Ferrero1995.pdf

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IEEE Transactions o n Power Delivery, Vol. 10, No. 1, January 1995

A FUZZY-SET APPROACH TO FAULT-TYPE IDENTIFICATION IN DIGITAL RELAYING

Alessandro Ferrero, Member, IEEE

Silvia Sangiovanni

Ennio Zappitelli

Dipartimento 1 Ingegneria Elettrica University of Rome - "La Sapienza" Via Eudossiana 18 00184 Rome - ITALY

Dipartimento di Elettrotecnica Politecnico di Milano Piazza L. da Vinci 32 20133 Milano - ITALY Absrracr - Sometime the operations that a relay is required to perform cannot be easily described in a deterministic way. A significant example of this situation is given by the operations a line relay must perform in order to detect the type of fault (line-to-ground, line-to-line, line-to-line involving ground). Recently, the mathematical theory of fuzzy sets featured many practical applications, mainly in industrial controls, and fuzzy-set processors are available to allow real time applications. This paper shows that a fuzzy-set approach can be useful even in digital relaying, whenever "fuzzy" decisions have to be undertaken. A possible application to the detection of the type of fault when symmetrical component relaying techniques are adopted is proposed and the results of simulation tests are given.

I. INTRODUCTION Almost all theories developed in the field of digital relaying assume that correct relay operations can be determined by means of deterministic computations on a well defined model of the system to be protected. Of course, the theoretical validity of this approach cannot be reasonably questioned. On the other hand, it is sometimes difficult to put it into practice, because of the complexity of the system model, the scarce knowledge of its parameters, the great number of information to be processed etc.. A typical example of this situation is the way line relays proceed to the determination of the nature of the fault (lineto-ground, line-to-line involving ground, line-to-line without involving ground), when only the fault currents are processed.

This paper was presented at the 1994 IEEE PES Transmission and Distribution Conference and Exposition held in Chicago, Illinois, April 10-15, 1994.

All situations that are not characterized by a simple and well defined deterministic mathematical model, can be more easily handled in a rather heuristic way approaching the problem in terms of the fuzzy-set theory. This mathematical theory is known since 1965, when it was first introduced by Zadeh [l] in order to simpllfy the approach to problems that are impossible (or at least very difficult) to describe in terms of deterministic variables, but could be more easily described in terms of fuzzy variables. This approach leads to the representation of these problems in terms of a set of simple rules and a number of simple membership functions. It presently finds its most attractive applications in the field of automatic controls, thanks to the recent availability of dedicated integrated circuits able to attain real-time implementation of the computations required to derive the correct result from the given rules and membership functions. This paper proposes an application of t h ~ stechnique to process the fault current symmetrical components in order to determine the nature of the fault. The advantages of this approach over more traditional techniques will be shown by computer simulation of the relay performances. 11. SYMMETRICAL COMPONENT RELAYING

A . Determination of the symmetrical components of the fault current. It was proved [2], [3], [4] that the presence of large negative and zero sequence components in the line current reveals the occurrence of a fault in the line itself and gives some information about the nature of the fault. The realization of digital protective relays based on the determination of the symmetrical components of the fault current appears attractive, since, under sinusoidal conditions, the determination of these components is quite immediate and can be attained by means of a simple linear combination of the sampled values of the line currents [2], [31.

0885-8977/95/$04.00 0 1994 IEEE

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Unfortunately, in case of fault, the line currents are no longer sinusoidal, because of the likely presence of harmonic components and an exponential decaying component. The accuracy in the determination of the symmetrical components of the fault current can hence decrease significantly. In particular, the presence of the exponential decaying component represents a critical factor, since, if not removed or attenuated, it may prevent the use of Fourier filter techniques in extracting the symmetrical components at fundamental frequency. Different techniques are used to attenuate the exponential decaying component (replica impedance, high-pass filter, ...). An effective method to remove this component was proposed by the Authors [ 5 ] . It was proved (see the Appendix for more details) that if the fault current is given by: if (t) = &-If .sin(wt +a)+ A e e - x and the following four samples are taken: where T is the fundamental period, the following quantities can be evaluated:

[

A , = A.e -

t i

.(1 + 3 ) ] / 2

and:

It was proved [5] that the time constant of the exponential decaying component is given by:

result as the more general Park transformation (or dqO transformation) when the reference dqO axis are stationary [61.

