高电压设备测试（High Voltage Equipment Testing）（英文版） 课件 Worksheet 4 Transformer Winding Deformation Test

《HighVoltageEquipmentTesting》TransformerWindingDeformationTest主讲人：何发武（副教授）OperatingWorksheet：OperatingWorksheet：TableofContents01Followme02Workshop03Training01FollowmeⅠ.TypesofTransformerFaultsThetransformerisoneofthemostimportantequipmentinpowersystems.Duringtransportation,thetransformermayencounterunexpectedcollisionsandimpacts.Whenoperatingunderfaultconditions,theimpactcurrentonthetransformerwillsubjectitswindingsandmechanicalstructuretomechanicalstresses,resultinginacertaindegreeofdeformationinthewindingsandcausingaccidentsduringoperation,asshowninFigure3-23.Figure3-23

TransformerexplosionandfireaccidentⅠ.TypesofTransformerFaultsDuetothesevereharmthatwindingdeformationposestotheoperationofthetransformerandpowersystem,previoustestingmethodswereunabletoeffectivelydetectsuchdefects.Verificationcouldonlybedonethroughhangingcoverinspection,whichnotonlyrequiredasignificantamountofmanpowerandresourcesbutalsoposedcertainriskstothetransformeritself.Moreover,inthecurrentoperationofpowersystems,itischallengingtohavelong-termpoweroutagesforthelargetransformer.Therefore,thefrequencyresponsemethodandlow-voltageshortcircuitimpedancemethod,whichcanquicklymeasureinternaldeformationsofwindingswithouttheneedforhangingcoverinspection,havebeenwidelyusedinon-siteoperations.ThetransformerstructureisshowninFigure3-24.Ⅰ.TypesofTransformerFaultsFigure3-24

TransformerstructureⅠ.TypesofTransformerFaultsThemainreasonforthedeformationofthetransformerwindingareshortcircuit,near-areashortcircuitormultipleovercurrentoperations,andcollisionduringtransportation.Themaincausesoftransformerfaultsareequipmentaging,impropermaintenance,overloadoperation,andelectricalfaults.Thethreemaintypesoftransformerfaultsareconcentratedonwinding,tapswitch,andbushingfailures,whichaccountforabout70%ofalltransformerfaults.ThereasonsandtypesoftransformerfaultsareshowninFigure3-25.Ⅰ.TypesofTransformerFaultsToanalyzetransformerfaults,factorssuchasoverheating(duetodeterioratingtransformeroil),bushingmainbodyissues(suchaspartialdischargeandmoistureproblems),electricalperformance(suchascoronadischarge),andon-loadtapswitch(suchasarcing)canbeanalyzed.Theseproblemsrunthroughtheentirelifespanofatransformer,alwaysbeingsubjectedtotheinfluencesofmultiplefactorssuchasheat,electricity,mechanics,andchemistry.(a)Transformerfaultscauses(b)TransformerfaultstypesFigure3-25

ThereasonsandtypesoftransformerfaultsⅡ.TheexternalforceonthetransformeranddeformationcauseThemaincomponentsofthetransformerarewindingandcore.Tosolvetheproblemsofheatdissipation,insulation,sealingandsafety,oiltank,insulatingbushing,oilstoragecabinet,coolingdevice,pressurereleasevalve,safetyairway,thermometerandgasrelayarealsoneeded.ThenormalappearanceofthetransformerandthewindingisshowninFigure3-26.Figure3-26

TransformerappearanceandinternalstructureⅡ.TheexternalforceonthetransformeranddeformationcauseTransformerwindingdeformationreferstoirreversiblechangesintheaxialorradialdimensions,includingdisplacementofthebody,distortion,bulging,displacementofwindings,andshort-circuitbetweenturns,causedbymechanicalforcesortheimpactoffaultshort-circuitcurrentsontheinternalcoilwindingduringtransportationoroperationofthetransformer.Afterthedeformationoftransformerwindings,theinsulationdistancechanges,leadingtoadecreaseinboththemechanicalandinsulationperformanceofthewindings,whichisdifficulttodetectthroughinsulationtestsandtransformeroiltests,resultinginlatentfaults.Ⅱ.TheexternalforceonthetransformeranddeformationcauseTherefore,windingdeformationposesamajorrisktothesafeoperationofthepowertransformer.Whenexposedtolightningovervoltageorshort-circuitaccidents,thewindingsmaynotbeabletowithstandthetremendouselectrodynamicforcesandcanbedamaged,leadingtobreakdownofinsulationbetweenturnsorlayersofthetransformer.Thiscancausesuddeninsulationaccidents,andeveninsulationbreakdownaccidentsmayoccurundernormaloperatingvoltageduetoprolongedpartialdischargeeffects.