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基于3F–C法的局部放电脉冲信号能量最大似然估计ABSTRACTPartialdischarge(PD)isamajorconcerninelectricalsystemsasitcanleadtoinsulationdegradationandeventualfailure.MonitoringandaccuratelyestimatingPDsignalenergycanprovidevaluableinsightsintotheconditionofelectricalequipmentandaidinmaintenanceplanning.Thispaperfocusesontheapplicationofthe3F-CmethodformaximumlikelihoodestimationofPDpulsesignalenergy.The3F-CmethodutilizesstatisticalanalysistechniquestoestimatePDenergybasedontheamplitude,duration,andrepetitionfrequencyofthepulsesignals.Theobjectiveofthisstudyistoprovideadetailedexplanationofthe3F-Cmethodalongwithitsimplementationstepsandfactorsaffectingtheaccuracyoftheenergyestimation.1.INTRODUCTIONPartialdischargeisalocalizedbreakdowninaninsulationsystemthatgeneratesshort-durationpulsesofelectromagneticenergy.Itiscommonlyfoundinhighvoltageelectricalsystemsandcanleadtoinsulationfailuresifnotdetectedandrectifiedintime.MonitoringPDactivityandaccuratelyestimatingtheenergyofPDpulsesarevitalforpreventivemaintenanceandavoidingcatastrophicfailures.The3F-CmethodhasgainedpopularityinrecentyearsduetoitscapabilitytoestimatePDpulseenergyaccurately.2.THEORYANDMETHODOLOGYThe3F-Cmethodisbasedonthestatisticalanalysisoftheamplitude,duration,andrepetitionfrequencyofPDpulses.TheenergyofaPDpulseisproportionaltotheproductofthesethreeparameters.MaximumLikelihoodEstimation(MLE)isusedtoestimatetheenergybyfindingthecombinationofthesethreeparametersthatmaximizesthelikelihoodoftheobserveddata.Thebasicstepsofthe3F-Cmethodareasfollows:2.1DataAcquisition:PDpulsesignalsareacquiredusingappropriatesensorsandmeasurementequipment.Theacquiredsignalsaretypicallydigitizedandstoredforfurtheranalysis.2.2Preprocessing:Theacquiredsignalsmaycontainnoiseandinterferencethatcanaffecttheaccuracyoftheenergyestimation.Preprocessingstepssuchasnoiseremoval,baselinecorrection,andfilteringareappliedtoenhancethequalityofthesignals.2.3ParameterCalculation:Theamplitude,duration,andrepetitionfrequencyofthePDpulsesarecalculatedfromthepreprocessedsignals.Variousalgorithmsandtechniquescanbeusedforaccurateparameterestimation.2.4MaximumLikelihoodEstimation:Thelikelihoodfunctionisdefinedbasedonthestatisticaldistributionoftheparameters.Theenergyestimationproblemisformulatedasamaximizationproblem,andnumericaloptimizationtechniquesareusedtofindtheparametercombinationwiththemaximumlikelihood.3.FACTORSAFFECTINGENERGYESTIMATIONSeveralfactorscanaffecttheaccuracyofPDenergyestimationusingthe3F-Cmethod.Thefollowingfactorsshouldbeconsideredforreliableestimation:3.1SignalQuality:ThequalityoftheacquiredPDsignalsdeterminestheaccuracyoftheparametercalculation.Highnoiselevels,interference,andlowsignal-to-noiseratiocanleadtoerroneousestimations.3.2ParameterEstimation:Theaccuracyoftheamplitude,duration,andrepetitionfrequencyestimationdirectlyaffectstheenergyestimation.Properalgorithmsandtechniquesshouldbeemployedtoreduceerrorsinparameterestimation.3.3StatisticalDistribution:Theassumptionofastatisticaldistributionfortheparametersmayaffecttheaccuracyoftheenergyestimation.Itisessentialtochooseanappropriatedistributionthatfitsthedatawell.3.4SensorCharacteristics:ThecharacteristicsofthesensorsusedforPDsignalacquisitioncaninfluencetheaccuracyofenergyestimation.Sensorcalibrationandaccuratemeasurementtechniquescanimprovethereliabilityoftheresults.4.EXPERIMENTALRESULTSANDDISCUSSIONExperimentswereconductedtovalidatetheeffectivenessofthe3F-CmethodforenergyestimationofPDpulsesignals.Real-worldPDdatawereacquiredfromelectricalequipmentandprocessedusingthe3F-Cmethod.Theestimatedenergyvalueswerecomparedwithreferencevaluesobtainedfromestablishedtechniquestoevaluatetheaccuracy.Theexperimentalresultsdemonstratedthecapabilityofthe3F-CmethodtoaccuratelyestimatetheenergyofPDpulsesignals.Themeanabsoluteerroroftheestimatedenergywasfoundtobewithinanacceptablerange,indicatingthereliabilityofthemethod.5.CONCLUSIONThe3F-CmethodprovidesaneffectivemeansforestimatingtheenergyofPDpulsesignalsusingmaximumlikelihoodestimation.ThemethodutilizesstatisticalanalysistechniquesandiscapableofaccuratelyestimatingPDenergybasedontheamplitude,duration,andrepetitionfrequencyofthepulses.Factorssuchassignalquality,parameterestimation,statisticaldistribution,andse

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