High-impedance f reasoning system

ntification using a fuzzy

F.G. Jota P.R.S. Jota

" k i n g ferni.s: High-impedance fault, Fuzzy recisorzing system, Fciult identification

Abstract: A methodology is presented to detect high-impedance faults in radial distribution feeders by means of fuzzy logic reasoning. The proposed technique is based on the analysis of the feeder responses to impulse waves which are periodically injected at the feeder inlet. These responses are compared to standard responses which were previously stored in a database. Standard responses correspond to responses of the feeder operating in normal configurations. A supervisory system processes the information in the database and, using a fuzzy inference machine, indicates possible occurrences of abnormalities. The proposed system has been tested in a real feeder; the relevant results are presented.

1 Introduction

High-impedance faults (HIFs) frequently occur in dis- tribution feeders. Since, in general, the values of the fault current are smaller than those of the load current, conventional protection systems cannot be adjusted to operate for HIFs. As a consequence, broken cables, laid on the soil, can be left energised for long periods of time. This represents a serious hazard to the general public with risks of electric shock, fire etc.

There are two basic types of high-impedance faults: active faults and passive faults. An active fault is characterised by the presence of an electric arc at the end of the broken cable [l , 21. Most of the techniques proposed in the literature to detect active faults use harmonic and nonharmonic frequencies generated by the arc [3-71. A passive fault is characterised by the absence of an electric arc. This kind of fault is more dangerous, since the conductor does not give any visual indication of a hazard condition. Furthermore, passive faults are even more cumbersome to detect. Thus, very few solutions have been presented in the literature; most of them based on the analysis of phase unbalance 181. Unfortunately, some electric distribution

0 IEE, 1998 I€€ Proceedings online no. 19982358 Paper first received 5th June 1997 and in revised form 15th April 1998 F.G. Jota is with the Department of Electronic Engineering, Federal Uni- versity of Minas Gerais, AV. Antanio Carlos, 6627, 31270-901 Belo Hon- zonte, MG, Brazil P.R.S. Jota is with the Department of Electrical Engineering, Federal Center for Technological Education, CEFET-MG AV. Amazonas 7675, 30510400 Belo Horizonte, MG, Brazil

systems normally present a high level of current unbalance.

An alternative approach to this problem is presented in this paper. Experimental results have shown that the proposed technique can successfully detect passive faults [9, 101. A real feeder of a Brazilian Energy Com- pany (CEMIG) has been used for this purpose.

2

The Brazilian electric distribution system is character- ised by many mono-phase and dual-phase loads. There- fore, it presents a high level of current unbalance among the phases, reaching up to 30%. Fault detection techniques that rely on phase unbalance, of course, cannot be applied in such cases. Besides, in the last 15 years, the number of nonlinear loads has increased sig- nificantly, and so has the frequency harmonics in the feeders [l 13. This means that methodologies based on the analysis of frequency harmonics or phase unbal- ance do not work properly in this kind of feeder.

In this work, the above problems have been over- come by using an alternative approach. In the pro- posed technique, a supervisory system periodically monitors the feeder response to impulse waves [9, 121. Field tests [lo, 131 have shown that the basic spectrum of the response of the feeder, which has been used for the experimental runs, is in the range of 6kHz- 12.5MHz. The signal is then sampled in intervals of 40qs and stored during 200ps. Under these conditions, neither the phase unbalance nor the noisy loads affect the measurements since low frequencies are not seen in the selected window.

The supervisory system has a decision core based on fuzzy reasoning [14, 151. The input signals are stored in the form of linguistic variables, and the result is given through fuzzy implications. The impulse response sig- nals are first compared to those of known configura- tions. The system then searches for evidence of the occurrence of high-impedance faults, by considering the degree of discrepancy among the measured signals (set of five repetitive measurements) and the responses stored in the database.

The processing of the measured signals is accom- plished in four stages: pre-processing, frequency domain conversion, discrepancy estimation and super- vision. To build the database, impulse waves are first applied to feeder inlets for each configuration.

The proposed methodology relies entirely on a survey to determine all possible operating configurations of the feeder. To do that, the staff responsible for plan- ning, operation and maintenance are asked to provide

Set-up used for field tests

IEE Pioc -Gene1 Tian5m D i w i b , Vol 145. No 6. November 1998 656

the relevant information about the feeder operating configurations. Load switchings do not affect the response of the system since the transformer is nearly a short-circuit in the frequency range of the impulse response, and therefore they have not been taken into account. For each configuration considered, the char- acteristic response of the feeder is measured and stored in the database. To improve the signal-to-noise ratio (SNR), five repetitive measurements are made and a weighted average is used as the representative signal. The stored responses are then taken as reference by the supervisory system.

