DepartmentofElectricalEngineering,FacultyofEngineeringandTechnology,JamiaMilliaIslamia,NewDelhi110025,India
Received5October2014;receivedinrevisedform1March2015;accepted4March2015 Availableonline21September2015
Abstract
Inthisproposedworkafuzzylogicbasedalgorithmusingdiscretewavelettransformisdevelopedforidentifyingthevarious faultsintheelectrical distributionsystem foranunbalanceddistributionelectrical powersystem.Thistechniqueiscapableto identifythetendifferenttypesoffaultswithnegligibleeffectofvariationinfaultinceptionangle,loadingandotherparameters ofthepowerdistributionsystem.TheproposedmethodistestedonIEEE13buselectricaldistributionsystemandonanIndian scenarioofdistributionsystem.Thecurrentofrespectivethreephasesisusedasinputsignalforfaultidentificationandtheresults obtainedfromtheproposedmethodaremorethansatisfactory.
©2015TheAuthors.ProductionandhostingbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Faultidentification;Fuzzylogic;Discretewavelettransform;Faultinceptionangle
1. Introduction
Nowadays,distributionsystemscarryalargeamountofpowerascomparedtoearliererabecauseofincreasein per capitalconsumption ofelectricity.Any, change isnot predictedinthe presenttrendinnearfuture anditwill sustainfordecadesatleastinIndiaandinotherdevelopingcountries.So,anydisturbanceinthepowersupplymay leadtodiscontinuationofpowersupplyanddegradationinthepowerquality.Distributionsystemisthemostvital componentintermsofitseffectonreliability,qualityofservice,costofelectricityandaestheticimpactonsociety.In anyindustrializedcountry,thedistributionsystemdeliverselectricityliterallyeverywheretakingpowerfromdifferent generatingstationtotheendusers.Twoforemostthingswhicharerequiredforquickrestorationofthefaultypartare faultlocationandtypeoffault.Similarly,indigitaldistanceprotectionsystemtheappropriateoperationofprotective deviceandaccurateclassificationofthefaultarenecessary(GraingerandStevenson,1994).
∗Correspondingauthor.Tel.:+919911314742.
E-mailaddresses:majidjamil@hotmail.com(M.Jamil),rajeevdit@rediffmail.com(R.Singh),sanjeev.eck@gmail.com(S.K.Sharma). PeerreviewundertheresponsibilityofElectronicsResearchInstitute(ERI).
http://dx.doi.org/10.1016/j.jesit.2015.03.015
2314-7172/© 2015TheAuthors.Productionand hostingbyElsevierB.V.This isanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Byseeingtheabovementionedbenefitsoffaulttypeidentificationalotofresearchworkiscarriedout(Aggrawal
etal.,1999;Linetal.,2001;Ferreroetal.,1995;WangandKeerthipala,1998;GirgisandJohns,1989;Protopapas
etal.,1991;Togamietal.,1995;Chenetal.,2000;Adu,2002).Previously,alargeamountofresearchworkhasbeen
doneintheelectricaltransmissionsystemastheycarrylargeamountofpowerandanydisturbanceonthetransmission systemwillaffectthewholepowersystem.Nowadays,distributionsystemisalsocarryingalargeamountofpower duetoincreaseinurbanizationandindustrializationindevelopingcountrylikeIndia.Moreovertheuseofunderground cablealsoincreasesthecomplexityinfaultidentification.So,distributionsystemfaulttypeidentificationisbecoming muchmoreimportant.
Although,alargenumberoftechniquesareavailableforfaultidentificationandclassification.Someofthemare baseduponcontinuousmonitoringof(1)Voltage,(2)Current,(3)Impedance,etc.Allthesetechniqueshavetheirown advantagesanddisadvantages(Alanzietal.,2014).
