译文原文

AnalysisofRelationshipBetweenAbnormalCurrentandPosition

DetectionErrorinSensorlessControllerforInterior

Permanent-MagnetBrushlessDCMotors

Dong-MyungLee1andWoo-CheolLee2

SchoolofElectronicsandElectricalEngineering,HongikUniversity,Seoul121-791,KoreaDepartmentofElectricalEngineering,HankyongNationalUniversity,Gyeonggi-do456-749,Korea

Wehaveanalyzedthecharacteristicsofterminalvoltagesusedtodetectrotorpositionininteriorpermanent-magnet(IPM)brushlessDC(BLDC)motorsinsensorlesscontrolbyemployingatwo-phaseconductionmethod.Wefoundthatadetectedzerocrossingpoint(ZCP)oftheopenphasevoltageadvancestherealrotorpositionduetoadditionalvoltagecomponentscausedbyvariationofinductancewithrotorposition.Weconcludethattheamountofpositionerrorisrelatedtorotorsaliency,load,andmotorspeed.Wealsopresenttherelationshipbetweenabnormalcurrentsandamountofpositionerrorsinthesensorlesscontrollerbyusingsimulationsthattakeintoaccountadditionalvoltagesinourmodelofterminalvoltagesandmotorneutralvoltageaswellasexperimentswithapositionsensor.WeverifiedthevalidityofouranalysisonIPMmotorshavingvariousmotorparametersundersensorlesscontrol.IndexTerms—Advanceangle,interiorpermanent-magnetmotor,positiondetectionerror,sensorlesscontrol.

I.INTRODUCTION

R

ECENTLY,variablespeeddrivingsystemshavebeenwidelydevelopedandadoptedinvariousareassuchashomeappliancesandautomobiles.Thisisduetohighdemandonenergysavingandnoisereductionaswellasthankstotechnologyadvancesinthepowerelectronicsarea,especiallyinvertersystems.BrushlessDC(BLDC)motors,whichhavehigherefficiency,biggertorqueinlow-speedrange,andlessnoisethanothermotorssuchasinductionmotors,arewidelyusedintheseapplications.BLDCmotorscanbeclassifiedintotwocategoriesassurfacemountedpermanent-magnet(SPM)BLDCmotorsandinteriorpermanent-magnet(IPM)BLDCmotorsbyhowmagnetsareinstalledintherotorcore.Here-after,theyarecalledasIPMandSPM,respectively.SensorlesscontrolofBLDCmotorsisdemandedforlow-costdrivingsys-temsanditisinevitabletooperatemotorsinsevereoperationenvironmentwherepositionsensorscannotbeinstalledsuchasinsideacompressor.ManyapproachestosensorlesscontrolforBLDCmotorshavebeenproposed[1]–[6].Also,severalresearchershavereportedaboutmotordesignconsiderationstoimprovetheabilityofpositiondetectionandcorrectionoffaultscausedbypositiondetectionerror[7],[8].BLDCmotorshavingatrapezoidalbackelectromotiveforce(EMF)areusu-allysuppliedbyrectangularcurrentsconducting120inoneelectricalcycle,whichissocalled120ortwo-phaseconduc-tionmethod.Inthisscheme,onemotorphaseisnotenergized,andtheterminalvoltage,whichcontainsinformationoftheEMFoftheopen-phase,isusedfordetectingrotorpositionbysensingthezerocrossingpoint(ZCP)ofterminalvoltagewithahalfofDClinkvoltage,.InthecaseofSPMs,theZCPofterminalvoltageisaccordancewiththatofEMFunderidealconditionssuchasnodelayinsensingcircuits.

