永磁同步电机极对数,内阻,Ld,Lq,背板电动势常数的测量(权威版)

1IntroductionThevectorcontrol,alsoknownasthefield-orientedcontrol(FOC),ofapermanentmagnetsynchronousmotor(PMSM)isthealgorithmoftenusedintoday’sadvancedmotorcontroldrives.Suchadvancedmotorcontrolalgorithmsrequirethesettingofmotorelectricalparametersforitsproperfunctionality.ThisapplicationnotedealswiththemeasurementofelectricalparametersneededforvectorcontrolofPMSM.TheelectricalparametersareneededtosetthecurrentPIcontrollergainstogetthedesiredclosed-loopperformanceandforBEMFobserverconstants.Theproposedmeasurementtechniquesdetermineanumberofpolepairs,astatorresistance,synchronousinductances,andanelectricalconstantwithcommonmeasurementequipment.AsummaryofPMSMsensorlesscontrolandexplanationofmotorcontroltermscanbefoundin[1].2MotorparametersneededforPMSMFOCOneofthepossiblemethodstosetthePIcontrollergains,istocalculatethemfrommotorparameters.ThecurrentPIcontrollergainsintimedomainarecalculatedfromthemotorelectricalparameters[1];seethefollowingequations.FreescaleSemiconductorDocumentNumber:AN4680ApplicationNoteRev.0,02/2013PMSMElectricalParametersMeasurementby:ViktorBobek©2013FreescaleSemiconductor,Inc.Contents1Introduction................................................................12MotorparametersneededforPMSMFOC...............13Motorpolepairs........................................................33.1Background.....................................................33.2Guide.............................................................34Statorresistance.........................................................54.1Background.....................................................54.2Guide.............................................................55Synchronousinductances..........................................75.1Background.....................................................75.2Guide...........................................................116Back-EMFconstant................................................126.1Background...................................................126.2Guide...........................................................137Conclusion...............................................................148References...............................................................149AcronymsandAbbreviatedTerms.........................15Equation1Equation2Whereω0isthenaturalfrequencyofthecurrentclosed-loopsystem(loopbandwidth)andξisthecurrentloopattenuation.Therefore,thePMSMvectorcontrolalgorithmtypicallyrequiresthefollowingparameters.Table1.ElectricalparametersneededforFOCElectricalparametersneededforFOCcurrentPIcontrollergainscalculationParameterDimensionDescriptionUsedinconstantcalculationRs(Ω)ResistanceoneofthemotorphaseCurrentPIcontrollerBEMFObserverLd(H)d-axisinductanceofonemotorphaseCurrentPIcontrollerBEMFObserverLq(H)q-axisinductanceofonemotorphaseCurrentPIcontrollerBEMFObserverAdditionalelectricalparametersneededforFOCKe(V.s/rad)ElectricalconstantBEMFObserverpp(-)MotorpolepairsSpeedandpositionmechanical/electricalquantitiesrecalculationThespeedPIcontrollergainsintimedomainarecalculatedfromthemotor/loadmechanicalparameters;seeEquation1onpage1andEquation2onpage2Equation3Equation4Whereω0ωisthenaturalfrequencyofthespeedclosed-loopsystem(loopbandwidth)andξisthespeedloopattenuation.Therefore,thePMSMvectorcontrolalgorithmtypicallyrequiresthefollowingparameters.Table2.Mechanical/loadparametersneededforFOCspeedPIcontrollergainscalculationParametersDimensionDescriptionUsedinconstantcalculationJ(kg.m2)TotalmechanicalinertiaSpeedPIcontrollerBm(N.m.s)ViscousfrictioncoefficientMoreprecisespeedPIcontrollergainssettingThemeasurementofindividualelectricalparametersisdescribedinthefollowingchaptersofthisapplicationnote.MotorparametersneededforPMSMFOCPMSMElectricalParametersMeasurement,Rev.0,02/20132FreescaleSemiconductor,Inc.Motorpolepairs3.1BackgroundThemotorpolepairsparameterdefinesaratiobetweenmechanicalandelectricalquantities(mechanicalvselectricalrotorposition/speed).Themotorpolepairsrepresentthenumberofnorthandsouthsegmentstherotorcontains.3.2GuideTheequipmentrequiredtomeasuremotorpolepairsdependonthemethodusedformeasurement.