Someintelligenttechniques,(generallyknownasknowledgebasedtechniques)ofthefaultclassificationin trans-missionlinearebaseduponNeuralNetwork(Aggrawaletal.,1999;Linetal.,2001);FuzzyLogicandFuzzyNeural Network(Ferreroetal.,1995;WangandKeerthipala,1998);andknowledgesystembasedapproach(GirgisandJohns,
1989;Protopapasetal.,1991).Allthesetechniquessufferfromamajordrawbackthatapropertrainingisrequiredfor
neuralnetworkandthesearenotsusceptibletohighimpedancefaults.Mostoftheresearchworkhasbeendonefor identifyingthevarioustypesoffaulti.e.whetherthefaultislinetoground,doublelinetoground,doublelinefault orthreephasefault.Recently,thephaseangleclassificationandfuzzylogicbasedschemes(Das,2006)havebeen publishedintheresearchpapers.Amajordrawbackoftheanglebasedmethodisthatitsaccuracyisonlyabout60%. Othertechniquessuchastheunder-impedanceandtorquetechniqueutilizethepositiveandzerosequenceimpedances oftheelectricaltransmissionline.Butthezerosequenceimpedanceofthe transmissionlinecannotbedetermined preciselyandare therefore,suitable fordistance relayswherethereach of the relaysisdefined.Afault recorder, however,isabletomonitoralltransmissionlinesemanatingfromastationandpossiblymostoftheadjoininglines. Furthermore,theunder-impedanceandtorquealgorithmsaresensitivetoclose-infaultswithstrongsourcesbehind them.It ispossiblethatfor suchfaultconditions morethanonemeasuringunit wouldestimateeitherthepositive sequencefaultimpedanceortheeffectiveoperatingtorqueisclosetothedesiredvalue.Thesetechniques,therefore, cannotbereliablydependedupontodeterminethefaultedphasesunderallfaultconditions.
Ananglebasedfaultclassificationapproach(Das,2006)possessesabetterbenefitasthedifferenceofloadcurrent andthefaultcurrent.Moreovertheuseoffuzzylogicprovidesgreaterflexibilityforfaultclassification,butremoving thedecayingfaultcurrentcomponentfromtheloadcurrentisverydifficultandgenerallyfuzzymembershipfunction overlappingprovidespoorresults.MultiResolutionWaveletTransformalgorithm(Gayatrietal.,2007)isveryfast andaccurateinclassificationoffault,butthemaindrawbackisthatitonlyidentifiesthetypeoffaulti.e.LG,LL,LLG andthreephasefault.
Theproposedschemeoffaultclassificationismoreaccurateasitcaneasilyclassifythetendifferenttypesoffault
i.e.threetypesoflinetogroundfault,threetypesofdoublelinetogroundfault,threelinetolinefaultandathree phasesymmetricalfault.Themainbenefitofproposedschemeisthatonlythreephaselinecurrentmeasurementis neededandnootherparameterorinformatione.g.circuitbreaker(CB)positionandisolatorisrequired.Thedeveloped methodistestedonIEEE13busdistributionsystemandonIndianpowerdistributionutility.Allthesignalanalysis, distributionsystemmodelsimulationandfuzzylogicsystemaredesignedinMATLAB®/SIMULINKenvironment.
2. Faultidentificationstrategy
Faultidentification strategy is achievedby implementing the discrete wavelet transform. The discrete wavelet transformis used tocalculate the change inenergy of aparticular energy level of measured current signals. The energiescalculatedfromdiscretewavelettransformarethenusesasinputsintothefuzzylogicsystem.
2.1. Discretewavelettransform
Thewavelettransformisatestedtoolforanalyzingandstudyingthesignalseffectively(Rizwanetal.,2013).The wavelettransformresolvesthemeasureddistortedsignalintodifferenttime–frequencydomains(Jamiletal.,2014). Wavelettransformusestheexpansionandcontractionofbasisfunctionstodetectvariousfrequencycomponentsin themeasuredsignal.Wavelettransformdecomposesthesignalintodifferentbandoffrequencies.Thebasisfunction
Fig.1.Multi-leveldecompositionofsignalX[n].
ismotherwavelet,whichusesthedilationandtranslationproperty.Here,largewindowsareusedtoobtainthelow frequencycomponentofthesignal,whilesmallwindowreflectdiscontinuities.
