current local characteristic parameters of overhead line 1198782
Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625
(2) It can not provide fault indication information ofother lines
(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]
This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results
It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in
Confidence degree
= information entropy measure of atom library
times ELM network accuracy
(27)
73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork
Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input
weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596
120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)
Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573
120591=
[1205961205911 120573
12059112]119879 and well-trained ELM network is obtained
from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown
Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]
Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14
74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15
From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows
Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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Active and Passive Electronic Components
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VLSI Design
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Volume 2014
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International Journal of
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DistributedSensor Networks
International Journal of
Journal of Sensors 11
Start
U0(t) gt 015Un
Obtaining zero sequence current of every branch line
Decomposed zero sequence current byatomic algorithm
network respectively
Is it the healthy line
Numerical size comparison
Judge the line ashealthy line
Judge the line asfault line
Display storageprinting
End
YesYes
Yes
Yes
Yes
No
No
No
No
No
Return
TV alarm
Adjusting arc suppressioncoil away from the
resonance point
Atom 1 atom 2 atom 3 and atom 4
TV is broken
Input the ELM1 ELM2 ELM3 and ELM4
multiplied ldquo1rdquo multiplied ldquo minus1rdquo
Arc suppression coil is series resonant
To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value
Are the ldquoyesrdquo votes more than the ldquonordquo votes
Figure 16 Fault line selection process
Table 5 Every atom characteristic parameters of cable line 1198784
Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043
Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo
Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line
The specific process of FLS is shown in Figure 16
8 Example Analysis
In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]
In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0
Overhead line positive-sequence parameters are 1198771=
017Ωkm 1198711= 12mHkm and 119862
1= 9697 nFkm zero
sequence parameters are 1198770= 023Ωkm 119871
0= 548mHkm
and 1198620= 6 nFkm
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
12 Journal of Sensors
SI
I
I
I
I
I
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
LineZ-T
RLC
RLC
RLC
RLC
Hybrid line S3
Overhead line S1
Overhead line S2
Overhead line Overhead line Load
SourceTransformer
Current probe
Voltage probe
Switch
Grounding resistance
Overhead line
Overhead line Overhead line
Cable line Cable line
Cable line
Arcsuppression
coil
+U
+Uminus
+Uminus
I
I
I
Cable line S4
IV V V
Figure 17 ATP simulation model
Cable line positive-sequence parameters are 11987711
=0193Ωkm 119871
11= 0442mHkm and 119862
11= 143 nFkm zero
sequence parameters are11987700= 193Ωkm119871
00= 548mHkm
and 11986200= 143 nFkm
The overhead lines 1198781and 119878
2are 135 km and 24 km
respectively Cable line 1198784is 10 km Hybrid line 119878
3is 17 km
where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates
that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871
119873= 12819mH 119877
119873=
402517ΩSampling frequency119891
119904is equal to 105Hz simulation time
is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase
angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878
1
9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878
4
with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]
According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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DistributedSensor Networks
International Journal of
Journal of Sensors 13
Table 6 Zero sequence current local characteristic parameters of cable line 1198784
Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462
Table 7 Fault voting result of overhead line 1198781under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
5 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is
healthy line
10 1000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is
healthy line
5 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198784is
healthy line
10 2000
Overheadline S1
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line
Overheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198783is
healthy line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198784is
healthy line
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
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DistributedSensor Networks
International Journal of
14 Journal of Sensors
Table 8 Fault voting result of hybrid line 1198783under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
17 100
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times (minus1) 08358 times 1 07375 times 1 254 gt 0855 Vote 1198784is
healthy line
9 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198784is
healthy line
17 1000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times (minus1) 26575 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times (minus1) 07375 times 1 25592 gt 08358 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
9 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times 1 26575 gt 07375 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
17 2000
Overheadline 119878
1
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07375 times (minus1) 3395 gt 0 Vote S3 isfault line
Cable line 1198784
09667 times 1 0855 times 1 08358 times 1 07375 times 1 3395 gt 0 Vote 1198784is
healthy line
training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1
According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according
to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878
1when the initial phase angle
is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Sensors 15
Table 9 Fault voting result of cable line 1198784under 0∘
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
10 100
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times (minus1) 07375 times 1 24167 gt 09341 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 1000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 1000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