•DCpowersupply•Three-phaseinverter,oscilloscope,handvelocitymeter,andacurrentprobe•Drivingmotor,oscilloscopeandavoltageprobeUsually,thenumberofthemotorpolepairsiswrittenonthelabelofthemotor.Ifthereisnoinformationregardingthenumberofpolepairs,itcanbedetermined.Seethefollowingsubsections.3.2.1MethodtodeterminelownumberofthepolepairsGuide:Thefollowingstepsdescribethemethodtodeterminethelownumberofmotorpolepairs.SeeFigure1.1.ConnectthephaseAwiretothepositivepotential(+)andphaseBandCtonegativepotential(-)ofthevoltagesource.2.Setacurrentlimitofthepowersupplytosuchalevelsothattheuserisabletorotatetheshaftmanually,andtherotorisalignedinthestableposition.Commoncurrentlimitisabout10%oftheratedmotorcurrent.Formorepowerfulmotor,thecurrentlimitislower.3.Drawaline/signforeverystablepositioninwhichtherotorisaligned.4.Numberofstablepositionsisequaltothemotorpolepairs.3MotorpolepairsPMSMElectricalParametersMeasurement,Rev.0,02/2013FreescaleSemiconductor,Inc.3Figure1.Methodforthedeterminationoflownumberofpolepairs3.2.2MethodtodeterminehighnumberofthepolepairItispossibletousetwomethodsfordeterminationhighnumberofpolepairs.Selectionofthemethoddependsonavailablemeasuringequipment.Anoscilloscopeisrequiredformeasurementinboththemethods•MethodA:acurrentprobeandaninverterusingVolt/Herzmethodtospinthemotorwithunknownparameters•MethodB:avoltageprobeanddrivingmotor,whichspinsthemotorGuideforMethodA:Thefollowingstepsdescribethemethodtodeterminethehighnumberofmotorpolepairs.1.SpinthemotorbyaninverterusingVolt/Herzmethodandsetthefrequencyinsuchawaythatthemotorwillspinataconstant,andpreferablyhigherspeed.2.Measurethephasecurrentfrequencyusingoscilloscopecurrentprobe.ThefrequencyofthephasecurrentmustbethesameasthatgeneratedbyVolt/Herzmethod.3.Measurethespeedofthemotorbysomehandvelocitymeter.Thespeedreadingmustbeconstant.4.Calculatethenumberofpolepairsusingtheequationgivenbelow.Theresultshouldbeveryclosetoanintegernumber.Equation5MotorpolepairsPMSMElectricalParametersMeasurement,Rev.0,02/20134FreescaleSemiconductor,Inc.Figure2.CurrentwaveformforthedeterminationofhighnumberofthepolepairGuideforMethodB:Thefollowingstepsdescribethemethodtodeterminethehighnumberofmotorpolepairs.1.Spinthemotorbyanexternaldrivingmotorataconstantspeed.2.Measurethegeneratedvoltagefrequency.3.Measurethespeedofthemotorbysomehandvelocitymeter.4.CalculatethemotorpolepairsusingEquation5onpage4.Statorresistance4.1BackgroundAresistanceofthestatorwindingRsisdefinedasaresistancebetweenaphaseterminalandthecenterofthewinding.Thewindingresistanceistemperaturedependent.Usuallytheresistancevalueat25°Corspecifiedtemperatureislistedinthemotor’sdatasheet.CalculateresistanceRatoperationaltemperaturet(°C)ofstatorwinding(ifthetemperatureisknown),usingtheresistancevaluemeasuredattemperaturet0(°C).Equation6whereαistheconstantdeterminedbythematerial(forcopper,α=0.004K-1)Equation7For50°Ctemperaturedifference,Rcanbecalculatedasgivenbelow.Equation84.2GuideTheequipmentrequiredtomeasurestatorresistancedependonthemethodusedformeasurement:•Digitalmultimeter•RLCmeter4StatorresistancePMSMElectricalParametersMeasurement,Rev.0,02/2013FreescaleSemiconductor,Inc.54.2.1DigitalmultimeterHighervaluesofstatorresistance(>10Ω)canbemeasuredbyadigitalmultimeter.Theusualstatorwindingconfigurationisthewye,sothefinalstatorresistanceishalfofthemeasuredresistance.Thefollowingfigureshowsthestatorresistormeasurementusingadigitalmultimeter.Figure3.Statorresistancemeasurementbyadigitalmultimeter4.2.2RLCmeterLowervaluesofstatorresistancecanbemeasuredbyanRLCmeter,forexampleMOTECHMT4080A.Thefour-terminalmeasurementreducestheeffectofthetestleadresistance.SeeFigure4.Usualmeasurementrangeisbetween(10mΩ–10kΩ).Beforethemeasurement,calibratetheRLCmeter(open-circuit,andshortcircuit).Theusualstatorwindingconfigurationisthewye,sothefinalstatorresistanceishalfofmeasuredresistance.StatorresistancePMSMElectricalParametersMeasurement,Rev.0,02/20136FreescaleSemiconductor,Inc.Figure4.Four-terminalmeasurementschematicSynchronousinductances5.1BackgroundThesynchronousinductancesofInteriorPermanentMagnetSynchronousMotor(IPMSM)windingaredifferent(Ld<Lq),becauseoflowerreluctanceinq-axis.ThesynchronousinductancesofSurfaceMountedPermanentMagnetSynchronousMotor(SMPM)motorarealmostequal,becausethepermanentmagnetsaresurfacemountedandreluctanceisthesameineveryposition,thatis:μPM≈μair→Ld≈Lq,whereμPMistherelativepermeabilityofthepermanentmagnet,andμairistherelativepermeabilityoftheair.Seethefollowingfiguredepictingthereluctancepathsofd-andq-axisinIPMSM.Figure5.Reluctancepathsind-andq-axisofIPMSM5SynchronousinductancesPMSMElectricalParametersMeasurement,Rev.0,02/2013FreescaleSemiconductor,Inc.7Inpractice,magneticcircuitsaresubjecttosaturationasthecurrentincreases.Especially,whencurrentIqisincreased,thevalueofLqisdecreased.SinceIdismaintainedtozeroornegativevalue(demagnetizing)inmostoperatingconditions,saturationofLdrarelyoccurs.ThefluxlinkageλmandLdaresubjecttoarmaturereaction.Seethefollowingfigure.Figure6.TypicalinductancecharacteristicofPMSMNOTEMajorityoftheapplicationsusesinglevalue;howeverthedeterminationofinductancesdependsonselectedworkingconditions.Inordertomeasuresynchronousinductance,theusersmustmaintainbalancedthree-phasecurrentcondition.WhentherotorisalignedwiththecenterofphaseAwinding,Ld(Lq)canbederivedfromthemeasuredequivalentinductanceLofthecircuit,asshowninthefollowingfigure.SynchronousinductancesPMSMElectricalParametersMeasurement,Rev.0,02/20138FreescaleSemiconductor,Inc.Figure7.InductancemeasurementcircuitDependingontherotorangleθel,itispossibletomeasureinductanceind-axisorq-axis,whereListhetotalinductanceforserial-parallelconnectionofthestatorwinding:Equation9Equation10WhentherotorisalignedwithphaseA(θel=0°)andlocked,thenthecurrentresponseisfirstorderRLcircuit.Equation11WhereτisatimeconstantofthecircuitEquation12Aftermeasuringτ,theinductanceLdcanbecalculatedasfollows.Equation13SynchronousinductancesPMSMElectricalParametersMeasurement,Rev.0,02/2013FreescaleSemiconductor,Inc.9Figure8.EquivalentphasemodelofPMSMind/qaxisforalockedrotorshaftSinceVd=(2/3)V,Vq=0,andIisthesameasIdandthetotalresistanceofthecircuitis(3/2)Rs,theequivalentinductanceseenfromthesupplysourceis(3/2)Ld.SimilarexplanationcanalsobeappliedtoLqwhentherotorislockedat90°electrical.5.1.1Q-axisalignmentTomeasuretheinductanceinq-axiswithoutaninverter,analignmenthastobedoneintotheq-axis.Thealignmentintod-axisisdonebyphaseAconnectedtothepositivepotential(+)andphaseBandCaregrounded(-).Itcanbeseenfromthefollowingfigurethat90°electricalshiftedpositioniswhenphaseBterminalisconnectedtothepositivepotential(+)ofthevoltagesource,phaseCisgrounded(-),andphaseAisfloating(NC).Figure9.Explanationofq-axisalignmentSynchronousinductancesPMSMElectricalParametersMeasurement,Rev.0,02/201310FreescaleSemiconductor,Inc.5.2GuideTheequipmentrequiredtomeasureinductancesinq-axisandd-axisareasfollows.•DCpowersupply,oscilloscope,currentandvoltageprobeFigure10.Setuptomeasureinductanceinq-axisGuidetomeasured-axisinductance(non-saturatedinductancemeasurement):Followthestepsgivenbelowtomeasurethed-axisinductanceLd.1.AligntherotortophaseA.PhaseAisconnectedtothepositivepotential(+)andphaseBandCaregrounded(-).2.Locktherotorshaft.3.Applynegativestepvoltage.PhaseAisgrounded(-)andphasesBandCareconnectedtothepositivepotential(+).Usuallevelofthecurrentisabout10%oftheratedphasecurrent.4.Measurethestepresponseofthecurrentbyacurrentprobe.SeeFigure11.5.CalculateinductanceLd.SynchronousinductancesPMSMElectricalParametersMeasurement,Rev.0,02/2013FreescaleSemiconductor,Inc.11Figure11.CurrentstepresponsewaveformGuidetomeasureq-axisinductance:Followthestepsgivenbelowtomeasuretheq-axisinductanceLq.1.Aligntherotortotheq-axis.ConnectthephaseBterminaltothepositivepotential(+)ofthevoltagesourceandphaseCisgrounded(-).PhaseAterminalisfloating.2.Locktherotorshaftfirmlybecausecurrentstepresponseinq-axiscreatestorque.3.Generateacurrentstepresponseinthisconfiguration:phaseAisconnectedtothepositivepotential(+)ofthevoltagesourceandphasesBandCaregrounded.4.CalculateinductanceLqinthesamewayasLd.Back-EMFconstant6.1BackgroundTheback-EMF(BEMF)constant(fluxlinkageofthePMdenotedbyλm)canbeobtainedbymeasuringtheno-loadlinevoltageVpkofthemotorwhileitisdriventhroughtheshaftataconstantspeedofωm.TheconstantgivesaratiobetweenBEMFvoltageandtheangularelectricalfrequency/speed.6Back-EMFconstantPMSMElectricalParametersMeasurement,Rev.0,02/201312FreescaleSemiconductor,Inc.Figure12.Three-phasemeasurementoftheBEMFconstant6.2GuideTheequipmentrequiredtomeasuretheBEMFconstantarelistedbelow.•Oscilloscopeandatleastonevoltageprobe•DrivingmotororhanddrillmachineThestepsgivenbelowmustbefollowedtodeterminetheBEMFconstant.1.Spinthemotorbyanexternaldrivingmotororahanddrillmachineataconstantspeed.Higherspeedispreferred,becausethevoltagemeasurementerrorislower.2.One-phasemeasurement:Measurethegeneratedphasevoltage(betweenonephaseterminalandneutralpointofthemotor).Usuallytheneutralpointisnotaccessible;thenmeasuretheline-to-linevoltage.Three-phasemeasurement:Iftheneutralpointisnotaccessible,it’spossibletocreatetheartificialneutralpointfromallthreevoltageprobeclipsconnectedtogether.SeeFigure13.3.CalculatetheBack-EMFconstantaccordingtoEquation14onpage13.Singlephasemeasurement(line-to-linevoltagemeasurement):Equation14Three-phasemeasurement(phasevoltagemeasurement):Equation15Back-EMFconstantPMSMElectricalParametersMeasurement,Rev.0,02/2013FreescaleSemiconductor,Inc.13Figure13.Three-phaseoscilloscopemeasurementoftheelectricalconstant7ConclusionTheapplicationnotesummarizesmethodsfordeterminingelectricalparametersofPMSM.Thepreciseparametersdeterminationisneededforsensorlesscontrolapplicationsanddesiredclosed-loopperformance.Theproposedmeasurementtechniquesdeterminethenumberofpolepairs,thestatorwindingsresistance,thesynchronousinductances,andtheelectricalconstantwithcommonmeasurementequipment.Theparametersaredeterminedusingmeasuredappliedvoltagesandrespondingcurrents.Asingle-phaseDCvoltagepowersupplycanbeusedtodeterminethesynchronousinductancesofthree-phasePMSMwithsufficientaccuracy.8References1.DRM110:SensorlessPMSMControlforanH-axisWashingMachineDrive,availableonfreescale.com.2.MOTECH4080AOperationManual,availableatmotech.com.twConclusionPMSMElectricalParametersMeasurement,Rev.0,02/201314FreescaleSemiconductor,Inc.9AcronymsandAbbreviatedTermsThefollowingtablecontainsacronymsandabbreviatedtermsusedinthisdocument.Table3.AcronymsandAbbreviatedTermsTermMeaningd-axisDirectaxisfFrequency(Hz)IPMSMInteriorPermanentMagnetSynchronousMotornMechanicalspeed(rpm)NCNotConnectedPMSMPermanentMagnetSynchronousMotorq-axisQuadratureaxisSMPMSurfaceMountedPermanentMagnetSynchronousMotorθelElectricalrotorpositionμAirRelativepermeabilityoftheairμPMRelativepermeabilityofthepermanentmagnetAcronymsandAbbreviatedTermsPMSMElectricalParametersMeasurement,Rev.0,02/2013FreescaleSemiconductor,Inc.15HowtoReachUs:HomePage:www.freescale.comWebSupport:http://www.freescale.com/supportUSA/EuropeorLo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Introduction MotorparametersneededforPMSMFOC Motorpolepairs Background Guide Methodtodeterminelownumberofthepolepairs Methodtodeterminehighnumberofthepolepair Statorresistance Background Guide Digitalmultimeter RLCmeter Synchronousinductances Background Q-axisalignment Guide Back-EMFconstant Background Guide Conclusion References AcronymsandAbbreviatedTerms