Wf(m,n)=2(−m/2)
f(t)Φ(2−mt−n)dt (1)
wheremisfrequencyandnistime.Inpracticewaveletseriesisgivenby
f(t)= k=∞ k=−∞ ckΦ(t−k)+ k=−∞ ∞ k=−∞ dikΦ(2it−k) (2) Φ(x)=√2 n h0Φ(2x−n) (3)
whereΦ(x)isscalefunctionandh0isthelowpassfiltercoefficient. Φ(x)=√2
n
h1Φ(2x−n) (4)
whereΦ(x)iswaveletfunctionandh1ishighpassfiltercoefficient.InFig.1variousdecompositionlevelsofwavelet
treeareshown,whereX[n]isthediscretesignal.
Thedecompositionlevelscanbeclassifiedintodetailandapproximatecoefficients.Thevariousdetailsand approx-imatecoefficientcontaindifferentenergiesatdifferentlevelofdecomposedsignal.Theseenergiescanbecalculated easilyandonthebasisoftheseenergiesfaultscanbeclassifiedeasily.
Theenergycontentofanydecomposedsignalisgivenbythefollowingformula:
E=|x|2 (5)
wherexisthewaveletcoefficientsatdecompositionlevel.
TheproposeddiscretewavelettransformisperformedonIEEE13busshowninFig.2(Kirsting,1991).
Letusconsiderthefaultonbusnumber633,thevariouscurrentsandvoltageswaveformsofthefaultedsystemat thesubstationareshowninFig.3.Thewaveletcoefficientandhencethevariousenergiesassociatedwiththesignals arecalculatedandresultsobtainedduringthefaultareshowninTables1and2.
2.2. Fuzzylogic
ItcanbeobservedfromTable2,thattheenergiesobtainedarefuzzyinnature.Therefore,fuzzylogicisusedfor faultidentificationtodifferentiatethetypeoffault.Fuzzylogicsystempossessescertainbenefitsoverneuralnetwork. Thefuzzylogicsystemworksonbysimplydefiningcertainrulesandresultscanbeobtained,butinneuralnetworka rigoroustrainingisrequired.Besidesthereisconvergenceofthealgorithmisalsoaproblem.
Fig.2.IEEE13bussystem. Table1
Typicalvalueofthedifferentenergies.
Typeoffault EnergyA(×1011) EnergyB(×1011) EnergyC(×1011) EnergyG(×1011)
A-G 1.342 0.0014 0.0019 0.1091 B-G 0.0028 1.3278 0.0018 0.1097 C-G 0.0025 0.0016 1.3425 0.1142 A-B 1.9717 1.8868 0.0015 0 B-C 0.0021 1.9774 1.9014 0 C-A 1.9183 0.0012 2.0119 0 A-B-G 2.1714 2.0964 0.002 0.0688 B-C-G 0.0028 2.1633 2.1246 0.0663 C-A-G 2.1382 0.0016 2.194 0.0673 A-B-C 2.5991 2.5649 2.6127 0 Table2
Typicalvalueofnormalizedenergy(fuzzyinputs).
Typeoffault EnergyA EnergyB EnergyC EnergyG
A-G 1 0.0010 0.0014 0.0905 B-G 0.0021 1 0.0013 0.0913 C-G 0.0019 0.0012 1 0.0934 A-B 0.9252 1 0.0010 0.0073 B-C 0.0151 1 0.9535 0.0013 C-A 0.9502 0.0006 1 0 A-B-G 1 0.9710 0.0009 0.0345 B-C-G 0.0013 1 0.9739 0.0339 C-A-G 0.9774 0.0007 1 0.0344 A-B-C 0.9991 0.9941 1 0
Intheproposedmethodthe approximationsare involved,the differentinputsortheantecedentsarerepresented byanappropriatecorrespondingfuzzyvariable.Astheantecedentpartsarevariableswhicharefuzzyinnature,the othervariablesintheremainingresultantpartsshouldbefuzzyinnature.Theaboveapproximaterulebasesystemis actuallya“FuzzyRuleBaseSystem.”Thetriangularmembershipfunctionhasbeenusedtorepresentallthesefuzzy variables(inbothantecedentandconsequentpartsofthefuzzyrules),inthisproposedwork.Thisfaultclassification modelusesthetriangularmembershipfunction,asshowninFig.4.Allthefourinputsarefedthroughbyusingfour triangularmembershipfunctions.
