解耦分析建模方法

IEEETRANSACTIONSONMAGNETICS,VOL.51,NO.3,MARCH20158100504ANewDecoupledAnalyticalModelingMethodforSwitchedReluctanceMachineShoujunSong,ManZhang,andLefeiGeSchoolofAutomation,NorthwesternPolytechnicalUniversity,Xi’an710072,ChinaThispaperproposesanewdecoupledanalyticalmodelingmethodforswitchedreluctancemachine(SRM).Thefluxlinkageisrepresentedbyasecond-orderFourierseries,andthecoefficientsoftheseriesarepositiondependent,whichcanbefurtherexpressedbyanothersecond-orderFourierseries.Theproposedmethodonlyneeds21datapointsfromfiverotorpositions.Then,thestatictorquecharacteristicsareanalyticallyobtainedbasedontheexpressionofthefluxlinkage.Theaccuracyofthemethodisverifiedbycomparingthecalculatedflux-linkageandstatictorquecharacteristicswiththosefrommeasurements.Withthecalculatedflux-linkageandstatictorquedata,thedynamicperformanceofSRMissimulatedunderbothmotoringandgeneratingmode.Thesimulationresults,suchasphasecurrentandmechanicalcharacteristics,agreewellwiththosefromtheexperiment,whichfurtherprovestheeffectivenessoftheproposedmethod.IndexTerms—Decoupledanalyticalmodel,dynamicperformance,fluxlinkage,Fourierseries,switchedreluctancemachine(SRM).I.INTRODUCTIONSWITCHEDreluctancemachine(SRM)hassimpleandruggedstructure,highefficiencyandreliability,widespeedrange,flexiblecontrol,andlowcost,anditissuitableforworkinginharshenvironment,suchashighspeedandhightemperature.Duetotheseoutstandingadvantages,SRMhasattractedincreasingattention[1],andiscompetitiveinmanyfields,includingaviationindustry,electricvehicle,windpowergeneration,householdappliances,andsoon[2]–[4].ItisrelativelydifficulttoderiveanaccuratemathematicalmodelforSRMduetoitsdoublysalientstructureandsaturatedmagneticfield,whichresultinstrongnonlinearitiesinflux-linkageandstatictorquecharacteristics[5].However,forperformancepredictionandadvancedcontrolofSRM,anaccuratemodeliscritical.ThereareseveralapproachestobuildthemodelofSRM,suchaslookuptabletechniques[6],magneticequivalentcircuitanalysis[7],neuralnetwork(NN)[8],andfinite-elementmethod(FEM)[9].MagneticequivalentcircuitanalysisandFEMarecomplexandtimeconsumingandintensivecomputationisneeded.TheNNandlookuptabletechniquesrequirenumeroussampledatafromexperimentsorFEM,whichinevitablytakesmuchtime.Insomeliterature,analyticalmodelingmethodsforSRMhavebeenpresented.In[10],anaccuratemodelingmethodforSRMisproposedbasedonexponentialfunction.However,theleastsquaremethodisadoptedtoobtainthecoefficients,whichistimeconsuming.In[11],theFourierseriesinexpressionofcurrent-dependentarctangentfunctionisutilizedtobuildthemodeloftheSRM.However,thecoefficientsinarctangentfunctioncannotbedirectlycalculatedandtheaccuracyofthemodeldependsonthemethodusedforcurvefitting.EffectivemodelingmethodsforSRMbasedonFourierseriesarealsoproposedin[12]and[13],buttheprocesstodeterminethecoefficientsoftheseriesisrelativelycomplexand/orneedsnumeroussampledata.ManuscriptreceivedMay19,2014;revisedAugust23,2014;acceptedOctober8,2014.DateofcurrentversionApril22,2015.Correspondingauthor:S.Song(e-mail:[e-mail]).Colorversionsofoneormoreofthefiguresinthispaperareavailableonlineatflux-linkageandstatictorquecharacteristicsofSRMisproposedbasedonFourierseriesexpansion.ThecomplicatedandnonlinearinfluencesofphasecurrentandrotorpositiononfluxlinkagearedecoupledandalimitedamountofsampledataisrequiredtodeterminethecoefficientsoftheFourierseries.Bytheproposedformula,thefluxlinkageandstatictorquewithanyphasecurrentandrotorpositioncanbecalculatedeasily.Thevalidityoftheproposedmethodisverifiedbycompari-sonbetweencalculatedandmeasuredcharacteristics.Finally,basedonthecharacteristicsobtainedbytheproposedmethod,thedynamicsimulationmodelofSRMisbuiltinMATLAB.Thesimulationresultsunderdifferentoperationconditionsarecomparedwiththosefromexperiments,anderrorsbetweenthemarefairlysmall,whichfurtherdemonstratesthattheproposedmethodiseffectiveandaccurate.II.DECOUPLEDANALYTICALMODELINGMETHODToimprovetheutilizationratioofmaterial,SRMalwaysoperateswithcertainsaturation,whichresultsinnonlinearelectromagneticcharacteristics.Thefluxlinkageψ(θ,i)isafunctionofphasecurrentandrotorposition,whichcanbeanalyticallypresentedbythefollowingFourierseries:ψ(θ,i)=a0(θ)+2m=1am(θ)cos(ω1mi)+2m=1bm(θ)sin(ω1mi)(1)ω1=π/(imax−imin)(2)wherecoefficientsamandbmareconstantforagivenpositionandcanbecalculatedwiththeflux-linkagedata.imaxandiminarethemaximumandminimumphasecurrentinthemeasureddata.Theunitofrotorpositionθisdegree.Inthispaper,thecoefficientsamandbmarecalculatedbyanothersecond-orderFourierseriesasfollows,whichisafunctionofθ:am(θ)=c0m+2n=1cnmcos(ω2nθ)+2n=1dnmsin(ω2nθ)(3)ω2=π/(θmax−θmin)(4)wherecoefficientscnmanddnmareconstantforeachmachine.θmaxandθminarethemaximumandminimumrotorpositionin0018-9464©2015IEEE.Personaluseispermitted,butrepublication/redistributionrequiresIEEEpermission.See