Having defined the complex quantity i = id + i,, it can be proved [ 5 ] , [6] that the fundamental frequency symmetrical components of the fault currents (those usually obtained, under sinusoidal conditions, by applying the well known Fortescue transformation) can be determined starting from the Fourier series components I k of the complex quantity i and the Fourier series components 10, of the scalar quantity io. In particular it is:

il,

Ir,/Js

and iio = I o l / & = I,/&> il” = where Il,, Iln, 110 are the phasors of the positive, negative and zero sequence currents. The proposed method was proved [5] to evaluate the symmetrical current components correctly even in presence of harmonic distortion and exponential decaying components. The time frame required to get the symmetrical current components is hence that required to perform a FFT algorithm on the complex quantity i and on the scalar quantity io. This time frame is as long as one fundamental period, if a full-cycle Fourier algorithm is applied, or less, if shorter window Fourier algorithms are applied [7]. The computation burden required to execute these algorithms depends on the number of samples taken and can be estimated to take less than a few hundreds of microseconds if modern DSPs are employed with a number of samples up to 128.

X

B. Determination ofthe nature of the fault. where x = 5 - t,, and its amplitude is given by:

It was also proved [5] that (1) and (2) keeps their validity even if the fault currents are distorted. The quantities defined in (1) and (2) can be used to remove the exponential decaying component from the acquired samples of the fault currents. Then, after having removed the exponential decaying component, the current symmetrical components can be evaluated from the line currents employing the following linear transformation:

T h s transformation is generally known as the Clarke transformation (or apO transformation) and gives the same

The analysis of the fault current symmetrical components gives information about the nature of the fault. Indeed, the presence of only the negative sequence component in the fault current indicates that a line-to-line fault not involving ground has occurred. The presence of a negative and zero sequence component indicates that a fault involving ground has occurred. In this case it is still possible to distinguish between lineto-ground and line-to-line involving ground faults taking into account the amplitude of the symmetrical components. Some computer simulations have been accomplished, using the EMTP program, in order to analyse different fault conditions on some typical Italian HV transmission lines, whose characteristics are shown in Table 1. The effects of CT saturation have not been taken into account in this simulation, since there are no theoretical reasons for supposing the proposed method more sensitive to these effects than other digital methods. Fig. 1 shows the ratio between the negative sequence component and the positive sequence one versus the distance of fault from the relay insertion point for line-toground and line-to-line involving ground faults in the line 3

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of Table 1. Similarly, Fig. 2 shows the ratio between the zero sequence component and the positive sequence one for the same conditions as those of Fig. 1l . Table 1 Impedances, voltages and currents typical for three-phase faults on 380 kV lines with rated current I=1600 A and with line time constant equal to 30 111s. Data in the table are obtained under the following hypothesis: maximum line length: 400 km minimumlinelength: 2km lineimpedance: 0.27 R h maximum source impedance: 150 R minimum source impedance: 4.4 R, corresponding to a maximum fault current I=5 k A (Data obtained under courtesy of ENEL - Italy).

