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342 IEEE Transactions on Power Systems, Vol. 12, No . 1, February 1997An Expert System for Fault Section Diagnosis of

using Fuzzy RelationsHyun-Joon Cho Jong-Keun ParkLG Electronics Research CenterSeoul 137-140, KOREA Department o f Electrical Engineering,Seoul National Universi

Seoul 15 1-742, KOAbstract - This paper proposes an expert system using fuzzy As earlier attempts, the rule-based expert systems were

relations to deal with uncertainties imposed on fault section proposed[ 1-31. Recently, the k now ledge representation anddiagnosis of power systems. We build saginal diagrams which inference procedures using the cause-effect network werefault sections using the sagittal diagrams. Next, we exam ine the fault[4-51. Neural networks were also employemalfunction or wrong alarm of relays and circuit breakersbased on the alarm information and the estimated fault section. diagnosis Of large pThe proposed system provides the fault section candidates in Diagnosis is th e procesterms of the degree of membership and the malfunction or diagnosis system uses the of relays and circuitwrong alarm. An operator monitors these candidates and is able breakers. Uncertainties sto diagnose the fault section, coping with uncertainties. information which makes the diagnosis unreliable haveExperimental studies for real power systems reveal usefulness of several sources. They in e protective relay failures,

inaccurate occurrence time, etc.[6]. Most of conventionaldiagnosis systems which are built on the basis of binary logiccannot effectively deal with these uncertaintdeal with these uncertainties, but theythem are just weighted summations. Ththe estimated fault sectionwere proposed in order to take into account theseuncertainties. However, this approach did not explicitlyestimate the probability of a fault at a section.

In this paper, we propose an expert system executingfault section diagnosis of powerrepresent the fuzzy relations for power systems, and diagnosewe examine the malfunction or wrong alarm ofcircuit breakers using the given

represent the for power systems, and diagnose presented for diagnosing multiple faults as well as single

the Proposed technique to diagnose faults that have uncertainty. breaker failures, local acqu n errors, transmission errors,I. INTRODUCTIONto now when a occurs in power systems, an expert inaccurate fault locations. Neural networkson power systems has estimated and restored the fault section

breakers. As automation progresses in various fields and thefault section diagnosis and restoration is also required inpower systems operation. For instance, when a fault occurs,the automatic diagnosis system suggests the possible ways toremove fault and assists an operator to protect the systemswith the best way in that situation.

Fault section diagnosis is to identify fault sections inand circuit breakers. Designing an automatic fault diagnosisSince these kinds of knowledge are experimental anduncertain, analytical modeling of fault section diagnosis isdifficult. This motivates researchers to use Artificial include uncertainties.Intelligence ap proaches, which h ave yielded desirable results.

with information On the 'peration Of and circuit diagnosis procedures logically becuase thneed for Of power increases, the automation Of possible to estimate the mal

stems to deal wipower systems by information On Operation Of First, we build sagi &agramS[ 01 whichsystem requires the domain Of experts* fault sections using the operations in fuzzy relation

whiIn the proposed system, w e present not only the faultsection candidates but also the section's possibility of being afault as the form of degree of membership. Therefore an96 W M 295-6 PWRS A paper recommended and approved by the IEEEpower System Engineering Committee of the IEEE Power Engineering operator of power systems can diagnose fault section taking

Society for presentation at the 1996 IEEEIPES Winter Meeting, January21- into account uncertainties. We implement the proposed25 , 1996, Baltimore, MD. Manuscript submitted July 31 , 1995; made system for real 345KVavailable for printing January 2, 1996, prove the usefulnesuncertainty.

