162 IEEE~~~~~~~~~~~~~~~~~~~~-- --------Indicon 2005 Conference. -Chnni.Inia 1-13 Dec 2005--

Transmission Line Fault Detection UsingTime-Frequency Analysis

S. R. Samantaray1, P. K. Dash2 and G.Panda3

Abstract - A new approach for fault detection in power systemnetwork using time-frequency analysis is presented in thispaper. The S-transform with complex window is used forgenerating frequency contours(S-contours), which distinguishesthe faulted condition from no-fault. Here the fault current datafor one cycle back and one cycle from the fault inception isprocessed through S-transform to generate time-frequencypatterns with varying window. The generated time-frequencypatterns clearly distinguishes the faulted condition fromun-faulted.Keywords - Fault detection, time-frequency analysis,S-contours.

I.INTRODUCTION

Ifferent types oftransient phenomena occur on the trans-mission line. From these transient phenomena, faults ontransmission lines need to be detected and classified ac-

curately, and cleared as fast as possible. In power transmis-sion line protection, faulty phase identification is veryimportant items which need to be addressed in a reliable andaccurate manner. Distance relaying techniques based on themeasurement of the impedalnce at the fundamental frequencybetween the fault location and the relaying point have at-tracted wide spread attention. The sampled current data at therelying point are used to detect and classify the fault involvingthe line with or without fault resistance present in the faultpath.Another pattern recognition technique based on wavelettransform[1,2] has been found to be an effective tool in moni-toring and analyzing power system disturbances includingpower quality assessment and system protection againstfaults. Although wavelets provide a variable window for lowand high frequency currents in the voltage and current wave-forms during fault, they are subject to inaccuracies due tonoise and the presence of harmonics. Another powerfultime-frequency analysis known as S-transform has[3-5]found applications in geoscience and power engineering . TheS-transform is an invertible time-frequency spectral localiza-tion technique that combines elements of wavelet transformsand short-time Fourier transform. The S-transform uses an

1"3Department of Electronics and Telecommunications Engineering.National Institute of Technology, Rourkela, Indiasbh_samant@rediffmail.com , gpandajnitrkl.ac.in2College of Engineering, Bhubaneswar, India: pkdashfIndia@yahoo.com0-7803-9503-4/05/$20.00 C2005 IEEE

analysis window whose width is decreasing with frequencyproviding a frequency dependent resolution. This transformmay be seen as a continuous wavelet transform with a phasecorrection. It produces a constant relative bandwidth analysislike wavelets while it maintains a direct link with Fourierspectrum. The S-transform has an advantage in that it pro-vides multi resolution analysis while retaining the absolutephase of each frequency. This has led to its application fordetection and interpretation of events in a time series like thepower quality disturbances [6].When the fault occurs on the power system, the fault current

is captured at the relaying point. After the signal is retrieved,it is processed through S-transform with complex window [7]to produce the time-frequency contours known as S-contoursto which distinguishes faults from un-faulted one. As s-trans-form is obtained by multiplying the real window with fouriersinusoid and the fourier sinusoid has time-invariant fre-quency, s-transform is unsuitable for resolving waveformswhose frequency changes with time. This problems can beovercome by using complex gaussian window with a user de-signed complex phase function. The phase function modu-lates the frequency of the fourier sinusoid to give bettertime-frequency localization of the time series. That means ifthe time series contains a specific asinusoidal waveform thatis expected at al scales, then the complex gaussian windowcan give better time-frequency resolution of event signaturesthan the un-modulated, real valued gaussian window of theoriginal signal

II. S-TRANSFORM WITH COMPLEX WINDOW

The original S-transform is defined as00

S(,f,p) = Jh(t){w( - t, f, p) x exp(-2nift)}dt, (I)

where w is the window function ofthe S-transform and p de-notes the set of parameters that determines the shape andproperty of w. The alternative expression of (1) with Fouriertransform can be given as:

S(,' ff, p) = JH(a + f)W(a, f, p) x exp(+2niax )da (2)-ao

162 IEEE Indicon 2005 Conference, Chennai, India, I I 1 3 Dec. 2005

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA. Downloaded on February 26, 2009 at 06:14 from IEEE Xplore. Restrictions apply.