-

-

Line ZJZ,

Short Line Line Short ZStime circuit length imped- circuit constant [ms] voltage [km] ance current ~~

[a]

[kVl *

1 2 3

0.1

I 1

4 5

6 7 8 9

10

0.1 0.1

1 1 1 10 10 100 100

200 200 200 110

I I

163 250

I

400

I

44

PA1 4.55

67.5 108

2.96 1.85

I

100 200 100

1

I 16.3 I

4.4

1 25.0 I

100

110

55

7.41

110 22

150

14.85 40.5

200 500

0.54

37.0

100

15

1.33

0.54

4.03 1.45

500 200 500

2 55.5 2 5.5

22

2.2 2.2

2.72

1.5

0

Indeed a line-to-ground fault at the end of the line is characterized by the same values of current symmetrical components as that of a line-to-line fault involving ground occurred at a distance about 60% to 80% of the total line length. The analysis of the ratio between the positive sequence current and the line rated current, as shown in Fig. 3, gives some further information, but does not still remove all ambiguities.

-

line-toline with ground line-toground

0.6

2

. I

6

Fi

\

4

4

\ I

C

2

0.4

.-

0

0.2

1

0 7

0

line-toline with ground line-toground

8

1 -

.

: 0.2

.

: 0.4

.

: 0.6

.

: 0.8

.

1

0.8

Fig. 2. Ratio between the zero sequence component and the positive sequence one in case of fault in the line 3, versus the distance of fault.

10

0

0.6

0.4

Fault distance [P.u.]

* at relay point.

U

0.2

I

1

Fault distance [P.u.] Fig. 1 . Ratio between the negative sequence component and the positive sequence one in case of fault in the line 3, versus the distance of fault.

The plots of Figs. 1 and 2 show that a procedure for the identification of the nature of the fault based only on the analysis of the above quantities may lead to incorrect results. The fault resistance was considered always nil. Fault simulations with nonzero fault resistance have been performed, showing no significant changes in the reported ratios between the symmetrical components of the fault current.

.

: 0.2

.

: 0.4

.

:

.

0.6

: 0.8

.

I

1

Fault distance [P.u.] Fig. 3. Ratio between the positive sequence component and the line rated current in case of fault in the line 3, versus the distance of fault.

The implementation of a deterministic algorithm able to derive the correct information about the nature of the fault from the elaboration of the above plots is difficult, probably cumbersome and is likely to result in a complex, heavy burden and time-consuming procedure. On the contrary, this situation represents a typical field of application for the new fuzzy-set techniques as shown in the next section.

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111. FUZZY-SET APPROACH A . Fundamentals

The basic difference between the deterministic and fuzzy approaches lays in the different ways the variables are handled. Let's consider, for example, a variable v, in the range *5. According to the assumed numerical values, it can be considered as belonging to the sets GN (great negative), SN (small negative), Z (zero), SP (small positive), GP (great positive). If the usual deterministic approach is employed, these five sets are separate and hence v can belong to only one of them at a time. In the fuzzy-set approach, v can belong to more than one set, according to a given membership function px(v) (where x stands for GN, SN, Z, SP, GP) whose values range usually in the field 0-1. This function determines the membership grade that the fuzzy variable v assumes in the corresponding fuzzy set x. In the example of Fig. 4, the variable ~ 3 . belongs 5 to SP with a membership grade psp(v)=0.33 and to GP with a membership grade pGp(v)=0.5. Of course it belongs to all other sets with a membership grade zero.

-J

GP

SN

GN

-4

-3

-2

-I

0

I

2

3

4

5 v

The fuzzy processor block represents the heart of the whole fuzzy-logic process. It evaluates the overall truth grade of a set of rules that describe the system in a "fuzzy" way [SI. These rules sound like: IF (a' = GP AND p'=SN) THEN (y' = SP) IF (a'= GP AND p'=Z) THEN (y' = GP) and a credibility factor in the range 0-1 can be associated with them. According to the fuzzy values of the input variables a' and p', to the given rules and to their credibility factors, the fuzzy output variable y' is obtained and converted into a numerical variable y by the "defuzzyfication" block F/N. B. Identijcation of the nature of the fault.