AnIPMisattractiveforhigh-speedoperationcomparedwithSPMsbecauseofabsenceofguidecansusedinSPMstoavoidmagnetsflyingawayfromrotorsbyacentrifugalforce.Inaddi-tion,IPMscangenerateareluctancetorquebenefitedfromtherotorsaliencybutthischaracteristiccausessomeerrorinde-tectingrotorpositiongettingfromtheZCPofterminalvoltage.References[9]and[10]havereportedthatthepositiondetec-tionerrorinIPMsisrelatedtorotorsaliencyandcurrents.How-ever,resultscausedbythepositiondetectionarenotdiscussedexceptdevelopedtorqueormotorefficiency.Therelationshipbetweenthepositionerrorandmotorspeedhasnotbeenexam-ined.Therefore,thispaperpresentsthattheamountofpositiondetectionerrorisvariedbyrotorsaliencyandloadconditionaswellasmotorspeed,andanalyzesunexpectedorunwantedabnormalcurrentcausedbyanexcessivelyimposedadvanceangle.SimulationsandexperimentsusingIPMshavingvariousparametershavebeencarriedouttodemonstratethevalidityoftheanalyses.

II.SYSTEMMODELINGWITHTRAPEZOIDALBACKEMFSFig.1showstwotypicaltypesofBLDCmotors,(a)SPMand(b)IPM.Fig.1(b)showsanIPMfeaturingarigidstructurewithmagnetsinstalledinsideoftherotorcore.ThestateequationofanIPMcanbegivenas

(1)

andrepresentthewhereisaderivativeoperator,

EMFs,andandarephasecurrents.and

aretheselfinductanceofphaseA,B,andC,respectively.

andaremutualinductances.IncaseofanIPM,the

motorinductancesarethefunctionoftherotorposition,becausetheeffectivelengthofairgapisvariedwiththerotorposition.

DigitalObjectIdentifier10.1109/TMAG.2008.923203

Colorversionsofoneormoreofthefiguresinthispaperareavailableonlineathttp://ieeexplore.ieee.org.

0018-94/$25.00©2008IEEE

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Fig.1.BrushlessDCmotors(a)SPM,and(b)IPM.

Fig.2.ConfigurationofsensorlesscontrollerforIPMmotorsanditsanalyticmodel.V;V;V:TerminalvoltagebasedonDClinkneutralpointV.V;V;V:PhasevoltagebasedonV.V:MotorneutralvoltagebasedonDClinkneutralpotential.

In(1),thederivativetermsothat(1)canbewrittenas

isequivalentto,

(2)

where

(3)

Fig.3.EMFwaveformsandswitchingsignalscorrespondingtosixoperationmodes.

Thecomponentsofthematrixareasfollows:

employstheschemethatdetectsrotorpositionbyusingtheter-minalvoltageofopen-phaseasillustratedinFig.2.Themea-sureterminalvoltagecomparingwithlevelofisusedfordetectingtherotorposition.InFig.3,mode1starts30afterdetectingZCPofA-phaseEMFinmode6.Toutilizeareluc-tancetorqueandtakeintoaccountthebuiltuptimeformotorcurrentsinhighspeedoperation,socalledadvanceangleisap-plied.Inthisstudy,anadvanceangleisdefinedastheangledif-ferentbetweenthestartingpointofmotorcurrentshownasandstartingpointofflatareaoftheEMFshownas.There-fore,Fig.3showstheconditionofzeroadvanceangle,andifcontrollercommandsmodechangejustafterdetectingtheZCP,whichmeanstheadvanceangleis30.Intwo-phaseconduc-tionmethod,inordertoregulatemotorcurrents,oneoftwoconductingphasesissuppliedbyPWMandtheotherphaseisenergizedwithoutswitching.Inotherwords,themotorspeedortorqueiscontrolledwiththevarianceofthePWMduty.ThedashedsectionofFig.3,whichisinthesecondhalfperiod,rep-resentsPWM,TheinvertersystemcandoPWMeitherinthefirsthalforsecondhalfperiod(hereafterFHPandSHP).ThisstudyusesPWMinSHP.

Fig.4(a)and(b)showsameasuredEMFandacalculatedEMFfromananalyticalsimulationmodel,respectively.AsshowninFig.1(b),amotorforthisresearchhas24slots.Underidealconditions,theEMFhasatrapezoidalwith120flatarea.

(4)

whereistheelectricalangleofrotorpositionrelativetophaseA,andisanangularvelocity.,and.andrepresent-axisinductance,and-axisinductance,respectively,andisaleakageinductance.Fig.2showstheconfigurationofsensorlesscontrollerforIPMmotorswiththeanalyticmodelandnotationsusedinthisanalysis.