I I

Where

H(f) = J h(t) exp(-2nift)dt (3),00

00

W(a, f, p) = J w(t, f, p) exp(-2tiat)dt (4)

The variable a and f having same units. For S-transform toconverge to H given by:

S(r, f, p)dt = H(f) (5)-cc

Forw to the window ofS-transforn, the following conditionmust be satisfied

W(T - t,f, p) exp(-2rcift)= A(r -t,f, p)exp{-2ni( -t,f,p)}

(6)where A and 4 are the amplitude and phase of w. If both

sides get multiplied by Fourier sinusoids, w becomes:

w(T - t, f, p) exp(-2irft)=A(T-t,f, p)exp{-2ii[ft+4(T t, f,pD

(7)As A and 4 are known, the instantaneous frequency can be

defined as the time derivative of the total phase. Then the in-stantaneous frequency can be given as:

F=f+-a(t -t,f,p)at

The pre-factor P is defined as

p= exp{ 2-ifr +2nrisign(f)xa Iogp + fik}

(10)where the positive parameter ca controls the degree ofphase

modulation. When Wcg = 0 the instantaneous frequencybecomes

F- cfCT + Ifl(, -t) (1

The discrete S-transform is obtained by sampling (2) in thefrequency domain and given by:

[MT ]m=-M2 [MT]m n

r+ 2irfmj]exm

(12)

where T is the sampling interval,M is the numbers ofsamplepoints andj is the discrete time index. m and n are discrete fre-quency indices. The discrete window function is obtained by

(8)

The S-transform gives the best localized spectrum when theanalyzing function matches with the shape of the time seriesofthe signal. The analyzing function is defined by multiplica-tion of the Fourier sinusoid with the Gaussian window withphase modulation through an appropriate complex factor andnormalization. This gives to complex Gaussian window [9]wcg

wcg k -t,f,a)

{p exp[- f 2(r t) ]exp(-21nif(T - t)

=+ 2nisign(f)a logp + lfl(@ - t)] t < T + a Ilfl,0, t > T +a/lf1f.

I[w m, n a(s

max c2 n22M 2 irink

k=max(-aM2II{,-M sI2 M2

xexp -2ii nk- sign(n) xlg(a M]nl

(13)

where P is defined as:

M / 2-1 n2k2l

xex p(-27ri[M -: Si(exp M2 Mk=max(-jM /InI,-M/2 2

x exp{_ 27ri[nk a sign(n) x log(aiy

(14)

where k is the discrete time index.

(9)

IEEE Indicon 2005 Conference, Chennai, India 1-1 1- 13 Dec. 2005 163

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA. Downloaded on February 26, 2009 at 06:14 from IEEE Xplore. Restrictions apply.

IEEE Indicon 2005 Conference. Chennai. India. 11 - 13 Dec. 2005

III.SIMULATION STUDY AND RESULTS2

0

-2

.4300 Km

EsRelayingPoint

I Fault12

10

A

2

Fig. 1. Transmission Line Model

aph ag

0Ea 100 150 200 250

0- ,- II - IC

0- Z20 ' ' C (, c

0 -

0 _-

0-

20 40 60 83 100 120 140 160 183 200 220

The 400 KV, 3-phase, 300 km power transmission studies isshown in Fig. 1. A cycle-to-cycle comparison of currents andthresholds are used to detect any abnonnality due to the oc-

currence of a Fault. Once a deviation is observed, the S-transform is applied to the data one cycle back and the one

cycle data from the point of occurrence of the deviation in thecurrent amplitudes. The sampling rate chosen is 6.4 kIHIz. Theparameters are chosen as: L(1)=0.9337e-3 H/km,L(0)=4.1264e-3 H/km, R(1)=0.01273 Ohms/km, R(0)=0.3864 Ohms/km, ,C(1)=12.74e-9 F/km, C(0)=7.751e-9F/km.Fig.2 through Fig.12 depict the results for different fault

condition with various operating mode. Fig.2 shows theS-contours for a-ph (a-g) fault at 20% of line with 20 ohmfault resistance (Rf). Similarly the Fig.3 shows the S-contoursfor b-ph at (a-g) fault at 20% of line with 20 ohm fault resis-tance ohm. It clearly seen that in case of faulted phase theS-contours are at higher frequency scale compared toun-faulted phase where S-contours are at lower frequencyscale. Fig.5 and Fig.6 depict the fault pattems for Line-Line(a-b fault) at 45% of the line with 50 ohm fault resistance.Similarly Fig.7 through Fig.9 show the S-contours resultedfrom S-transform in case ofLine-Line-Ground fault at 65% ofthe line with 80 ohm fault resistance. It is clearly seen that incase of faults the S-contours are at higher values compared toS-contours generated for phase without fault. ForLine-Line-Line faults at 80% of line with Rr 100 ohm, thegenerated S-contours are shown in Fig. 10 and Fig. I .Fig. 12depicts the S-contours for Line-Line-Line-Ground fault at90% of the line with 150 ohm fault resistance.From the above results the fault is recognized by pattern rec-

ognition approach where faults and no-faults are clearly dis-tinguished from the position of the S-contour levels in thegenerated time-frequency patterns. In case of faults theS-contours are concentric at higher frequency scales where as

in un-faulted condition the S-contours are concentric aboutLower frequency scale.