The fuzzy-set approach briefly described in the previous section can be employed for the identification of the nature of the fault, and in particular in ascertaining whether the fault is a line-to-ground fault or a line-to-line fault involving ground. The plots in Figs. 1 and 2 suggest that the actual value of the negative and zero sequence components of the fault current can be employed for this purpose. Fig. 3 shows that also the actual value of the positive sequence component can be useful. The following fuzzy variables have been considered: negative sequence over positive sequence WP), zero sequence over positive sequence ( Z P ) and positive sequence over the rated current (P/C). For these variables, the following fuzzy sets have been defined: Z (zero), S (small), M (medium), L (large). According to the plots in Figs 1, 2 and 3, the membership functions shown in Figs. 6, 7 and 8 have been defined for the N P , Z P and P/C variables respectively, in case of faults in the line 3 of Table 1.

Fig. 4. Example of h z z y sets and membership hnctions 1

The procedure followed in a fuzzy-set approach is described by the block diagram in Fig. 5 . The numerical variables a and p are converted into the fuzzy variables a' and p' by the N/F blocks, following the procedure shown in Fig. 4. The N/F blocks give also the membership grades px(a' ) and P,(P' 1.

.

0

0

0.5

1

N/P

ROCESSOR

Fig. 5 . Block diagram of a hzy-set procedure

Fig. 6. Membership hnction for the N/P variable

It is worth while to note that the definition of the membership functions is an arbitrary procedure, based on the knowledge of the phenomena to be controlled. In this case, the membership functions have been assigned with the aim to define, for each fuzzy variable, ranges of values typical

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for the considered fault types, in accordance with the plots of Figs. 1 trough 32.

\

1

I

I

0.00

0.56

0.11

IL

LL

Fig. 9. Example ofthe fuzzy procedure output in case of line-toground fault at 65% length of line 3 in Table 1.

L

0

2 C

!

.

.

.

,

0.5

,

,

.

In this case a line-to-ground fault was simulated at the 65% length of the line 3 in Table 1. The procedure result indicates a credibility factor of 0.56 that the fault is a line-toground fault, a credibility factor of 0.11 that the fault is a line-to-line fault involving ground and a credibility factor zero that the fault is a line-to-line fault not involving ground, thus recognizing the nature of the fault correctly. Different fault conditions in all lines reported in Table 1. have been simulated and the procedure recognized the nature of the fault always correctly, having determined the membership functions for the input variables according to the line characteristics. Table 2 and Table 3 report the fuzzy procedure output in case of line-to-ground and line-to-line fault involving ground on line 3, for different fault distances.

,

Fig. 7.Membership hnction for the ZE' variable

0

5

10

p /c

Fig. 8. Membership function for the P/C variable

The output variable F, that indicates the nature of the fault (F=LL: line-to-line fault without involving ground, F=LG: line-to-ground fault, F=LLG: line-to-line fault involving ground) is obtained applying the following simple 8 rules3 (CF: credibility factor), which have been derived as well from the analysis of the plots in Figs. 1 , 2 and 3. 1. IF (N/P=L AND Z/P=Z) THEN (F=LL), CF=l 2. IF (N/P=S AND Z/P=S AND P/C=M) THEN F=LLG; CF=l 3. IF (N/P=L AND Z/P=L AND P/C=M) THEN F=LG, CF=1 4. IF (N/P=M AND Z/P=M AND P/C=S) THEN F=LG, CF=1 5 . IF (N/P=M AND Z/P=M AND P/C=L) THEN F=LLG; CF=1 6. IF (N/P=L AND z/p=L AND P/C=L) THEN F=LLG; CF=l 7. IF (N/P=M AND Zm=M AND P/C=M) THEN F=LLG; CF=0.9 8. IF (N/P=S AND Z/P=S AND P/C=S) THEN F=LG; CF=0.25 After the defuzzyfcation procedure, the variable F is given along with its credibility factor as in the example reported in Fig. 9.