TheDClinkhasvirtualgroundnotatedas.Fig.3showsEMFsandgatesignalscorrespondingtosixoperationalmodesdividedinto60inonecycle.Themotorspeedortorqueisreg-ulatedbymotorcurrentsconductedduring120withregula-tionofpulsewidthmodulation(PWM).Amongmanymethodsforthesensorlesscontrolusing120conduction,thisresearch

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Fig.5.Pathofmotorcurrentsduringmodetransitionfrom(a)mode5to(c)mode6through(b)freewheelingperiod.

Fig.6.Terminalvoltagewaveformsofopenphaseinmode6fordetectingmotorpositionwithPWMduring(a)FHPand(b)SHP.

Fig.4.EMFwaveformsfrom(a)measurement,and(b)analyticmodel.

However,duetosloteffectsinmotors,theactualEMFhasvoltageripplesasshowninFig.4.ThemeasuredEMFshows15%slotripplewith11thharmonics.Therefore,theshapeofEMFscanbemodeledassummationofatrapezoidalandtheharmonicsaslistedin

%

ofopenphasewithPWMdoneinthe(a)FHP,or(b)SHP,re-spectively.AsillustratedinFig.3,themotorcurrentisregulatedbyPWMdoneinSHPinthisstudy,andtheterminalvoltages,

,andofaSPM,inmode6afterfreewheelingforthe

andareturnedoncanbeexpressedascasethat

(6)

Incalculating(6),motorneutralvoltage,

usingtheconditionsand

,iscalculatedby

(7)

Inmode6,Fig.3showsthatastheEMFshavethesamemagnitudewithdifferentsign,sothatin(6)be-comeswhenslotripplesareneglected.IncaseswherePWMisoff,i.e.,isoff,thecurrentisfreewheelingthrough

,sothatand.A-phaseter-the

minalvoltageforthiscaseappearsas(8)

(5)

where

constant.

isarippleangle,and

representsaspeed

III.MOTORTERMINALVOLTAGE

A.OpenPhaseTerminalVoltageofSPMMotors

Forsimplicityandbetterunderstanding,terminalvoltagesofSPMareinvestigatedinthissectionbeforeconsideringeffectscausedbythevariationofinductanceaccordingtorotorpo-sitionwhichexistsinIPMmotors.Inthisstudy,theterminalvoltagesofA-phaseinmode6areusedforexplanation.Fig.3showsthatinmode6A-phasebecomesopen-phaseandtheter-minalvoltageofA-phasecrossingzeropointinformstherotorposition.Inmode5,andswitchesareconductingasshowninFig.5(a).Whenmode5ischangedtomode6,isturnedoffandisswitchedon.WhileA-phasecurrentisfreewheelingthroughdiode,theterminalvoltageofA-phaseisclampedto.AfterA-phasecurrentdecreasestozero,theA-phasebecomesopen-phase,whichenablesustoshowtheEMFofA-phase.Fig.6showstheterminalvoltage

(8)

Usingtheaboveanalysis,theterminalvoltagesforopenphaseaccordingtoPWMperformedineitherfirstorsecondhalfpe-riodarelistedinTableI.

B.OpenPhaseTerminalVoltageofIPMs

Fig.7showstheshapedifferenceoftheterminalvoltagefor(a)SPM,and(b)IPM.IncaseofSPM,neglectingslotripples,theZCPofEMFandthatofopenphaseterminalvoltageareidenticaltoeachother.However,thatinanIPMshowsdifferentcharacteristics.AsillustratedinFig.7(b),theZCPofterminalvoltageforanIPMandthatforanEMFdoesnotoccuratthesametime.TheZCPofvoltageadvancestheZCPofEMF.ThishappensbecauseinductancesofIPMvaryaccordingtotherotorposition.Inthisstudy,theangledifferencebetweentheZCPof

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TABLEI

TERMINALVOLTAGESOFOPENPHASECORRESPONDINGTO

PWMPERFORMEDINFHPORSHP

TABLEII

ADDITIONALVOLTAGESAPPEARINGINTERMINALVOLTAGESOF

OPENPHASEINIPMMOTORS

Inmode6,,and,sothatthefirsttermin(12)becomeszerobutthesecondterm

isnotzero.ThesecondtermisoneofthevoltagedifferencesappearinginterminalvoltageinIPMs.Thisadditionalvoltagereflectingthederivationinterminalvoltageisdefinedas.Inaddition,thereexistsanotherterminanopenvoltageas

in(9).InSPMwithconditionthat,andnotedas

,theopenphasevoltageisconsideredas

incalculating(6).However,thatinIPMshasthefollowingform

:byusing(1)withthecondition

(13)