Fig.3.Currentandvoltagewaveformduringfaultatbus633.
Thevaluesofthreeedgesoftriangleforalltentypesoffaulthavebeentakeninsuchamannerthatthetriangular membershipfunctioncorrespondstoanyparticulartypeoffault,andissymmetricaboutthetakendecimalnumber. ThiscanbeconfirmedfromTable3.Thus,thedifferentthreeedgeswhichhavebeenassignedtorepresentthefuzzy faulttypesareshowninTable4.
InTable3,B3representsphase-A,B2representsphase-B,B1representsphase-CandB0representstheground.
Theappropriatethreeedgesarecalculatedforshowingthefuzzyvariablesfordeclaringthedifferenttypesoffault. Themethodforselectingthethreeedgesisasfollows.Inthebeginning,inordertorepresentthetypeoffaultcorrectly, abinarylogicsystemisdeveloped.Inthiscodingsystem,afourdigitbinarynumber(B3B2B1B0)isgeneratedto representthetypesoffault.Thecompletechartcontainingthebinarynumberswithrespecttoeachtypeoffaultand theircorrespondingequivalentdecimalnumbersareshowninTable3.Theserulesareusedinoutputoffuzzysystem.
ThefuzzylogicdevelopedasschemeshowninFig.5isusedforapplyingtheproposedmethod.
ThecrispinputsarefourinnumberwhicharethenormalizedenergiesofthemeasuredcurrentsofphaseA,phase B,phaseCandzerosequencecurrentrespectively.Theyarecalculatedfromthesampledvaluesoftheduring-fault
Table3 Faultcodetable.
Faulttype B3 B2 B1 B0 Equivalentdecimalnumber
A-G 1 0 0 1 9 B-G 0 1 0 1 5 C-G 0 0 1 0 3 A-B 1 1 0 0 12 B-C 0 1 1 0 6 C-A 1 0 1 0 10 A-B-G 1 1 0 1 13 B-C-G 0 1 1 1 7 C-A-G 1 0 1 1 11 A-B-C 1 1 1 1 15 Table4
Fuzzyvariableforrepresentationofdifferenttypesoffault. Faulttypes Triplets
A B C A-G 8.5 9 9.5 B-G 4.5 5 5.5 C-G 2.5 3 3.5 A-B 11.5 12 12.5 B-C 5.5 6 6.5 C-A 9.5 10 10.5 A-B-G 12.5 13 13.5 B-C-G 6.5 7 7.5 C-A-G 10.5 11 11.5 A-B-C 14.5 15 15.5
Fig.4.Triangularmembershipfunction.
currentsof respectivethreephasesi.e.phaseA,phaseBandphaseC.Because,thevaluesarecrispinnature; they arethenneededtobeconvertedintotheircorrespondingfuzzyvariables.Inthispaperthesingletonfuzzifier(Mendel, 1995)hasbeenadoptedforthefuzzificationoftheassignedvalues.
Afterfuzzification,thefuzzifiedinputsareusedtodetectthefaultandusedasinputstotheFuzzyInferenceSystem (FIS).TheFISbasedupontheproposedfuzzyrules,classifiestheappropriatetypesoffaultasitsoutput.Theoutput
Fig.6.TypicalFISEditorofFuzzyLogicToolBoxinMATLAB®.