Ⅱ.Theexternalforceonthetransformeranddeformationcause1.TypesofImpactForcesonWindings(1)ElectrodynamicforcesduringnormaloperationDuringnormaloperation,electrodynamicforcesareusuallysmall.However,iftherearedefectsinthewindingduringthemanufacturingprocess,suchasloosewindings,unevenwiresorburrs,entryofblocksintothebendingareaofcommutation,insulationdamageatcommutationpoints,andunevenwedges,thevibrationcausedbyelectrodynamicforcescanfurtheramplifythesedefects.Asaresult,thewindingmaydeformduringnormaloperation.Thereisalsoapossibilityofprolongedfrictionbetweenwiresandblocks,leadingtoinsulationdamageanddischarge.Additionally,ifthethermalstabilityofthewindingisinsufficient,windingdeformationfailuresmayoccurduringnormaloperation.Ⅱ.Theexternalforceonthetransformeranddeformationcause(2)SuddenShort-CircuitElectrodynamicForcesDuringasuddenshort-circuit,theshort-circuitcurrentcanbeseveraltimestotensoftimeshigherthanthenormalratedcurrent.Theelectrodynamicforcesexperiencedbythewindingsaredirectlyproportionaltothesquareofthecurrent.Therefore,inthecaseofashort-circuit,theelectrodynamicforcescanbetenstohundredsoftimeshigherthanduringnormaloperation.Althoughthedurationofashort-circuitisshort,thepowerfulsurgeofcurrentsubjectsthetransformerwindingstosignificantandunevenelectrodynamicforces.Thisisparticularlytruewhenashort-circuitoccursatthetransformer’soutputornearby,wherethecombinationofhighshort-circuitcurrentandrelativelylowshort-circuitimpedanceresultsinevengreaterelectrodynamicforces.Theseforcescancausevarioustypesofdeformationinthewindings,makingthemtheprimarycauseoftransformerwindingdeformation.Ⅱ.Theexternalforceonthetransformeranddeformationcause(3)DirectmechanicalimpactforceThetransformerisoftensubjectedtoexternalaccidentalmechanicalimpactforcesduringmanufacturing,transportation,installation,andmaintenanceprocesses.AccordingtoNewton’smechanicstheorem(F=ma),thetransformercasingwillexperienceaccelerationordecelerationinthesamedirectionastheexternalforce,alteringitspreviousmotionstate.Thiscanresultinchangessuchastransitioningfromresttomotion,increasingordecreasingvelocity,ortransitioningfrommotiontorest.Theinternalwindings,duetoinertia,willcontinuetomaintaintheiroriginalstate.Asaresult,relativemovementoccursbetweenthecasingandthewindings,becomingthecauseofwindingdeformation.Dependingonthespecificconnectionbetweenthetransformerwindingsandthecasing,differenttypesofdeformationordisplacementmayoccurinthewindings.Ⅱ.TheexternalforceonthetransformeranddeformationcauseWhenatransformerissubjectedtomechanicalorelectromagneticforces,whetherthewindingsdeformandtowhatextenttheydeformareprimarilyinfluencedbytwofactors:①Theabilityofthetransformerwindingstowithstandtheimpactforce,whichmainlydependsonthematerial,structure,manufacturingprocess,andstressuniformityofthewindings.Ⅱ.Theexternalforceonthetransformeranddeformationcause②Thecharacteristicsoftheimpactforceappliedtothewindings,includingitsmagnitude,duration,frequency,mode,andrange.Theleads,taps,inter-windingconnections,intermediateconnections,tapconnections,internalweldedjoints,andgapsduetoinsufficientwindingorcompressioninthetransformerwindingsareallstructurallyweakpointsthatarepronetodeformation.Eventhetransformerofthesamefactoryandspecificationsmayvaryduetomanufacturingdeviations,safetyfactordeviations,andotherrandomprobabilities.Insummary,ifthemechanicalstrengthofatransformerisinsufficienttowithstandpowerfulmechanicalandelectromagneticforces,thewindingswillexperiencevarioustypesofdeformationanddisplacementfaults.Ⅱ.Theexternalforceonthetransformeranddeformationcause2.CausesofTransformerWindingDeformationCommontypesoftransformerfailuresinclude:suddeninternalshort-circuitfaultsinsidethetransformercausedbyexternalshort-circuitimpacts,inter-layerandinter-turnshort-circuitfaultscausedbythebreakdownofthemaininsulationofatransformerduetoovervoltage,andinsulationdamagecausedbypoorsealingofhigh-voltagebushingsresultinginmoistureingress,asshowninFigure3-27.Figure3-27