1. Motivation of Fuzzy Set Theory

0885-8950/97/$10.00 0 996 IEEE

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These are the general reasons why we use fuzzy set theory1. The interfaces of the expert system on the exp ert sideas well as on the user side are with human beings.Therefore communication in a "natural" way seems tobe the most appropriate; and "natural" means,generally, in the language of the expert or user. Thissugg ests the use o f linguistic variables.2. The knowledge base of an expert system is arepository of human knowledge. Since much ofhuman knowledge is imprecise in nature, it is usualthat the knowledge base of an expert system is acollection of rules and facts that are neither totallycertain, nor totally consistent. The storage of thisvague and uncertain portion of the knowledge byusing fuzzy sets seems much more appropriate thanthe use of crisp concepts and sym bolism.3. As mentioned above, the "management ofuncertainty" plays a particularly important role.Uncertainty of information in the knowledge baseinduces uncertainty into the conclusion. Th erefore the

inference engine has to be equipped withcom putatio nal capabilities to analyze the transmissionof uncertainty fi-om the premises to the conclusionsand associate the conclusion with some measure ofuncertainty that is understandable and properlyinterpretable by the user.

in expert systems:

For fault diagnosis in power systems, there are manysources of uncertainties mentioned in the prev ious section. Itis required to deal with these uncertainties effectively. Priorto the entry of fuzzy set theory into our ma them atics, theonly well-de velop ed mathematical apparatus for dealing withuncertainty was probability theory. Especially for diagnosis,Bayesian networks based on probability theory are veryuseful. But the ideas and techn iques have not sp read muchbecause the ideas and techniques are not that easy tounderstand[111. Moreover they are somewhat inappropriatefor power systems as mentioned in [ 9 ] . For example, thecomputational effort grows rapidly with the size of the net,and special handlings are needed to treat multiple connectednets such as power systems. Furthermore, they focus onfinding the best belief marking and can be extended to asecond best explanation only. This is not proper for theproblem such as multiple faults. However, the proposedsystem using fuzzy relations works well for the large-scaledpower systems and it is not difficult to construct the sagittaldiagrams for complex power systems. And it is easy tounderstand.

2. Protection System of Power SystemsThere are various ways to operate relays according tosystems. In general, protection systems are composed of

343

L3DbL3Ds

Subscripts of relays:n : main protectionb : backup protection ( zone 1)s : hackup protection (zone 2)

Fig 1. Sample model for power systems.

main protection relays(MPRs) and some backup protectionrelays (BPRs). In this research, we choose the system as inFig. 1.The procedure of protection when a fault occurs is asfollows. If a fault occurs in Line 1, MPR LlAm and LlCmtrip CB1 and CB2, respectively. If there are some problemsto trip the circuit breakers and the fault section is not isolated,BPRs operate. If CB1 is not tripped, zone 1 BPR LlA b tripsCB 1. If CB2 is not tripped , BPR L 1Cb trips CB2. If the faultline is not isolated after these actions, on B us A, zon e 2 BPR- it is not shown in Fig 1- trips connected circuit breaker,and on Bus C, BPR L2Bs of Line 2 and L3Ds of Line 3 tripCB3 and CB6, respectively.These protection systems are composed based on thepossibility that not all devices operate correctly. MPR andzone 1 BPR must protect 100% of the section in which therelays are installed. If the relays are set to do that, they mayobse rve the fault in the adjacen t section and isolate thesection at which a fault doe s not occur. For this reason, theserelays are set to protect abo ut 85% of the section. In the caseof zone 2 BPR which o bserv es the fault in the adjacentsection, since the length of its own section and that of theadjacent section is not equal, it is set to protect 120% - 150%of its own section accord ing to the length of both sections.Therefore, if the length of the adjacent section is very long incomparison with the length of its own section, it is moredifficult to observe the fault in the adjacent section. Theprotection ranges of relays are shown in Fig. 2.Basically, since protection of power system contains

85%zone1120 -150% ~zone2

Fig 2. Protection range of relays.

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344uncertainties as mentioned above, it is difficult to diagnosethe fault section with the inference engine on the basis ofbinary logic. This is the reason that we use fuzzy relations.