TableIIsummarizestheadditionalvoltagecomponents,

and,existedinterminalvoltagesinanopen-phaseofIPMs.InmodelingforvoltagesinIPMs,thereisonemorefactortobeconsidered,whichistheneutralvoltageofmotors,.TheforSPMiscalculatedas(14)butthatforIPMis

forIPMshasthatisdifferent.Equation(15)expressing

notshowninforSPMs

(14)(15)

Theneutralvoltageofmotor,,forSPMisobtainedusingtherelationbetweenterminalvoltagesandphasevoltagesasshownin(16)withconditionsthat

(16)

TheconditionthatissatisfiedinIPMsaswell.However,inIPMhastheformnotbut

,sothat,whichrepresentstheamountof

voltagevariationinthemotorneutralvoltagecorrespondingtothemotorposition,appearsintheneutralvoltageofIPMs,andusingaboveconditionsthistermcanbeexpressedas

(17)

where(11)

Afterrearrangingthederivativetermsin(11),itgives

(12)

Authorized licensed use limited to: CHONGQING UNIVERSITY. Downloaded on March 21,2010 at 11:14:18 EDT from IEEE Xplore. Restrictions apply. Fig.7.Zerocrossingpointofterminalvoltagein(a)SPMand(b)IPM.

EMFandthatofterminalvoltageisdefinedaspositiondetectionerrorasshowninFig.7(b).

ComparedwiththevoltageinopenphaseforSPMshownin(6),thatforIPMhasformofthefollowingequation,inwhich

andrepresentanadditionalvoltagecomponentinEMFandthatinterminalvoltagevariedwithrespecttothemotorposition,respectively

(9)

Amongadditionalcomponents,andiscalcu-latedusingtheLmatrixexpressedin(1).Incalculating(7)foropenphasevoltageinSPMs,followingconditionissatisfied

(10)

Ontheotherhand,sincethetermofsummationofmotorphasevoltageitcanbewrittenas

existsinIPMs,theisnotbut

2078IEEETRANSACTIONSONMAGNETICS,VOL.44,NO.8,AUGUST2008

Fig.8.Measuredcurrentwaveformsundercontrolwith(a)advanceangle=20and(b)advanceangle=30.

Fig.9.Terminalvoltageprofile(100V/div.,2ms/div.)anditsphasecurrentwaveform(1A/div.)withadvanceangle=28,andload=0:820N1mat3600RPM.

IV.POSITIONDETECTIONERRORSINIPMMOTORSA.EffectofExcessiveAdvanceAngle

Fig.8showsmeasuredphasecurrentwaveformsundersen-sorlesscontrolwithdifferentadvanceanglesas(a)20and

showsthecurrent(b)30.Fig.8(b)foradvanceangle

flowingintheoppositedirectionafterthefreewheelingshowninadottedline,andthiscurrentiscalledanabnormalcur-rentinthisstudy.EventhoughthereexistabnormalcurrentsasshowninFig.8(b),theirmagnitudeissmallandtheshapeisalmostrectangular.Therefore,theoutputsofIPMssuchasrevolutionspeedandtorquemaynotbeseriouslyaffectedfromunexpectedcurrents.However,operatedunderotherconditionswithIPMshavingdifferentmotorparameters,thephasecurrentmayhaveanexcessivelylargenegativecurrentandbigover-shootsasshowninFig.9.TheabnormalcurrentsinFig.9arecausedbythepositiondetectionerror,notbythemalfunctionofcontrol.Thefollowingsectionwillexplaintherelationbe-tweentheabnormalcurrentandpositiondetectionerror.TheopenphasevoltagelistedinTableIIinmode6fordetectingZCPofA-phaseEMFcanberewrittenas

Thetermin(20)canbeexpressedas(21)withsubstitutingtermsofandwithcomponentsin(4)