Transformerwithinter-layerandinter-turnshortcircuitfaultscausedbylightningstrikeⅡ.TheexternalforceonthetransformeranddeformationcauseThewindingdeformationtestisanecessaryitemforthetransformerduringfactorydelivery,handoveracceptance,andafterexperiencingshort-circuitaccidents.Whenatransformersuffersvariousshort-circuitfaultcurrentsduringoperation,alargeshort-circuitcurrentwillflowthroughthetransformerwinding.Undertheinteractionwiththeleakagemagneticfield,alargeelectrodynamicforcewillbegenerated.Atthistime,eachwindingwillbearhuge,unevenradialandaxialelectrodynamicforces,causingthecoiltobecomedeformedinashorttimeundertheeffectofheatingandelectrodynamicforce,andevenleadingtointerphaseshort-circuitsandwindingburnout.Ⅱ.TheexternalforceonthetransformeranddeformationcauseAdditionally,duringtransportationandinstallation,thetransformermaysuffercollisionimpactsthatwillcausemechanicaldisplacementanddeformationofthewindings,leadingtoserioustransformeraccidentssuchasinsulationdamage,windingshort-circuit,andburnout.Furthermore,theexistenceofdeadzonesorfailuretoactintheprotectivesystemwillalsocausethetransformertowithstandtheactionofshort-circuitcurrentsforalongtime,whichisoneofthereasonsforthedeformationofthewinding.Ⅱ.TheexternalforceonthetransformeranddeformationcauseExternalshortcircuitscausingthedeformationoftransformerwindingsisacommonfaultduringthetransformeroperation,seriouslythreateningthesafeoperationofthesystem.Thetransformeradoptssemi-hardcopper,self-adhesivetranspositionwire,windingcoilwithhardinsulationcylinder,andinnerandoutersupportbarsofencryptioncoiltoimprovetheanti-short-circuitabilityofthetransformer,whichisbasedontheconsiderationofimprovingtheanti-radialshort-circuitability.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetection1.PurposeofTransformerWindingDeformationTestThetransformerwindingisthemainpartoftransformeraccidents,andthepoorshort-circuitresistanceoftransformerwindingsisthemaincauseoftransformeroperationaldamage.Afterthetransformerwindingdeforms,itcanstilloperatenormallyforaperiodoftime.Sinceconventionalelectricaltestssuchasresistancemeasurement,ratiomeasurement,andcapacitancemeasurementaredifficulttodetectwindingdeformation,thisposesaseriousthreattothesafeoperationofthepowergrid.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionOntheonehand,thedeformedtransformeriscausedbychangesininsulationdistanceordamagetotheinsulatingpaper.Whenencounteringovervoltage,thewindingmayexperienceinter-layerorinter-turnbreakdown.Alternatively,underthelong-termworkingvoltage,insulationdamagegraduallyexpands,ultimatelyleadingtotransformerdamage.Ontheotherhand,afterthewindingisdeformed,itsmechanicalperformancedecreases.Whenitexperiencesasubsequentshortcircuitaccident,itcannotwithstandthetremendousimpactforceandmaysufferdamage.Therefore,testinganddiagnosingtransformersthathaveundergonemechanicalandelectromagneticforcesresultinginwindingdeformationisessential.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetection2.MethodsforDetectingTransformerWindingDeformationFornewlyinstalledtransformersandrepairedtransformers,itisgenerallynecessarytoconductwindingdeformationdetection.Currently,itiscommontousemethodssuchaspre-factoryinspection,post-installationinspection,routineinspectionsduringoperation,andcomprehensiveinspectionsafterfaults.Bymeasuringandanalyzingrelevantcharacteristicparameters,itispossibletodeterminewhethertherearedeformations,displacements,orotherabnormalphenomenainthewindings.