111. FUZZY RELATIONS & SAGITTAL DIAGRAMSFOR POWER SYSTEMSA crisp relation represents the presence or absence ofassociation, interaction, or interconnectedness betweenelements of two or more sets. This concept can begeneralized to allow for various degrees or strengths ofrelation or interaction between elements. Degrees ofassociation can be represented by membership grades in afuzzy relation in the same way as degrees of set membershipare represented in a fuzzy set[lO].Any relation between two sets X an d Y is known as abinary relation, and is usually denoted by R(X r ) . A binaryfuzzy relation can be represented easily by a sagittaldiagram. Each of the seis X, Y is represented by a set ofnodes in the diagram. Elements of X x Y with nonzeromemb ership grades in R(X; r ) are represented in the diagramby lines connecting the respective nodes. These lines arelabeled with the degree of membership.For power systems, we propose sagittal diagrams that havethree sets o f nodes; [set 1 - sections, set 2- relays, set 3 -circuit breakers]. For the sample model in Fig. 1, weconstruct sagittal diagrams as Fig. 3. We build thesediagrams considering the causal operations of relays andcircuit breakers in the occurrence of fault, and the causality isdenoted by arrows. The label on the line is determinedstatistically considering the un certainties of operation an d thepriorities of relays and circuit breakers when fault occurs. Asa MPR is most closely related to a section, the label of thisline is 0.8, and the label of the line that connects a zone 1

n08@E3

BPR to a section is 0.7. As a zone 2 BPR controls the circuitbreaker of the next section, decreasing the value some more,the label of the line that a zone 2 BPR tion is0.55. In the same way, 1s o f the lines that connectcircuit breakers to relaysconsidering the characteristic o tion of relays and

exposed outside. Holine is well protected against disturbances. Therefore we setthe labels between relay and circuit ers larger than thelabels between sections and relays. case of a bus, thedegree of memb ership is adjusted ac g to the number oflines connected to a bus. As the number of lines connected toa bus increases, so does the uncertainty of the bus. Thus, thelabels of the bus that have many lines are smaller than thelabel of the bus that have a fewwe build sagittal diagrams for pIf a circuit breakerzone 2 BPR must notsection. An inhibit0 e "O---"s introduced torepresent this rule. W e will describe it in the next section.

d by a MPR or a zso as not to isolate

IV. DIAGNOSIS PROCEDURE1. Fuzzy Union & IntersectionThe union of two fuzzy sets A and B is specified in generalby a function of the form

Fig 3 Sagittal diagrams for th e sample model.

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345For each element x in the universal set, this function takesas its argument the pair consisting of the element'smembership grades in set A and in set B and yields themembership grade of the element in the set constituting theunion of A and B . Thus,

Several classes of functions have been proposed whoseindividual members satisfy all the axiom atic requirements forthe fuzzy union[lO]. One of these classes of fuzzy unions isknown as the Yager class and is defined by the function

where values of the parameter w lie within the open interval(0 , * >.The discussion of fuzzy intersection closely parallels thatof fuzzy union. The fuzzy intersection of the Yager class isdefined by the function

i,(a,b) = 1- min[l, ((1 - a ) , + (1 - b ) w ) l 'w ] (4)where values of the parameter w also lie within the openinterval ( 0 , ~ .The operation s ust as these are also used in fuzzy relation.Considering the characteristic of the sagittal diagram andfault section diagnosis of power systems, we choose w = 3. inthis research.

2. DiagnosisThe decision making process of the section's being in the

Fault set is as followe d:The intersection of the labels of the lines that makea path to be through set 1, set 2, and set 3, providedthat both the nodes of set 2 and set 3 op eratestep 2 The union of the step 1's results for the pathsconnected to one section (or a node of set 1)The step 2's result is determined as the degree ofmembership of the section's being in the fault set.

One thing that should be noticed is the node related toinhibitory circle shown in Fig. 4. If the node B (that is

i(0.8, 0.9)=0.792\

Fig. 5 . Example of diagnosis with sagittal diagram.connected with an inhibitory circle) and the node A (thatmakes a path with B ) operate, the nodes C, D, and E are notincluded in operation to d etermine the degree of membershipof the section S.