Fig.7.SimulinkmodelofFISinMATLAB®.
oftheinferencesystemisalsofuzzyinnature.Thesefuzzyoutputsdirectlycannotbeusedtodeclarethefault,but firstneededtobedefuzzifiedtodetermineactualtypeofthefaultcorrectly.TheCentroidDefuzzificationfunctionhas beenimplementedfordevelopingthepurposedFIS.ThesimulationoftheFLSmethodhasbeencarriedoutinthe FuzzyLogicToolboxoftheMATLAB®/Simulinksoftware(asshowninFig.6)(Matlab,2015).Thesimulinkmodel ofdevelopedFISsysteminMATLAB®isshowninFig.7.
Therulesforthegivenfourinputscorrespondingtotheenergylevelsoffourcurrentstoobtaintheresultareas follows:
1. IfEnergyAis“nearabout1”andEnergyBis“nearabout0”andEnergyCis“nearabout0”andEnergyGis “nearabout1”thenthefaulttypeis“A-G”.
2. IfEnergyAis“nearabout1”andEnergyBis“nearabout1”andEnergyCis“nearabout0”andEnergyGis “nearabout0”thenthefaulttypeis“A-B”.
3. IfEnergyAis“nearabout1”andEnergyBis“nearabout1”andEnergyCis“nearabout0”andEnergyGis “nearabout1”thenthefaulttypeis“A-B-G”.
Table5
FLSoutputfordifferentfaultatbus633.
Typeoffaultatbus633 Fuzzyoutput
A-G 9.52 B-G 5.52 C-G 3.44 A-B 12.5 B-C 6.5 C-A 10.5 A-B-G 13.5 B-C-G 7.44 C-A-G 11.4 A-B-C 15.5 Table6
FLSoutputforfaultatdifferentbusIEEE13bussystem. Busno. Typesoffault
A-G B-G C-G A-B B-C C-A A-B-G B-C-G C-A-G Threephasefault
671 9.52 5.52 3.44 12.5 6.5 10.5 13.5 7.44 11.4 15.5
634 9.5225 5.5265 3.412 12.5 6.5 10.5 13.5 7.44 11.4 15.5
4. IfEnergyAis“nearabout1”andEnergyBis“nearabout1”andEnergy Cis“nearabout1”andEnergy Gis “nearabout1”thenthefaulttypeis“symmetrical”.
ThedifferenttentypesoffaultsarebeingsimulatedbyusingdifferentvaluesofRfandFaultInceptionAngle(FIA). TheresultsusingdifferentvaluesofRfandFaultInceptionAngle(FIA)obtainedarealmostsimilar,asonlythechange inenergyismeasured.Hence,itisindependentfordifferentvaluesofFIA.Thetypicaloutputof FLSfordifferent faultsatIEEE13busradialdistributionsystematbus633isshowninTable5.
3. Resultsanddiscussion
Theproposedalgorithmistestedusingthesimulatedaswellasrealtimedata.Thedifferentsourcesforthetestdata are
1) MATLABgenerateddata.
2) IEEE13busradialdistributionfeeder.
3) FaultdataofdistributionsystemofJanpur(M.P.,India)providedbyMIPOWERCompany(showninFig.8).
ForafaultatbusP27thevariousresultsareshowninTable6andthecorrespondingvalueofthefuzzyoutputis alsoshowninTable7.
Afaultdetectionsystembasedonfuzzylogicanddiscretewavelettransformhasbeendesignedinthiswork.This designisvalidatedonIEEE13busradialdistributionsystemandradialpowerdistributionnetworkusingrealtime
Table7
FLSoutputforfaultatdifferentbus:distributionsystem,Janpur(M.P.,India). Busno. Typeoffault
A-G B-G C-G A-B B-C C-A A-B-G B-C-G C-A-G Threephasefault
P25 9.02 5.18 3.30 11.87 6.5 10.45 12.85 7.12 11.38 15.45
Fig.8.SLDofdistributionsystem,Janpur(M.P.,India).