6 2000
Overheadline 119878
1
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times (minus1) 26133 gt 07375 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line
10 2000
Overheadline 119878
1
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198781is
healthy lineOverheadline 119878
2
09667 times 1 07125 times (minus1) 09341 times 1 07375 times 1 26383 gt 07125 Vote 1198782is
healthy lineHybrid line1198783
09667 times 1 07125 times 1 09341 times 1 07375 times 1 33508 gt 0 Vote 1198783is
healthy line
Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line
1198781is accurately checked out through the comparison of the
values above even if the grounding resistance value is as highas 1000Ω
Table 8 offers the selection result of hybrid line 1198783when
the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the
corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878
3
Table 9 offers the selection result of cable line 1198784when
the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
16 Journal of Sensors
Table 10 Information entropy value of every atom library
Main componentatom library
Fundamental atomlibrary
Transientcharacteristic atomlibrary number 1
Transientcharacteristic atomlibrary number 2
Information entropyvalue 09792 09583 09861 09861
Table 11 Test result of every ELM network
Samples styleELM
Correct samplesnumbertotal number Accuracy rate
Main componentatom library 2324 958333
Fundamental atomlibrary 2024 833333
Transientcharacteristic atomlibrary number 1
2124 875
Transientcharacteristic atomlibrary number 2
1924 791667
Total 8396 864583
in this paper can select fault line accurately when groundingfault of cable line occurs
9 Applicability Analysis
Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878
1when grounding fault occurs at 10Ω
and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network
It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the
selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘
Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness
10 Conclusions
A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research
(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently
(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system
(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Sensors 17
Table 12 Fault voting result with strong noise
(a) Fault voting result of overhead line 1198781
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 5
Overheadline S1
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times (minus1) 07807 times (minus1) 1737 gt 16024 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198784is
healthy line
10 500
Overheadline S1
09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line
Overheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid line1198783
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(b) Fault voting result of hybrid line 1198783
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results
Fault lineselectionresults
5 500
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times (minus1) 07807 times 1 25177 gt 08217 Vote 1198784is
healthy line
14 2000
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198782is
healthy lineHybrid lineS3
09384 times (minus1) 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 33394 gt 0 Vote S3 isfault line
Cable line 1198784
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198784is
healthy line
(c) Fault voting result of cable line 1198784
Faultlocationkm
TransitionresistanceΩ
Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line
selection results
4 200
Overheadline 119878
1
09384 times 1 07986 times 1 08217 times 1 07807 times (minus1) 25587 gt 07807 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
8 10
Overheadline 119878
1
09384 times 1 07986 times (minus1) 08217 times 1 07807 times 1 25408 gt 07986 Vote 1198781is
healthy lineOverheadline 119878
2
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198782is
healthy lineHybridline 119878
3
09384 times 1 07986 times 1 08217 times 1 07807 times 1 33394 gt 0 Vote 1198783is
healthy lineCable lineS4
09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
18 Journal of Sensors
0 001 002 003 004minus200
minus100
0
100
200
300
t (s)
i 0t
(A)
(a) 10Ω to ground fault
0 001 002 003 004minus15
minus10
minus5
0
5
10
15
t (s)
i 0t
(A)
(b) 2000Ω to ground fault
Figure 18 Zero sequence current with strong noise
and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference
(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime
Notations
ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China
References
[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008
[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011
[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008
[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011
[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013
[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013
[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010
[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013
[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007
[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012
[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Sensors 19
[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010
[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993
[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005
[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007
[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013
[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012
[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013
[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013
[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012
[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008
[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003
[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin
control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005
[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012
[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012
[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006
[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009
[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009
[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011
[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014
[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014
[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867
infincontrol for production networks of autonomous
work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010
[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of