3 Preprocessing of measured signals

The impulse wave, which is injected at the feeder inlet, travels along the transmission line, bringing information about the actual status of the feeder at the time of the signal injection. After each new measurement is taken, the response signal is pre- conditioned, converted to the frequency domain and then compared to signals stored in the database. Sets of measurements with large dispersions are considered inconsistent and are therefore discarded. The real and imaginary components of the preprocessed signals are then calculated by means of the fast Fourier transform (FFT) algorithm [16]. Analyses of typical responses have shown that, for the purposes of this work, 20 frequencies were sufficient to satisfactorily characterise the measured signals.

Since the impulse responses were stored in 5000 sam- pling sets (corresponding to a total measuring time of 2 0 0 ~ at a sampling rate of 40qs), the measured response is decomposed in two windows: W,, W,. For each window, the real and imaginary components of the 20 frequencies have been calculated, thus making a total of 80 components (Rfl,wl, Imfl wl, Rfi,wz and

It has been observed that the discrepancies among the five responses had no standard behaviour. Never- theless, the vast majority of the deviations were very small (less than 2.50/0), a few could be classified as medium (between 2.5 and 5%) and very few exhibited high discrepancies (greater than 5%). Owing to the heu- ristic nature of the process used to classify these dis- crepancies, the deviations of each measurement to each reference are represented as fuzzy numbers. A fuzzy set has been defined for the fuzzy variable ‘deviation’: small, medium and large (their membership functions are shown in Fig. 1).

Imfi w2),=1,2, 20 per signal.

I small medium large

deviation,% Fig. 1 Input fuzzy set

The deviation between the sampled (measured response) and each reference (impulse response to a standard configuration) constitutes the actual input data of the supervisory system (6Rfj, wl, armfi, wl, 6Rf;, wz and armf;, m)i=,,2,,,20, for each reference.

IEE Proc. -Gener. Transm. Distrib., Vol. 145, No. 6. Noveniber 1998

4 Supervisory system

During the supervision stage, the deviations corre- sponding to each of the measured signals are presented to the supervisory system. The analysis of the feeder responses is carried out in three steps, as described below.

4.1 Step I: frequency analysis In this step are considered both real and imaginary parts of the frequency components of the signal stored in each window. First, the deviations of their values from the reference are fuzzified. The degrees of mem- bership (p) of each frequency component of the chosen fuzzy variables (small (pJ, medium (p ,J, large (pJ), for each set of measurements, are compared. For each fre- quency, every possible combination of the four fuzzy values (corresponding to the real and imaginary parts of each window) is analysed. The chosen rules check whether the relative deviations are within acceptable limits; if they are, the system indicates a great coher- ence in the data; otherwise it indicates some disagree- ment, which could mean faulty operation. In the current system, the number of different rules is 34 = 81, where 3 is the number of input fuzzy variables (small, medium and large) and 4 is the number of input com- ponents for each frequency (the four deviations 6R~f , wl, armf;, wl, 6Rfi, and SImf7, w). The choice of rules has been made in engineering terms using rules of thumb to describe the more likely event.

Table 1 shows the set of rules used here, emphasising the antecedents and the consequents considered in each one (marked with an ‘0’). The variables marked with an ‘x’ are not used in the composition of that rule. The MAX-MIN inference method [17] has been used to cal- culate the output variable, which is the coherence level of the signal. The membership functions of the fuzzy variable coherence are the same as used for the variable derivation (shown in Fig. 1).

As an example, consider the first rule in Table 1. It can be written as

if GRfi,wl is small and GRfi,wa is small and 61mf;,wl is small and

SImfi,wz is small then Cfi ,R1 is large

where Cfi,RI is the coherence of the frequency compo- nent i (thus the term frequency coherence) given by rule 1. Thus, the degree of membership of the variable Cfi,RI ( I = 1, 2, ..., 81) to the fuzzy variable large corre- sponds to the union of the input variable deviations (AND operation) or the minimum of the membership grades to the variable small. The result of rule 1, for example, is given by

P I ( C f z , R l ) = min [Ps(6Rfi,Wl), P s ( 6 R f i , W 2 ) :

Ps ( 6 I m f z,w1), Ps (6Im.k w2 11 (1)

If each input element belongs to only one variable, then only one rule is activated at one time because, in this case, only one combination of antecedents of that rule is not zero. If it belongs to two variables, then 16 (24) rules are activated. The output of other rules will be identically zero.