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionAfterthedeformationoftransformerwindings,variousabnormalphenomenaareusuallyobserved.Manycharacteristicparameters,suchaselectricalparameters,physicaldimensions,geometricshapes,andtemperature,showsignificantdifferencescomparedtonormalconditions.Basedonthis,multiplemethodsfordetectingwindingdeformationhavebeendeveloped.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionAfterexperiencingashort-circuitimpact,thetransformerisgenerallyinspectedforitsinsulationconditionusingroutineelectricaltestitemsandinsulationoilanalysis.Theinspectionresultsindicatethatsometransformershavepassedtheelectricaltestsandinsulationoilanalysiswithinthespecifiedrangeofpreventivetestprocedures.However,duringtheinspectionofhangingcover,significantdeformationofthewindingsorseverelooseningofinsulationpadswasdiscovered.Thisindicatesthatroutineelectricalandoiltestsarenoteffectiveindetectingwindingdeformationdefectsintransformers.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionAlthoughtheinspectionofthehangingcoverisintuitive,itrequiresasignificantamountofmanpowerandresources,anditisstilldifficulttodetermineifthereisdeformationintheinnerwindings.Tocompensatefortheshortcomingsofroutineelectricalmethodsandwindingenclosureinspections,severalmaturedetectionmethodsarecommonlyusedfordetectingtransformerwindingdeformation.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetection(1)Short-circuitImpedanceMethodTheprincipleoftheshort-circuitimpedancemethodistomeasurethecurrentandvoltagevaluesinthetransformerwinding,calculatetheshort-circuitimpedancevalueofthewinding,andcomparethechangeintheshort-circuitimpedancevaluebeforeandafterthedeformationofthetransformerwinding.Basedonthechangeintheleakagereactancevalueinthetesttransformerwinding,thedeformationordisplacementofthewindingcanbedetermined.Theshort-circuitimpedanceofatransformerreferstotheequivalentimpedanceattheinputendofthetransformerwhentheloadimpedanceofthetransformeriszero.Itreflectstheinducedmagneticpotentialformedbytheleakagemagneticfluxbetweenthewindingsorbetweenthewindingsandtheoiltank.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionTheshort-circuitreactancecomponentofthetransformeristheleakagereactanceofthetransformerwinding.Atacertainfrequency,theleakagereactancevalueofthetransformerisdeterminedbythegeometricsizeofthewinding.Anychangeinthestructuralstateofthetransformerwindingwillinevitablycauseachangeintheleakagereactanceofthetransformer.Duringmeasurement,thehigh-voltagesideofthewindingisconnectedtothepowerfrequencyACsource,andthelow-voltagesideisshort-circuited.ThewiringprincipleisshowninFigure3-28.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionFigure3-28

Wiringdiagramfordeformationtestingoftransformerwindingusingtheshort-circuitimpedancemethodⅢ.PurposeandMethodsofTransformerWindingDeformationDetection(2)LowVoltagePulseMethodUndertheinfluenceofhigherfrequencyvoltage,themagneticpermeabilityofthetransformercoreisnearlythesameasthatofair.Thewindingitselfcanberegardedasapassivelineardistributedparameternetworkcomposedoflinearresistors,inductors,capacitors,etc.ItsequivalentcircuitisshowninFigure3-29,whereLrepresentsinter-layerinductance,Krepresentslongitudinalcapacitance,andCrepresentsgroundcapacitance.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionFigure3-29

EquivalentcircuitoftransformerwindingⅢ.PurposeandMethodsofTransformerWindingDeformationDetectionTheprincipleofthelowvoltagepulsemethodistoapplyastablelowvoltagepulsesignaltooneendofthetransformerwindingwhilerecordingthevoltagewaveformsattheterminalandotherterminalssimultaneously.Bycomparingtheexcitationandresponseinthetimedomain,amoreaccuratejudgmentcanbemadeabouttheconditionofthewinding.Whenthewindingofthetransformerundergoesdeformation,parameterssuchasinductanceandcapacitanceincorrespondingsectionswillchange.Applyingapulsevoltageexcitationattheinputendwillcausechangesintheresponseattheoutputend.