In Fig. 5, if LlAm, LlCb, L2Bs, CB1, CB2, and CB3operate, the degree of membership of L1 is ~( 0. 79 2, .673) =0.929. Since LlCb and CB2 operate and make a path, thepath made by L2Bs and CB3 is ignored. If LlCb or CB2 didnot operate, the degree of membership of L1 would beu(0.792,0.509) = 0.857.By the process above, we can determhe the degrees ofmembership of sections' being in fault set. Comparing othercandidates' degrees of mem bership, we can diagnose the faultsection not only in single fault but also in multiple faults.That is, if the two section's deg rees of membership are closeto 1, both the sections may b e fault, that is, multiple faults.Furthermore, by synthesizing the result of the justificationwith this, more reliable fault section diagnosis can beachieved.

V. JUSTIFICATIONConsidering the causality of operating devices in fault, wejustify whether the fault section estimated in section IV isprecise or not.As mentioned in section 11.2, the sequential operationsproceed when a fault occurs. These operations are embodiedin sagittal diagrams by the magnitude of labels, arrows andinhibitory circles.The fault of a node in set 1 causes the operation of the

node in set 2 connected with the line having the largest label,and this causes the no de in set 3 connected to this to operate.If the node in set 3 does not operate, the node in set 2connected with the line having the second largest labeloperates, and this causes the node in set 3 to operate. If thisoperation also fails, the node in set 2 connected with the lineFig. 4. Inhibitory circle

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346of inhibitory circle operates, and these cause the node in set 3connected to this to operate.By applying these rules, we can examine the malfunctionor wrong alarm for the estimated fault section. However, theinformation that we get is uncertain, so we diagnose thesection that contains a few malfunctioning devices or wrongalarms as a fault rather than find the section that contains fewthose.

VI. IMPLEMENTATIONWe constructed an expert system for real power systems,345KV power lind systems of Korea, with the data of KoreaElectric Power Corporation (KEPCO). A part of the powersystems is shown in Fig. 6. The numbers of power lines andbuses are marked for convenience, and relays are notindicated in that figure.In designing the expert system, we make data files thatrepresent the structure of power systems, and mark theindexes of lines, buses, relays, and circuit breakerssystematically. For example, relay L29-27m represents MPRin line 29 at the side of bus 27, and CB47 is circuit breaker inline 24 at the side of front bus. By doing this we can easilymodify the system according to the structure change. Theonly thing that we have to know is the index of power lineand the index of bus to be connected w ith the power line.When run on 80486 PC , the proposed system took lessthan 1 second to diagnose the fault section. Since thecomputation procedure of the system is simple and theinference procedure of the system focuses on the operatingrelays and circuit breakers, and the sections related to thosedevices, computation time will not matter for larger scaledsystems than the tested power systems.

VII. CASE STUDYExtensive tests for various cases occurred at the 345KV

, L32

19 20 21Fig 6 345KV power line systems

power line systems have been performeperformance of the proposed expert systetest results for two represediagnosed .[Case 11 Line 30 fault (occurred at 1158, Sep. 13, 1994)

ive cases that are not easy to be

operated relay : L30-23m, L30-24m, L25-20stripped circuit breaker :CB50, CB59, CB60KEPCO's analysis:L30-23m, L30-24m - right operatioL25-20s - obscure operationThe result by operation and justification is shown in Table1. From the results, the possibility of Line 30's single fault islarge. Line 29's degree is small enough to be ignored and theline has many malfunctioning devices. The result of Line 29

is caused by the wrong operation of relay L25-20s related toline 30.[Case 21 Bus 22 fault (occurred at 09:00, O ct.operated relay : L24-1 Sm, L25-23b, B 22mtripped circuit breaker :CB47, CB49, CB5 1KEPCO's analysis:B22m - right operationL24-47m, L25-23b - wrong operation

The result by operation and justification is2. From the results, the possibility of Bus 22'large. Though Line 24's degree and Linelarge, the lines have many malfunctioning devices and MPRsof both lines did not operate. Therefore possibLine 24 and Line 25 is small. In case the MPsection operates wrong,with degree of members cult to diagnose fault section

TABLE 2. THE RESULT OF CASE 2

I degree of membership I malfunct ion or wrong a l m II24-20m, L24-20b, CB48, L25-23s,L2 4 I 9, = 0.792 I L26-22s, L27-21s, CB54 I2 5 r(0,7,0.8)= 0 73 L25-23m, L25-20m, L25-20b, CB50,L24-18~ , 26 -22~ , 27-21~ , B54

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347of Fault Location Algorithms," IEEE Trans. Power De live y, vol. 4,no. 2, April 1989, pp. 978-985.

