基于励磁涌流变压器的建模与仿真的神经网络(IJISA-V4-N5-1)

I.J.IntelligentSystemsandApplications,2012,5,1-7PublishedOnlineMay2012inMECS()DOI:10.5815/ijisa.2012.05.01Copyright©2012MECSI.J.IntelligentSystemsandApplications,2012,5,1-7NeuralNetworkbasedModelingandSimulationofTransformerInrushCurrentPuneetKumarSingh1andDKChaturvedi2DepartmentofElectricalEngineering,FacultyofEngineering,DayalbaghEducationalInstitute,[e-mail]1,[e-mail]2Abstract—Inrushcurrentisaveryimportantphenomenonwhichoccursduringenergizationoftransformeratnoloadduetotemporaryoverfluxing.Itdependsonseveralfactorslikemagnetizationcurve,resistantandinductanceofprimarywinding,supplyfrequency,switchingangleofcircuitbreakeretc.Magnetizingcharacteristicsofcorerepresentsnonlinearitywhichrequiresimprovednonlinearitysolvingtechniquetoknowthepracticalbehaviorofinrushcurrent.Sinceseveraltechniquesstillworkingonmodelingoftransformerinrushcurrentbutneuralnetworkensuresexactmodelingwithexperimentaldata.Therefore,theobjectiveofthisstudywastodevelopanArtificialNeuralNetwork(ANN)modelbasedondataofswitchingangleandremanentfluxforpredictingpeakofinrushcurrent.BackPropagationwithLevenberg-Marquardt(LM)algorithmwasusedtotraintheANNarchitectureandsamewastestedforthevariousdatasets.ThisresearchworkdemonstratesthatthedevelopedANNmodelexhibitsgoodperformanceinpredictionofinrushcurrent’speakwithanaverageofpercentageerrorof-0.00168andformodelingofinrushcurrentwithanaverageofpercentageerrorof-0.52913.IndexTerms—InrushCurrent,ANN,switchingangle,Remanentflux,Modeling,Simulation,Transformer.I.INTRODUCTIONInrushcurrentisveryimportantissuefortransformerdesigner.Iteffectsonrelaycoordinationbecauseoftentotwentytimes(evenmore)ofratedcurrentduringtransientperiod.Theseabnormalbehaviorsofinrushcurrentcausesrelaytooperate.Secondharmonicbasedrelaydiscriminatethisabnormalityinpowersystem[1].Transientperiodofcurrent(exponentialdecay)dependsoncircuittimeconstant.TransformerisR-LcircuitwithtimeconstantofLtoR.Resistanceisverysmallforlargeratingoftransformer,causeslargetransientperiodbutitisrelativelyhigherforsmallratingoftransformerandalsocausesfastdecayactionininrushcurrent.Intensityoftheinrushcurrentdependsontheinstanceofthesinusoidalvoltageinwhichitisswitchedonaswellasoncharacteristicsoftheferromagneticcoresuchasitsresidualmagnetismanditsmagnetizationcurve[2].MagnetizingcharacteristicofcoreexplainedbyANNmodel[8-9].Peakinrushcurrentofnonlinearinductorinserieswithresistoriscalculatedbyanalyticformula[3].Jameli[5]showedtransformerinrushcurrentwithdifferentoperatingconditions.Ali[10]showedanalyticcomputationofinrushcurrentusingFEMmodeling.Variousprotectivesystemsfortransformers,basedonthedifferentialrelayingsystemweredevelopedinrecentyears[4].Varioustechniquesbasedoncomplexcircuitsormicrocomputersareproposedtodistinguishinrushcurrentfromfaultcurrent.However,thetransformerstillmustbearwithlargeelectromagneticstressimpactcausedbytheinrushcurrent.Inthispaper,firsttransformerequationispresentedwhichwasusedforcalculationofInrushcurrent.Thenasingle-phasetransformerwassimulatedinMATLAB.Simulationwasperformedtoobtainvariousdatasets.Thesedatasetswerethenutilizedtodeveloptwoneuralnetworks(ANN).Onenetworkwasusedforinrushcurrentmodelingandsecondnetworkformodelingofinrushcurrent’speak.II.INRUSHCURRENTEquivalentcircuitofsinglephasetransformer[2]duringnoloadconditionisshowninfigure1.Figure1:EquivalentcircuitofSinglephasetransformerInrushCurrentcanbedeterminedbyfollowingequations.()()()(1)VmSin(wt+angle)RpLpRcIm2NeuralNetworkbasedModelingandSimulationofTransformerInrushCurrentCopyright©2012MECSI.J.IntelligentSystemsandApplications,2012,5,1-7()(2)im=αSinh(βλ)(3)WhererP,LPandrcrepresentsprimarywindingresistance,primarywindinginductance,andcorelossesresistancerespectively.im(eqn3)ismagnetizingcurrent.A.DatacollectionDatasetswerecollectedusingsemi-analyticsolutionwiththehelpofMATLABprogramming.Thesesetsincludingdifferentvaluesofinrushcurrentatparticularremanentflux,magnetizingcurrent,timeandswitchingangle.Onedatasetwaspreparedforinrushcurrentvaluebasedondifferentvalueofremanentflux,magnetizingcurrent,andtimebutatconstantswitchingangle.Seconddatasetwaspreparedforinrushcurrent’speakvaluebasedondifferentswitchingangleandramanentflux.III.CASESTUDYThisstudywascarriedon120-VA,60-Hz,(220/120)Vtransformer[2]andinrushcurrentobtainedfromequations(1)and(2)usingadiscretetime,with83.333μs.TheequivalentcircuitofthistransformerisshowninFigure1anditsparameters(220-Vwinding)arerP=15.476Ω;LP=12mH;rc=7260.Forthetransformermagnetizationcurve,asgiveninequation(3),thefollowingparametersdeterminedexperimentallywereused:α=63.084mA;β=2.43.IV.NEURALNETWORKNeuralNetworkconsistsofthreelayersnamelyinputlayer,hidden(Processing)layer(s),outputlayer.Inputdatafedtonetworkthroughinputlayer,afterthatprocessingtakesplace.Outputvaluecomesoutatoutputlayerwhichwillcomparewithtargetvaluetofindouterror.BackpropagationwithLMalgorithmisusedtominimizethiserrororreducingtolerancerange.NeuralNetworkhasbeautytogiveaccuratevaluedependsoninputvalueafterwelltrainin