(21)

Equation(21)showsthatisaffectedbytheseverityofmotorsaliency,motorspeed,rotorposition,andmotorcurrent.The

intheequationrepresentsthemagnitudeofloadcurrent

torquesothat(21)showsthatthepositiondetectionerrorbe-comeslargerforhigherspeedandaheavierload.Here,repre-sentsanelectricalangleofEMFandithasarangefrom30to30inmode6.Hence,hasarangeof–withthemaximumvalueatwhichistheZCPoftheEMF.B.ExperimentsandSimulationstoVerifythePositionDetectionErrorinIPMs

Inordertoevaluatethemagnitudeoftherotordetectioner-rorsofIPMs,experimentsusingapositionsensorandsimula-tionsforthesensorlesscontrollershavebeencarriedout.Forsimulations,appliedvoltagesaremodeledcorrespondingtothestatusofPWM.Duringthefreewheelingperiod,terminalvolt-ordependingonthedirectionagesareeitherof

ofphasecurrents,andthevoltageslistedinTableIIareusedincalculatingtheopen-phasevoltagesafterthefreewheelingactionsareterminated.Motorphasecurrentsareobtainedby

forIPMexpressedin(15).usingtheterminalvoltagesand

Insimulations,thevoltagelevelforinverteroutputsarechosen

orinsteadoforzero.Therefore,zeroas

voltagelevelinsimulationresultsisequivalenttolevelshowninexperimentalresults.Anencoderisusedfordetectingmotorposition,andthemotorspecificationforthisverification

V/(rad/s),mH,andmH.is

Fig.10showsthemeasuredterminalvoltageandaphasecurrent.Inthisexperiment,PWMdoneinFHPwith25ad-vanceangleiscommanded,i.e.,PWMstarts5aftertheZCPoftheEMF.ThetimedifferencebetweentheZCPoftheterminal

,voltage,whichisshownasadottedlinethatintersects

andthestartingpointofthephasecurrentis500s.SincethemodechangeiscarriedoutbasedontheinformationfromanencodernotfromtheZCPoftheterminalvoltage,thetimedif-,illustratedinFig.10caninformhowmuchference,

(18)

whereistotalsummationofadditionalvoltagesexistingin

open-phase.Byusing,andlistedinTableII,cor-respondingtoeachmodecanbecalculated.Inmode6,thefol-lowingconditionsaresatisfied:

negative

positiveand

(19)

Tosimplifytheanalysis,neglectingthetermsofderivationandsubstituting,andinTableIIinto.Itgives

(20)

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Fig.10.AngledifferencebetweentheZCPofterminalvoltageandstartingpointofphasecurrentintheexperimentusinganencoderfordetectingtherotorpositionwithload=0:58N1mat3600RPM.

Fig.12.Simulationresultsofterminalvoltage(100V/div.,2ms/div.),andcur-rentwaveforms(1A/div.)operatedwiththesameconditionofFig.9.

V.ABNORMALCURRENTCAUSEDBYPOSITIONDETECTION

ERRORANDEXCESSIVEADVANCEANGLEItisshownthattheZCPofterminalvoltageadvancestheac-tualZCPasshowninFig.7,anditisverifiedbytheexperi-mentsandsimulationscarriedoutintheprevioussection.Duetothischaracteristic,IPMshavealargeradvanceanglethancommanded.Forexample,iftheexperimentsshowninFig.10donewithsensorlesscontrolwith20advanceangle,theef-fectiveanglebecomes36.6becauseof16.6positiondetec-tionerrorinthesystem.Also,theresultantexcessivelyimposedadvanceanglesmaygenerateunwantedcurrentsasshowninFig.9.Fig.12showsthesimulatedcurrentwaveformsobtainedunderthesameconditionforFig.9,andthereexistsanabnormalcurrentaswell.

Fig.13illustratesthetermsconsistingof(18),whicharerepresentingthesummationofEMFsandshowingaddi-tionalvoltagecomponents.Theterminalvoltageforopenphase,,isequalto.

and,firstconsidertheAmongthetwotermsof

thatbecomesamorenegativevalueforbiggerpositionerror.