[4] Y. Sekine, H. Okamoto, T. Shibamoto, "Fault Section EstimationUsing Cause -Effect Network," in Proceedings of 2nd Symposium onExpert System Application to Power Systems, July 1989, Seattle,Washington, U.S.A. pp. 277-282.

[5] C. Yang, H. Okamoto, A. Yokoyama, Y. Sekine, "Expert System ForFault Section Estimation of Power System Using Time SequenceInformation," in Proceedings of 3rd Symposium on Expert SystemApplication to Power Systems, April 1991, Tokyo-Kobe, Japan, pp.587-594.

[6] C. Rodrigue z, S. Rementeria, C. Ruiz, A. Lafuente, J. I. Martin, J.Muguerza, "A Modular Approach to the Design of Neural Networksfor Fault Diagnosis in Power Systems," in Proceedings of theInternational Joint Conference on Neural Networks, vol. 3, 1992,Baltimore, MD, U.S.A., pp. 16-23.[7] S warup K. S., Chandrasekharaiah H. S., "Fault Detection andDiagnosis of Power Systems Using Artificial Neural Networks," inProceedings of the 1s t International Forum on Applications of NeuralNetworks to Power Systems, 1991, Seattle, WA, U.S.A., pp. 102-106.[8] K. H. Kim, J. K. Park, "Application of Hierarchical Neural Networksto Fault Diagnosis of Power Systems," EZectricaZ Power & Energy

Systems, vol. 1 5 , no. 2, 1993, pp. 65-70.[9] C. L. Chen; S. N. Talukdar, "Causal Nets for Diagnosis," inProceedings of 4th Symposium on Expert System Application to Pow erSystems, Jan. 1993, Melbourne, Australia, pp. 379-386.Prentice Hall, 1988.[IO] G. J. Klir, T. A. Folger, "Fuzzy Sets, Uncertainty, and Information,"

[l 11 E. Chamiak, "Bayesian Networks without Tears," AI Magmine, vol.12, no. 4, 1991, pp. 50-63.Academic Publishers, 1991.[I21 H. J. Zimmermann, "Fuzzy Set Theory and Its Applications," Kluwer

[13] F. Hayes-Roth, D . A. Waterman, D. B. Lenat, "Building Expert[14] H. J. Cho, J. K. Park,H. J. Lee, "A Fuzzy Expert System for Fault

Diagnosis of Power Systems," in Proceedings of the InternationalConference on Intelligent System Application to Power Systems, Sep.1994, Montpellier, France, pp. 217-222 .

Systems," Addison-Wesley, 1983.

For the cases which include uncertainties like these twocases, the conventional methods based on binary logic [1-51cannot provide the information necessary for the diagnosis,such as degree of mem bership, to cope with the uncertainties.Neural networks approaches [6-71 can neither provideenough information, such as malfunctioning devicesparticular, to do so. The proposed system provides variouskinds of information and enables the operator to diagnose thefault section correctly in those case s as well.VIII. CONCLUSIONS

In this paper, we have proposed an expert system usingfuzzy relations to deal with the uncertainties of powersystems information. We have bu ilt sagittal diagrams whichrepresent the fuzzy relations for power systems, anddiagnosed fault section by the operation in fuzzy relations.We have also examined the malfunction or wrong alarm ofrelays and circuit breakers based on the alarm informationand the estimated fault section.By representing a fault section with the degree ofmembership and the malfunction or wrong alarm, theproposed system presents the section's possibility of beingfault. That is, the section that has a great degree ofmembership and a few malfunctions and wrong alarms isregarded as a fault section.We have implemented the proposed system for real powersystems, and the extensive tests for various cases havedemonstrated the performance of the system. Furthermore,applying threshold to the degree of membership, theproposed system can be easily applied to the automation ofsubstations.