Fig.2. S-contours for a-ph (a-g) fault at 20% of line withRf=20 ohm.

bpt' at ag

-2 I I I

0 50 100 150 200 250

40-20.

50 100 150 200

Fig.3. S-contours for b-ph (a-g) fault at 20% of linewith Ri=20 ohm.

0

-2

0 100 20050

40

20

50 100 150 200

Fig.4. S-contours for c-ph (a-g) fault at 20% of linewith Rf=230 ohm

CQ . w

164

4

1P

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA. Downloaded on February 26, 2009 at 06:14 from IEEE Xplore. Restrictions apply.

Indicon 2005 Conference, Chennai, India, 11-13 Dec. 2005

bph at abg

50 100 150 200 250

120100

604020

0 50 100 150 200 260

Fig.5. S-contours for a-ph (a-b) fault at 45% of linewith Rf'50 ohm.

bph at ab

2

1*0 -

-10

00*8060 -

40-20-

50 100 160 200 250 40

'. 1 20 :I~~

50 100 150 200

60 100 160 200

Fig.8. S-contours for b-ph (ab-g) fault at 65% of linewith Ri80 ohm

oph at abg

0

-10 60 100 150 200 250

eo.

50 100 150 200

Fig.9. S-contours for c-ph (ab-g) fault at 65% of linewith Ri=80 ohm

Fig.6. S-contours for b-ph (a-b) fault at 45% of linewith Rf'50 ohm.

apn at ang

50 100 150 200

Fig.7. S-contours for a-ph (ab-g) fault at 65% of line with Rff80 ohmn.

aph at abc

0

-_U0

100 r60 100 160 200 250

60 100 160 200

Fig. 1O. S-contours for a-pb (abc) fault at 80% of linewith RilI00 ohm.

]V.CONCLUSION

This paper presents a patterns recognition approacb for faultdetection using time frequency analysis. The fault current isprocessed through the S-transformnwith complex window and

2aph at ab R

0

_0_

0

5.

0-

-5 L0 50 100 150 200

12010080604020

m

. . . . .

165

I

-

5;

250

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA. Downloaded on February 26, 2009 at 06:14 from IEEE Xplore. Restrictions apply.

IEEE Indicon 2005 Conference, Chennai, India, 11-13 Dec. 2005

tlpn at afoAt

2

0

-20 50 100 150 200 250

-1000'604020

50 100 150 200

Fig. 11. S-contours for b-ph (abc) fault at 80% of linewith Re-100 ohm

it generates time-frequency patterns or S-contours. The S-

aph abog

0

-5

-1U50 100 150 200 250

contours are concentric at higher frequency scales for faultedcondition but in case of un-faulted phase the S-contours areconcentric about lower frequency scales, which clearly distin-guishes faults from no-fault condition. As S-transform is veryless sensitive to noise, the proposed method is very accurateand robust for protection of transmission line.

REFERENCES

[1] O.A.S Yaussef, "New Algorithms for phase selection based on wave-let transforms", IEEE Transactions on Power Delivery, vol-17, 2002,pp.908-914.

[2] A.H.Osman and O.P.Malik, "Transmission line protection based onwavelet transform", IEEE Transactions on Power Delivery, vol-19,No.2, 2004, pp.515-523.

[3] Mansinha L., Stockwell R. G. and Lowe R.P., 1997, 'Pattern analysiswith two dimensional spectral localization: Application oftwo dimen-sional S-transforms', Physica A, 239, pp.286-295.

[4] Pinnegar C.R and Mansinha Lalu., 'The S-transform with windows ofarbitrary and varying window, Geophysics, vol-68, pp.381-385, 2003.

[5] Stockwell R.G.,Mansinha L. and Lowe R.P., 'Localization of com-plex Spectrum: The S-transform', Jour. Assoc. Expl. Geophysics,July-1996, vol-XVII, No-3, pp. 99-114.

[61 Dash P.K., Panigrahi B.K. and Panda G., 'Power quality analysis us-ing S-transform', IEEE Power Delivery, vol. 18, pp.406-411,2003.

[7] R.Pinnegar, L.Mansinha, "time local fourier analysis with a scalable,phase modulated analyzing function: the s-transform with a complexwindow", Signal Processing, Elsevier Science, vol.84, pp.1 167-1176,2004.

50 100 150 200

Fig. 12. S-contours for a-ph (abc-g) fault at 90% of linewith Rrl 50 ohm.

166

Ir 3Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA. Downloaded on February 26, 2009 at 06:14 from IEEE Xplore. Restrictions apply.