dataandMATLAB®/Simulinksoftware.ThevaluesofenergiesfordifferenttypesoffaultsareshowninTable8.The finalresultsofFLSareverypreciseandshowninTable9.Itisabletodetectallthetentypesoffaultsi.e.A-G,B-G, C-G,A-B,B-C,C-A,A-B-G,B-C-G,C-A-Gandthreephasesymmetricalfault.Ithasbeenfoundthatfaultscould occurinradialdistributionsystemswithallpossiblecombinations;hencetheimportanceofthefuzzymembership functionsindeclaringthevarioustypesoffaultisproved.Thesimplicityofthedesignbasedonthefuzzylogic,means adrasticreduction inloadloss andenergylossondistributionsystemsduetoprolongedoutagesleadingtolonger feederdowntimeduringfaultedconditions.Thevariousconclusionsandresultsdrawnfromthestudyare:
Table8
Typicalvaluesofnormalizedenergy:Janpur(M.P.,India).
Typeoffault EnergyA EnergyB EnergyC EnergyG
A-G 1 0.1174 0.0911 0.0724 B-G 0.0955 1 0.1234 0.079 C-G 0.121 0.0922 1 0.077 A-B 1 0.6007 0.2670 0 B-C 0.2738 1 0.6127 0 C-A 0.6196 0.2634 1 0 A-B-G 0.8536 1 0.0176 0.2172 B-C-G 0.0178 0.8306 1 0.2136 C-A-G 1 0.0171 0.8174 0.2150 A-B-C 1 0.9753 0.9811 0
Table9
FLSoutputfordifferentfaultatbusP27.
TypeoffaultatbusP27 Fuzzyoutput
A-G 9.52 B-G 5.52 C-G 3.44 A-B 12.5 B-C 6.5 C-A 10.5 A-B-G 13.5 B-C-G 7.44 C-A-G 11.4 A-B-C 15.5
1) The proposedmethodhasaccuracy of around 95%for the lightlyunbalanced system(i.e.for less unbalanced system).
2) TheproposedmethodprovidesgoodresultsfordifferentvaluesofFIAanditindependentofFIAvariations. 3) Forsakeofaccuracythe8levelsymletmotherwaveletisused.
4) Theproposedalgorithmhasfuzzymembershipfunctionwhichadaptaccordingtotheexperimentalresultsobtained.
4. Conclusion
Theoperatingconditionsandelectricalparametersinanelectricalpowerdistributionsystemvaryoverawiderange becauseof dynamic nature of thepower systemanddiversenatureof load. The structureof any electricalpower distributionsystemoftenchangesbecauseofthechangingofloadpatterns,switchingofpowersystemequipments, suddenbreakdownofgeneratingunits,etc.Thefaultresistance,faultinceptionangleanddifferentloadingconditions ofelectricalpowerdistributionsystemalsoaffecttheperformanceofanyfaultdetectionandclassificationmethod.
Theproposedmethodisfoundtobequitesatisfactoryinclassificationoffaulttypesforboththedistributionsystems
i.e.forIEEE13bussystemandforutilitydistributionsystemJanpur,MadhyaPradesh(India).Butthespaceconstraint forcedustoshowtheresultsofthefaultthatoccuratthebus633.Theproposedmethodisfullyeffectiveinclassifying alltentypesoffaultsandforanypossiblecombinationofdifferentpowersystemparameters.Thefaultinceptionangle consideredfortheproposedresearchis0.90andthevalueoffaultresistanceis0.Theresultsoftheproposedmethod arenotaffectedbydifferentvaluesofFIAs,faultresistanceandotherdistributionparameters.Theobservationofthe results(asshowninTable2)showsthatthevaluesofthenormalizedenergiesofrespectivethreephasesarecrispin natureandusuallyvariesfrom0to1.TheoutputoftheFISdependsuponthetypeoffaultandhencethedefuzzified outputvariesfrom1to15(asshowninTable3).
Thetestingoftheproposedmethodundervariousoperatingconditions,differentfaultresistanceandfaultinception anglesandcorrespondinglyresultobtainedshowsthattheresultsaresatisfactory.
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