,i.e.,,isequaltoiftheEMFshaveatrapezoidalshapewith120flatarea.However,becauseof

doesnotequalasshowninFig.13,theslotripples,

andespeciallyduringtheperiodbetween–thedifferenceinmagnitudebecomeslargerandlargerasthedetectedZCPisadvanced.Second,thetermalsohasanegativevalueattheendpointoffreewheelingasthepositionerrorgetsbigger.FromTableI,itcanbeknownthattheterminalvoltageof

,orIPMforPWM-ONorPWM-OFFis

,respectively.Existenceofabnormalcurrentsisre-,andlatedtothemagnitudeofduringPWMoff,i.e.,

stayinglowerthanlevel.Whetherorthedurationof

notislessthandependsonpositiondetec-tionerroraswellastheamountofcommandedadvanceangle.Forinstance,highspeedand/orheavyloadmakestheZCPofoccurearlierthanthatforlowspeedand/orlightload.Also,largeadvanceanglesuchas25increasesthepossibilitythat

islowerthanattheendoffreewheelingac-tionbecausethefreewheelingwillbeterminatedintheperiod

Fig.11.Simulatedterminalvoltage(100V/div.,0.5ms/div.),phasecurrent

(1A/div.),andEMFwaveforms(100V/div.)inmode6forPWMdonein(a)FHP,and(b)SHPwiththesameconditionsofFig.10.

themeasuredterminalvoltageadvancestheactualZCPoftheEMF.Thecommandedadvanceangleis25andmotorspeedis120Hzinelectricalfrequency,sothatthetimedelayfromtheZCPtothestartingpointofthecurrentshouldbe115.74s[1/120Hz].However,asshowninFig.10thetimedifferenceismeasuredas500s,whichisequivalentto21.6inelectricaldegrees.Therefore,thepositiondetection

,inotherwords,theZCPoftheerroris16.6

terminalvoltageadvancestheactualrotorpositionby16.6.Fig.11(a)and(b)showssimulationresultsshowingterminalvoltagesandphasecurrentwaveformswhenPWMisdonein(a)FHPor(b)SHP,respectivelywiththesameoperationcondi-tionsforFig.10.Bothsimulationresultsshowthatthepositiondetectionerrorsareroughly500s,andthesevaluesareaccor-dancewithexperimentresultshowing500stimedifference.

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Fig.13.Componentsconsistingofterminalvoltageforopenphase.

Fig.15.SimulatedwaveformsofterminalvoltageandA-phasecurrentinSPMmotors.

TABLEIII

AMOUNTOFPOSITIONDETECTIONERRORFORIPMMOTORS

HAVINGDIFFERENTMOTORPARAMETERS

Fig.14.PathofabnormalcurrentafterfreewheelingthroughD0.

whenandhavemorenegativevaluesuchastheperiodpriorto.ThewaveformsinsidethecircleinFig.13showsthecasethatabnormalcurrentsexistduring.During

islowerthanduetoearlymodethisperiod,

changecausedbythepositiondetectionerrorandthelargead-—andmakesvanceangle,whichresultsinaforwardbiasof

thecurrentflowingthroughthediodeinphaseAasshowninFig.14.Therefore,itcanbeconcludedthatabnormalcurrentoc-cursinthecasesofheavyloadandhighspeedwithexcessivelyimposedadvanceangle,andthemagnitudeanddurationofbelowleveldeterminesthelevelofabnormalcurrents.ThewaveformsofterminalvoltageandphasecurrentsforSPMareexaminedbyusingsimulationstoinvestigatethecurrentwaveformsaffectedbyvoltagesinopenphase.Fig.15shows,andforSPMs.SimilartoIPMs,open

orforPWMphasevoltage,,isequalto

onandoff,respectively.Fig.15showsthatthereisnoposition

andthatofdetectionerror.Inotherwords,theZCPof

isidenticaltoeachotherincaseofSPMs.Thewaveformshowninsidethecircleillustratesthatthemagnitudeofter-minalvoltageforPWMoff,,isalwaysbiggerthan

becauseoftheabsenceoftermthatgeneratespositiondetec-tionerrorinIPMs.Forthecasethat–isturnedonduring

,theterminalvoltageshouldbe.Sincethis

isclampedtoandA-phaselevelisbelow

.However,thiscurrentdoesnotcurrentflowsthrough

flowcontinuously.ItdecreasestozeroatthenextPWMoff

becomes,whichishigherthan,event.Since

-becomesreversebiasedwhenPWMswitchisoff,sothat

anditresultsindiscontinuouscurrentincreasedanddecreased

,inbyswitching.Ontheotherhand,theabnormalcurrent,

becausethepotentialFig.13continuouslyflowsduring

Fig.16.Positiondetectionerrorscorrespondingtorotorspeed.

ofopenphasevoltageislowerthaneventheswitch

-isturnedoff.