Though the hzzy sets are usually overlapping, the defined Z and S sets are not overlapping, since, in none of the considered fault conditions, the defined fuzzy variables can assume values in the range that is not covered by the membership functions. It is worth while to note that only 8 rules out of the 64 possible different combinationsare sufficient to detect all possible fault types. Indeed, according to the plots in Figs. 1 through 3, none ofthe possible fault conditions can result in a combination of the input fuzzy variables other than the 8 listed above.

Line-to-ground Fault distance % of the line length fault CF

Line-to-line fault CF (ground involved)

5 10 20 30

1 1 1

0 0 0 0

45

0.72

0

0.11

80 90 100

0.56 0.64 0.70 0.62 0.17

1

0.03 0 0 0

The data reported in these tables show that the identifcation of the nature of the fault is always assured. The identification reliability is also good: only two situations occur (60% of the line in Table 2 and 100% of the line in Table 3) where the final decision on the fault type may be not reliable enough. In case the difference between the two credibility factors falls below a predefined "safety" value

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volved), which is the most difficult situation to handle with the usual deterministic approach.

V. APPENDIX

I

Fault distance Line-to-ground % of the line length fault CF

-

10

I

20 30

1

I I

0.01 0 0

Line-to-line fault CF (ground I involved) I

I

0.42 0.66

I

0.80

II

In order to identlfy the exponential decaying component, the fault current is supposed to be sinusoidal, with a superimposed exponential component: (Al) i f ( t ) = f i . I f -sin(ot +a)+ A .e-x Two samples ikt,) and i&tl+T/2), T=2n/o, are taken. It can be readily checked that the average value of the exponential component over the interval (t,+T/2, t,) is given by: A, = [iAt,+T/2) + i&tl)]/2 (A21 From (Al), it follows:

and hence:

Similarly, if two other samples ikb) and i&+T/2) are taken, the average value of the exponential component over the interval (b+T/2), b is given by:

Of course a further improvement of the method can be obtained by means of a proper tuning of the membership functions, according to the actual line characteristics. Different tuning methods can be applied for the minimization of the output error [9] and hence for the maximization of The ratio: the fault type selectivity. e As far as the time required to perform the fuzzyfkationA1 -defuzzyfcation procedure is concerned, it is closely related A2 e-tg to the digital processor employed. At present time, dedicated processors are available that allow real-time execution leads to the determination of the time constant z as: of this procedure. The computation time required to identify X z=the fault type can be estimated in about 500ps

-‘t

I

IV. CONCLUSION An application of the fuzzy-set logic was proposed to the

identification of the nature of the fault on a transmission line. The approach in terms of fuzzy-set procedures was proved to be effective in implementing a simple fuzzy procedure (8 rules) to solve a problem that requires more complex algorithms when approached in a deterministic way. The computer simulations performed on different fault situations on typical Italian H V transmission lines give full evidence that the proposed method accomplishes a reliable identification of the nature of the fault. In particular, the proposed method is quite effective in assessing whether a fault involving ground is a simple lineto-ground fault or is a line-to-line fault (with ground in-

\

where x = % - t, can be as short as one sampling period. From (A3) and (A5), the amplitude of the exponential decaying components is given by:

Eqs. (A5) and (A6) allows to evaluate the amplitude and the time constant of the exponential decaying component of the fault current. Having determined these two values, each sample of the fault current can be modified by subtracting the corresponding value of the exponential component, so that this component can be completely removed. Though the evaluation of (A5) and (A6) represents a heavy computation burden, high execution speed can be

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nevertheless attained in their determination if look-up tables are employed. Eqs. (A5) and (A6) have been evaluated under sinusoidal conditions. They come basically from considering that the values assumed by the sinusoidal component of (Al) are opposite at every T/2. This assumption is verified also under nonsinusoidal conditions, provided that only odd harmonic components are present in the fault current. If this is not true, the algorithms does not remove the exponential component completely, but simply attenuates it. However, since the even harmonic components are generally negligible in the fault current of HV transmission lines, (A5) and (A6) can be still considered valid also under nonsinusoidal conditions.