ACKNOWLEDGMENTSThe authors would like to thank Mr. I.-D. Kim and hiscolleagues at KEPCO for their valuable comments on thepractical implementation and data supply for fault sectiondiagnosis of real power systems.

REFERENCES[ l ] K. Tomsovic, C. C. Liu, P. Ackerman, S. Pope, "An Expert System asa Dispatcher's Aid for the Isolation of Line Section Faults," IEEETrans Power Delivery, vol. 2, no . 3, July 1987, pp. 736-743.[2] Eleri Cardoz o, Sarosh N. Talukdar, "A Distributed Expert System For

Fault Diagnosis," IEEE Trans. Power Systems, vol. 3, no . 2, Ma y1988, pp. 641-646.[3] Adly A, Girgis, Melissa B. Johns, "A Hybrid Expert System ForFaulted Section Identification, F ault Type Classification and Selection

Hyun-joon Cho (S' 1995) received the B.S. and M.S. degrees from SeoulNational University, Korea in 1 993 and 1995, respectively. Now he isworking at LG Electronics Research Center. His research interest isArtificial Intelligence and its application to power systems and IntelligentControl.Jong-keun Park (M ' 1994) received the B.S. degree from Seoul NationalUniversity, Korea in 1973 and the M.S. and Ph.D. degrees from theUniversity of Tokyo , Japan in 1979 and 198 2, respectively He is aprofessor and chairman of Department of Electrical Engineering at SeoulNational University, Korea. His present research interest are analysis,control and protection in flexible AC transmission systems(FACTS),electromagnetic environment and application of Artificial Intelligencetechniques to power systems.

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348Discussion

Fushuan Wen an d C. S. Chang (Department of ElectricalEngineering, National University of Singapore, 10 KentRidge Crescent, Singapore 119260): We would like tocongratulate the authors for their interesting paper. Theauthors comments on the following remarks would be greatlyappreciated:1. It is not clear why the authors choose w=3 for Equations(3) and (4). n our opinion, it is possible that different faultdiagnosis results can be obtained if different w values areused. Thus, w is a very important parameter in th e proposedfault diagnosis method, and it is necessary to present ageneral guideline on how to choose w properly.2. For large scale power systems, many sagittal diagrams canbe formed (each section corresponds to a sagittal diagram). Infact, it is not necessary to form all sagittal diagram s for eachfault diagnosis scenario, and only a few sagittal diagramswhich are related to the reported alarms are needed. Thus, itappears necessary to develop a systematic algorithm todetermine which sagittal diagrams should be formed,especially for large scale pow fr systems.Once again, we congratulate the authors for their interestingcontribution.Manuscript received February 27, 1996.Hyun-Joon Cho (LG Electronics Research Center) andJong-Keun Park (Seoul National U niversity) :The authors thank the discussers for the kind com ments onthe paper. The opinion of authors on each remark is asfollows:1, The authors agree with the discussers that choosing the wvalue is importan t and difficult matter. T he followin gs are the

reasons for us to choose w =3 and we think that they may beY.s performs a operationwhich increases in streng value of the parameter wincreases. The intersection function performs oppositely. Thevalue w=3 means somewhat soft union and somewhat hardintersection. In the fault section diagnosis of power systems,

the possibility of fault is high if the relays of both endsof a section operate and the circuit breakers. In sagittaldiagrams, by using a soft union we can get a larger valuewhen both relays operate than one relay does. This reflectsthe fact that we could obtain more trustworthy diagnosiswhen there are two pieces of information than one. If thevalue of one path is too large, it could dominate the sectionsmembership degree regardless of the other paths operation.In order to prevent this a somewhat hard intersection wasused. Although it is possible to use the value 2.5 or 3.was accepted as the most appropriate value through vsimulations.2. The system doesnt form sagittal diagrams when faultoccurs. The concept and structure of sagittal diagrams andthe diagnosis procedure was embodied in the program of theexpert system. The system need only the data files thatrepresent the structure of power systems systematically aswritten in the paper. Since the inference procedure focuseson the reported alarms and computes the related sectionsmembership degrees, the size of power systems will notmatter.

a guideline on how to chooThe union function of th

Manuscript received April 2, 1996.