TableIIIliststhemagnitudesofpositiondetectionerrorsobtainedfromexperimentsandsimulationsforIPMAand

V/(rad/s)withdifferentBhavinganidentical

29mH,and37mH,respectively.saliencysuchas

,itisexpectedthattheSincetwomotorshavethesame

motorhavingbiggersaliencyshowsalargerdetectionerror.TheexperimentsandsimulationsshowsthatB-typemotorwithhighersaliencyhasalargererrorandabnormalcurrentsfromlowerrunningspeedeventhesameadvanceangleisappliedforthesensorlesscontrol.Forinstance,A-typemotorhasthepositiondetectionerrorof24.3underoperationalconditionsof140Hzand1.74A.Ontheotherhand,eventhespeedof

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VI.CONCLUSION

AcharacteristicofmeasuredterminalvoltagethatisusedtodetectrotorpositionofIPMBLDCmotorscontrolledwith120conductionmethodhasbeenanalyzed.ThispaperhasshownthatadetectedZCPofIPMadvancesthatofrealEMFbecauseinductancesofanIPMmotorvarycorrespondingtotherotorpo-sition.Thepaperhaspresentedthatthepositiondetectionerrorisrelatedtomotorinductance,loadconditionaswellasmotorspeed.ThesimulationsandexperimentsemployingapositionsensorhaveshownthattheZCPofterminalvoltageadvancestheactualZCPofEMF.Inaddition,thispaperhasanalyzedthatanexcessivelyimposedadvanceanglemaycauseabnormalcurrentsinthesensorlesscontroller,andthisproblemofexistingunexpectedcurrentswasdiminishedbyreducingthemagnitudeoftheadvanceangle.ThesimulationandexperimentresultsdemonstratedwithIPMmotorshavingvariousmotorparame-tershaveverifiedthevalidityoftheanalyses.

ACKNOWLEDGMENT

ThisworkwassupportedbytheHongikUniversitynewfac-ultyresearchsupportfund.

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Fig.17.(a)Measuredterminalvoltageprofile(100V/div.,2ms/div.)anditsphasecurrent(1A/div.)undersensorlesscontrolwithadvanceangle=20at3600RPM,and(b)simulationresultsofterminalvoltage(100V/div.,2ms/div.),anditscurrentwaveforms(1A/div.)byreducingtheadvanceanglefrom28to20withload=0:82N1m.

motorandcurrentislowerthanthatforA-typemotorsuchas120Hzand1.650A,theerrorforB-typeIPMsis25.Boththeexperimentandsimulationshowthatwhentheerrorbecomeshigherthan23–24,abnormalcurrentsstarttoappearinopen-phaseafterfreewheeling.

Fig.16illustratesthatpositionerrorsaccordingtotherotorspeedwiththesameloadconditionof1.5Afromsimulations.Fig.16clearlyshowsthattheamountofthepositionerrorisproportionaltotherotorspeed,andtypeBmotorhasbiggerpositiondictionerrorsthantypeAmotorduetoalargerrotorsaliency.Fig.17showsthemeasuredandsimulatedterminal

withvoltageanditsphasecurrentwithadvanceangle

thesamespeedcommandof120Hz,andswitchingfrequency

kHz.ComparedwithFig.12,Fig.17clearlyshowsthatthereducedadvanceanglefrom28to20commandeliminatesthe

afterfreewheelingishigherthanabnormalcurrentsbecause

.

ManuscriptreceivedSeptember27,2007;revisedApril5,2008.Corre-spondingauthor:W.C.Lee(e-mail:woocheol@hknu.ac.kr).

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