Alessandro Ferrero (M88) was bom in MIlano, Italy, on December 9, 1954. He received the M.S. degree in Electrical Engineering from the "Politecnico di Milano" University, Milano, in 1978. In 1983 he joined the Dipartimento di Elettrotecnica of the Politecnico di Milano as a Researcher on Electrical Measurement. From 1987 to 1991 he was Associate Professor of "Measurement on Electrical Machines and Plants" at the University of Catania, Catania, Italy. Since 1991 he is Associate Professor of Electrical Measurements at the Dipartimento di Elettrotecnica of the "Politecnico di Milano" University, Milano, Italy. His current research interests are concemed with the application of digital methods to Electrical Measurements. He is a member of the Italian Informal C.N.R. Group on Electrical and Electronic Measurements and he is Member of the North Italy Chapter of the IEEE IM Society.

VI. REFERENCES

Zadeh L. A., "Fuzzy sets", Informat. Control, no. 8, 1965, pp. 338-353. A. G. Phadke, T. Hlibka, M.,Ibrahim, "Fundamental basis for distance relaying with symmetrical components", IEEE Trans. Pow. App. Syst., vol. PAS-96, pp.635-646, MarcWApril 1977. A. G. Phadke, T. Hlibka, M. Ibrahim, "A microcomputer based symmetrical components distance relay", Proc. of PICA, May 1979, Cleveland, USA. Protective relays. - Application guide, GEC Measurements, England, 1987. A. Ferrero, S. Sangiovanni, E. Zappitelli, "A new algorithm for digital relaying with symmetrical components", Proc. IMEKO TC-4 International Symposium on Intelligent Instrumentation for Remote and On-Site Measurements, Brussels, 12-13 May 1993, pp. 341-345. A. Ferrero, G. Superti-Furga, "A new approach to the definition of power components in three-phase systems under nonsinusoidal conditions", IEEE Trans. Instr. Meas., Vol. IM-40, 1991, pp. 568-577. E. A. Udren, "Foundations of relaying algorithms", IEEE Tutorial Course "Microprocessor relays and protection systems", 1988, pp. 17-30. T. Takagi, M. Sugeno, "Fuzzy identification of systems and its applications to modelling and control", IEEE Trans. Sys, Man, Cyber., Vol. SMC-15, 1985, pp. 116132. A. Boscolo, F. Drius, "Computed aided tuning tool for fuzzy controllers", Sec. IEEE Fuzzy Con$, San Francisco, CA, March 1993.

Silvia Sangiovanni was born in Rome, Italy. She received the M.S. degree in Electronic Engineering from the University of Rome in 1990. She is now working towards her Ph.D. in Electrical Engineering at the Department of Electrical Engineering of the University of Rome. Her current research interest are in the field of Digital Signal Processing applied to the Electrical Measurements. She is a member of the Italian Informal C.N.R. Group on Electrical and Electronic Measurements.

Ennio Zappitelli was bom in Pisa, Italy, on September 12, 1928. In 1955 he received the MS degree in Electrical hngineering from the University of Pisa, Pisa, Italy. In 1960 he joined the University of Rome as an assistant professor of Electrical Measurements From 1980 to to 1987 he was full professor of Electrical Measurements at the University of Pisa. Since 1987 he IS full professor of Electronic Instrumentation at the Department of Electrical Engineering of the University of Rome "la Sapienza". His research interests are concerned with the application of digital methods to the Electrical Measurements and to Electronic Instruments-tion. In this field, he is presently concemed with the applications of digital techniques to protective relays. He is a member of the Italian Informal C.N.R. Group on Electrical and Electronic Measurements and he is Member of the North Italy Chapter of the IEEE IM Society.