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionThelowvoltagepulsemethodisappliedinon-sitetests,butitissusceptibletovariouselectromagneticinterferencesduringthetestingprocess,resultinginpoorrepeatability.Moreover,itisnotsensitivetofaultsinthefirst-endpositionofthewinding,makingitdifficulttodeterminethelocationofwindingdeformation.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetection(3)CapacitanceVariationMethodTheprincipleofthecapacitancevariationmethodisthateachwindingofatransformercanbeequivalenttoanetworkcomposedofresistance,capacitance,inductance,andotherelements.Theequivalentcapacitanceofthewindingdirectlyreflectstherelativepositionofthewindings,thewindingstothecore,thewindingstothetankandground,andthestructuralcharacteristicsofthewindings.Whenthetransformerismanufactured,thecapacitanceofeachwindingisrelativelyconstant.Aslongasthetransformerhasnotexperiencedshort-circuitimpacts,evenundertheinfluenceoftemperatureandhumidity,thecapacitancevariationisminimal.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionAfterthetransformerexperiencesashort-circuitimpact,ifthewindingisnotdeformedoronlyslightlydeformed,thechangeincapacitanceisalsosmall.However,ifacertainwindingisseverelydeformed,thecapacitancevariationwillbesignificant.Accordingtothe“PreventiveTestingRegulationsforPowerEquipment,”thetanoftransformerwindingsshouldbetestedeveryonetothreeyears.Duringtransformerhandoveracceptanceandpreventivetesting,thetanofeachwindingismeasured,andthecorrespondingcapacitancecanbecalculated.Therefore,basedonthechangesincapacitanceoftransformerwindings,itispossibletodeterminewhetherthewindingshaveundergonedeformation.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionThistestingmethodissimpleandconvenient.However,duetotheinherentscatterofthewindingcapacitances,ithaspoorsensitivitytofaultssuchasbulgesanddistortions.Itcanbeusedasasupplementarytestmethodfordetectingwindingdeformations.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetection(4)UltrasonicReflectionMethodTheprincipleoftheultrasonicreflectionmethodistoutilizeanultrasonicprobeplacedonthesurfaceofthetestedobjecttoemitultrasonicwavesatacertainfrequency.Theultrasonicwavespropagateinsidethetestedobjectinlongitudinalwavemode.Whenencounteringaninterfacebetweentwodifferentmedia,reflectionoccurs,andthewavesreturnalongacertainpathtobereceivedbytheultrasonicprobe.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionBymeasuringthetime,ittakesfortheultrasonicwavestobeemittedandreceived,thepropagationtimeintervaltoftheultrasonicwaveswithinthetestedmediumcanbeobtained.Fortransformerwindingsandthesteelwallsofthecasing,thedistancebetweeneachpointonthewindingsurfaceandthesurfaceoftheoiltankisaconstantvalue.Ifthereareabnormalfaultssuchasindentation,protrusion,ordisplacementofthewindings,thedistancewillchangeaccordingly.Bycomparingthemeasurements,thedeformationstatusofthewindingscanbedetermined.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionWhendetectingthedeformationoftransformerwindingsusingultrasonicwaves,theultrasonicprobeisplacedonacertainpositionofthesteelwallofthetransformercasing,andacouplingagent(butter)isusedtomaketheprobetightlycontacttheoutercasingofthetransformerandalignthecenteroftheprobewiththewindingtobemeasured.Undertheactionofasynchronoussignal,theemissioncircuitexcitestheultrasonicprobetoemitultrasonicwaves.Theultrasonicwavespassthroughthesteelwallandtransformeroilandarriveatthetransformerwinding.Reflectedwavesaregeneratedonitssurfaceandreturnedalongacertainpath.Similarly,theypassthroughthetransformeroilandthesteelwallofthetransformercasingandreachtheultrasonicreceivingprobe,generatingareceivingelectricalpulsesignal.Byprocessingwitharelatedcircuit,thetimettakenfortheultrasonicwavestopropagateandcompleteoneroundtripinthetransformersteelplateandoilcanbeobtained.