The procedure is the same for all frequencies (i = 1, 2, ..., 20) of each window (W, and W2), and it is

651

Table 1: Complete set of rules

output

61mfi,, coherence

s m I s m I

o x x o o o x o x o o o

x x o o o o

o x x o o o

x o x o o o x x o o o o

o x x o o o

x o x o o o

x x o o o o o x x o o o

x o x o o o

x x o o o o

o x x o o o

x o x o o o

x x o o o o o x x o o o

x o x o o o

x x o o o o

o x o o o o

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o @ Q O O o o o o o o o x o o o o o

x x o o o o o x x o o o

x o x o o o

x x o o o o o x x o o o

x o x o o o x x o o o o o x x o o o

x o x o o o

Rule

Input

6Rfj.d

- 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30 31

32

33

34

35

36

37

38

39 40

41

s m I

o x x o x x

o x x

o x x o x x

o x x

o x x o x x

o x x

o x x

o x x

o x x

o x x

o x x o x x

o x x

o x x

o x x o x x

o x x

o x x

o x x

o x x o x x

o x x

o x x

o x x

o o x x o x x o x x o x

x o x x o x

x o x x o x

x o x

x o x

x o x

x o x x o x

x o x

s m I s m I

o x x o x x

o x x o x x o x x o x x

o x x x o x

o x x x o x

o x x x o x

o x x x x o o x x x x o

o x x x x o

x o x o x x

x o x o x x

x o x o x x

x o x x o x x o x x o x

x o x x o x

x o x x x o

x o x x x o x o x x x o

x o o o x o

x o o o x o

x x o o x x

x x o x o x x x o x o x

x x o x o x

x x o x x o

x x o x x o

x x o x x o

o x x o x x o x x o x x

o x x o x x o x x x o x

o x x x o x

o x x x o x

o x x x x o

o x x x x o

o x x x x o x o x x o x

x o x x o x

x o x x o x x o x x x o

x o x x x o

Rule

- 42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71 72

73

74

75

76

77

78

79

80

81

x = do not care, s = small, m = medium, I = large

repeated for each sample 0' = 1, 2, ... 5 ) and for each reference k . Therefore, it is executed 200 k times (20 x

Cfz,R2 is small or

2 x 5 x k). The membership grade of the variable frequency

coherence, C,, is the intersection (OR operation) of the input variables or the maximum of the membership grades of the antecedents. Thus, for the fuzzy variable small

Cfa,R81 is small then C$a is small

or

P s ( ~ ; , ) = max [ & ( c f , , R i ) , P s ( C f z , ~ 2 ) , . . . , P s (c f 2 , R 8 1 ) ]

if C f 2 , R 1 is small or (2) IFF Prnr -Gmpr Trnnrm Drvfrih Vol 145 No 6 iVovember 1998 < C O

4.2 Step 2: averaging sample and reference coherences To determine the coherence to the reference k for a given sample j , cs , ,k , we decided to take the average of the frequency coherence (Fig. 2):

1 2o C S j , k = - c;i

20 (3) 2=1

The variable Cs,,+ is called sample coherence, since it incorporates the information of all frequency compo- nents for a particular measurement.

frequency coherence c;,to Cfio

average lil sample coherence for reference k

I average 1 r$mnce coherence

Fig.2 Averaging sample and reference coherence

From the sample coherences, a single coherence to each reference k can be calculated as the average of the variables sample coherence of all samples j . This varia- ble is then called reference coherence (Crk), as shown in Fig. 2.

k reference coherences Crl to Cr,

global coherence analysis

global coherence

Fig. 3 Reference analysis

4.3 Step 3: Reference analysis The values of the reference coherences Crk are finally analysed, considering the relative values of CYL (Fig. 3). This analysis follows the rule in Table 2, where the choice of the threshold value (5.5) is explained below.

Table 2: Final inference

Rule Comments

if Crk< 5.5, Vk, then there is a HIF in the feeder

else if max Cr, is unique

then the measured signal is classified as coherent (compatible with the standard configuration k) which has the maximum Cr, else the data are discarded and new measurements have to be taken

(i)

(ii)

(iii)

k

(iv)

4.4 Comments concerning Table 2 (i) The values of C r k are obtained from the variable c s j , k , whose maximum value is 6.5; this is achieved

when all &C>) = ,um(C>) = 0 and all PAC',> = 1, for all samples and all references (Le. CYfi = 6.5). Its mini- mum value is 1.5 &(efi) = 1 and pm(C>) = PAC',) = 0 for all k). If c r k is fuzzified, values greater than 5.5 correspond to a degree of membership (to the variable large) greater than 0.5. This simply means that the var- iable large predominates over the others. (ii) If the samples are not classified by any reference, then this means that the feeder is operating in an unknown configuration. The decision system classifies this condition as a HIF. (iii) When two standard configurations are very similar, their responses can sometimes be misinterpreted. If this case occurs, the rule assumes that the more likely con- figuration is the one that presents the highest coher- ence. (iv) This eliminates the situation where the decision sys- tem cannot recognise which configuration is opera- tional.