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionTheadvantageofthismethodisthatitissimpletooperate,hasgooddirectnessandrepeatability.However,thedisadvantageisthattheresultsvarygreatlyinthepresenceorabsenceofoil,andthetestresultsareeasilyaffectedbytemperature.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetection(5)VibrationMethodTheprincipleofthevibrationmethodistouseavibrationsensorattachedtothetransformertanktomonitortheconditionofthewindingsandironcoreonline.Thecharacteristicvibrationvectorsofawell-performingtransformer(includingthespectra,powerspectra,energyspectra,etc.,ofthewindingandironcorevibrationsignals)areusedasreferenceindicators.Onceafaultoccursinthetransformerwinding,thechangesinthecurrentvibrationcharacteristicvectorswillbequicklyreflected.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionTheadvantageofthevibrationmethodisthatthetestingsystemisnotelectricallyconnectedtotheentirepowersystem,achievingonlinemonitoringsafelyandreliably.Itsdrawbackisthatthepowertransformercanexperienceshort-circuitfaultsatanytimeduringoperation.Ifafaultoccursintheinternalwindingofasuddenlyshort-circuitedtransformer,itwillresultincontactbetweentheenergizedwindingandtheoiltank,whichmayhavehighvoltage.Inaddition,transientinductioncanalsogeneratehighpotentialonthetransformerbody,affectingthesafetyoftestingequipmentandpersonnel.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetection(6)FrequencyResponseAnalysis(FRA)MethodTheworkingprincipleoftheFrequencyResponseAnalysismethodistodetecttheamplitude-frequencyresponsecharacteristicsofvariouswindingsofatransformeratdifferentfrequencies.Afterquantifyingthemeasurementresults,atransferfunctioncharacteristiccurveofthetransformerwindingisgenerated.Thisallowsforlongitudinalcomparisonsofthesametransformeratdifferentperiodsortransversecomparisonsofthetransformerofthesametype.Byassessingthedegreeofchangeintheamplitude-frequencyresponsecharacteristics,itispossibletodetermineifthereisdeformationinthetransformerwindings.Insimpleterms,afrequencyisappliedtotheendofthetransformerwinding,andtheresponseismeasuredattheotherend.Ifthereisasignificantdifferenceintheresponse,itindicatesthepresenceofdeformation;ifthedifferenceissmall,itindicatesgoodconsistency.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionAthigherfrequencies,thewindingsofatransformercanbeequivalenttoapassivelineartwo-portnetworkcomposedofdistributedparameterssuchascapacitanceandinductance.TheinternalcharacteristicsofthisnetworkcanbeexpressedasatransferfunctionH(j).Whenthestructureofthetransformerisfixed,therelationshipbetweentheparametersandfunctioncurvesofthetransformerwindingsisdetermined.Whenchangesoccurinternallyinthetransformer,thedistributedparametersofthewindingsalsochange,resultingincorrespondingchangesinthefunctioncurves.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionIfthewindingsdeform,thedistributedinductance,capacitance,andotherparametersinsidethewindingswillinevitablychange,causingthezerosandpolesofthetransferfunctionH(j)oftheequivalentnetworktochange.Asaresult,thefrequencyresponsecharacteristicsofthenetworkchange.Byestablishingthefunctionalrelationshipbetweentheinputexcitationandoutputresponseoftheinstrumentandplottingitpointbypoint,thetransferfunctioncharacteristiccurvethatreflectsthecharacteristicsofthetransformerwindingscanbeobtained.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionThetransferfunctionistheratiooftheoutputtotheinputofapassivetwo-portnetworkexpressedinLaplacetransformform.ThefrequencyresponsecharacteristicsrefertotherelationshipbetweenthetransferfunctionH(j)ofthenetworkandtheangularfrequencyundersinusoidalsteady-stateconditions.ThevariationoftheamplitudeofH(j)withisusuallyreferredtoasthemagnitude-frequencyresponsecharacteristic,andthevariationofthephaseofH(j)withisreferredtoasthephase-frequencyresponsecharacteristic.Ⅲ.PurposeandMethodsofTransformerWindingDeformationDetectionSweepfrequencydetectioninvol