5 Experimental results

The proposed methodology has been tested in a real feeder of CEMlG (Minas Gerais State Energy Com- pany), located in Caratinga, Brazil. The feeder, used in all tests presented here, is composed of urban and rural parts. Therefore, the feeder cable length is different for each phase. To accomplish the tests, a phase of 120.9 km of conductors has been chosen; the farthest test point is distant 14.83km (of conductors) from the measuring point. The impulse wave, which has been used in all tests, has 1 ps of front time and 2 5 0 ~ of tail time.

approx. 8 km c

Fig.4 Sketch of thefeeder

A sketch of the feeder is presented in Fig. 4, in which all testing points (switches) are clearly marked. It has been considered that, in normal operating conditions, only one switch is open at a time. Therefore, the feeder has 12 operating configurations and 12 references were considered, i.e. it has been assumed that it could operate with any of these switches open (combinations of two or more open switches have not been considered).

To generate a large number of different conditions, 24 tests have been performed. They consisted of open- ing, one by one, the 11 switches (Fig. 4) and measuring the feeder response for each configuration. In addition,

IEE Proc.-Gener. Transm. Distrib., Vol. 145, No. 6, November 1998 659

Table 3: Sequence of tests performed in the real feeder

H,F Similar to Operated switch Test standard

2 3 4 5 6 7 8 9 10 11 12 lorn configuration

1

2 x

3 x X

4 X

5 X X

6 X

7 X X

8 X

9 X X

10 X

11 X X

12 X

13 X X

14 X

15 X X

16 X

17 X X

18 X

19 X X

20 X

21 X X

22 X

23 x x

24 X

s c 1

s c 2

s c 3

sc4

s c 5

SC6

s c 7

SC8

s c 9

SClO

sc11

sc12

after the opening of the switch, a cable has been con- nected to its active point to simulate a HIF close to the switch, and the impulse response was measured. Since the methodology relies on known configurations, pas- sive high-impedance faults close to operating switches are the most difficult to detect because of the similarity of their responses to that of a standard configuration. This is true whenever the point of reflection (the bro- ken cable or the open switch) is approximately the same distance from the substation. Note that an open- ing of a switch is like a HIF for all references other than the corresponding open switch.

These tests are tests 2 to 23 in Table 3. Two more tests have been performed; one with all switches closed, and one with a HIF in an arbitrary point of the feeder (not in a switch). These are, tests 1 and 24 in Table 3, respectively.

During the classification process, the intelligent sys- tem considers, one by one, the 12 references stored (SCi, i = 1, ... 12) in the database. Thus, for a given ref- erence, it is expected that only one of the performed tests would not be classified as a HIF.

Fig. 6 shows the classification of the supervisory sys- tem for references SC3 and SC,, respectively, (tests 2 and 14) i.e. the calculated value of the reference coher- ence (Fig. 2). The axes on the left-hand side of Fig. 6 correspond to the test number (1, 2 ... 24), and the axes on the right-hand side correspond to the membership grade of each fuzzy variable. In this stage, it is expected that only a test similar to the considered reference would be classified as a known configuration, i.e. test 4 as SC, and test 14 as SC, (Table 3).

From Fig. 5 , it can be seen that, using the standard configuration SC3 as a reference, only test 4 is classi- fied as known configuration (Crsc3 > 5.5), as expected. All other events are correctly classified as faults. Test 5 represents a high-impedance fault 10m after switch 3 (see its exact position in Fig. 4). Although its Crsc3 value is high (= 5.2 as shown in Fig. 5 ) , it is still less than the threshold 5.5, and it is then classified as a HIF and not as a normal configuration. As pointed out above, this is the most difficult event to be detected since the fault configuration has practically the same response as that of SC3. In this test, the supervisory system has successfully detected the fault, although in other similar cases it has failed (as in the next example).

Fig. 5 ence

Output offuzzy system using standard configuration SC, as refer-

660 IEE Proc.-Gmer. Transm. Distrib., Vol. 145, No. 6. November 1998

As seen from Fig. 6, tests 14 and 15 (Table 3) are classified as standard (similar to SC,) since Cr,, > 5.5 in both cases. In these cases, the HIF 10m from switch 8 (test 15) has not been distinguished from a normal configuration (switch operation). The similarity between the two responses is so great that there is very little difference in their spectrum representations and the supervisory system could not distinguish one from the other.

30

I I - - - - - - - I '

20 -

,' m test15 8 'test14

10-

I 0

1

Fig. 6 erence

Output ojjuzzy system using stunhrd configuration SC, CIS ueJL

Now, considering all the references together (global coherence value, Fig. 3), the supervisory system has correctly classified all operated switches (i.e. test 1 as SCI ... test 22 as SCI2). Considering HIFs at 10m from each switch (tests 3, 5, ... 23), 42% were correctly classi- fied as HIFs and 58% were classified as normal opera- tions.

Considering each reference separately (reference coherence, Fig. 2), as discussed above, it is expected that only one of the performed tests would not be clas- sified as a HIF. Presenting, for example, all 24 tests to reference SCI only, test 1 has then to be classified as a normal operation. Using this reasoning, the system has classified correctly 95.6% of the tests as HIFs (note that these HIFs are not actual faults; they actually cor- respond to open switches in other parts of the feeder).

6 Conclusions

A technique to detect HIFs has been presented. The proposed supervisory intelligent system has been shown to be capable of distinguishing the majority of normal operations from abnormal events. A fuzzy system has been developed to analyse the actual responses of the feeder and to compare them with the standard responses stored in a database.

The proposed methodology has presented satisfac- tory results when applied to a real feeder. The normal operations of switches (standard configurations) have been correctly classified. For HIFs located on different parts of the feeder (excluding those very close to switches), 95.6% were correctly classified as HIFs. As stated above, these are in fact 'simulated' HIFs, and therefore more conclusive HIF tests in different parts of the feeder should be conducted. This high percent- age has to be seen as encouraging and warrants further investigations.

When the HIFs occur close (up to 10m) to a switch, 42% were correctly classified as HIFs; the others were classified as normal. In other words, the system pre- sented a very good result for all tests, except when the

IEE Proc -Gener Trunsm Dtrtrth Val 145, No 6, Noveinher 1998

HIF had almost the same changing effect in configura- tion as a switch. Nevertheless, in cases of doubt, at least the localisation of the possible fault is known (since the system indicates correctly the corresponding switch near which the fault may have occurred). Since the tests presented here have been performed without AC voltage, all identified HIFs were of the passive type.

If, for any reason, the reflected wave of a faulty sys- tem becomes similar to that of a standard configura- tion, additional information has to be considered by the supervisory system. The determination of the dis- tance where the event took place, for example, is one of the response characteristics that can be considered, to improve decision reliability. This refinement is cur- rently under investigation. In addition, whenever possi- ble, the operation of the suspected switch can be checked, and consumers' complaints will be decisive in this process.

Another advantage of this methodology is that it can be easily upgraded. For each new configuration, it is only necessary to append its response to the standard database and add one more comparison in the final stage of the supervision rules (Table 2). The algorithm itself does not need to be changed. We also believe that the algorithm could be applied to different feeders; only the database and, possibly, the fuzzy sets (depend- ing on the analysis of the deviation) have to be changed.

Although a combination of two or more switches has not been considered here, it should be stressed that, in the event of the simultaneous operation of more than one switch, two different scenarios have to be consid- ered: (a) one of the switches turns the others non-operational (b) two or more switches disconnect different parts of the feeder. In case (a) , the proposed methodology works as if only one switch had been operated. In case (b), the overall response will not be similar to any standard configura- tion and the supervisory system will confuse it with a genuine HIF. The only way to decide whether it is a HIF or the operation of multiple switches is to deter- mine the distance of the events. If the closest event to the substation coincides with a switch, then the response can be considered with that switch open and the measured response can be analysed to determine the distance of the second event. This procedure is being considered as an improvement to the proposed methodology.

To be successful, this methodology requires that all operation configurations are first correctly considered. If, for example, any configuration is missing, the sys- tem will obviously consider it as a HIF.

7 Acknowledgment

The authors acknowledge the technical and financial support of the Minas Gerais State Energy Company (CEMIG); in particular, they would like to thank the engineers Lairton Vilela, Paulo S.A. Rocha, Fernando O.R.A. Mello and Mauricio A. Tolonelli for fruitful discussions and support during the development of this work.

66 I

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662 IEE Proc.-Gener. Tuansm. Distrib., Vol. 145, No. 6, November 1998