永磁直线同步电机低速负载性能(中英文对照)

一、外文资料译文：正弦PWM电压源逆变器供电的永磁直线同步电机低速负载性能司纪凯陈昊汪旭东袁世鹰上官璇鹰〔1.中国矿业大学信息与电气工程学院徐州2210082.河南理工大学电气工程与自动化学院焦作454000〕摘要对于开环低速区由正弦PWM电压源逆变器供电的永磁直线同步电机〔PMLSM〕而言，与工作在高速情况的PMLSM负载性能不同，本文采用场路耦合时步有限元的方法研究PMLSM驱动水平运输系统的两种负载工况：轻载与重载。结果显示，PMLSM工作在重载情况下的负载性能较轻载优，且电机的工作电流随着负载的增大而减小。仿真与实验结果验证了该方法的有效性及正确性。关键词：永磁直线同步电机，负载性能，正弦PWM，电压源逆变器，时步有限元法，场路耦合1引言永磁直线同步电机〔PMLSM〕已广泛应用于多种领域，因为该电机具有高效性、高精度的控制性等特点,从自动化的运输操作系统到复杂精细的军事设备都会运用到它。然而，对于在较低速情况下的PMLSM的负载性能的研究是非常必要的，并且同步旋转电机和PMLSM在高速情况下也有很多不同的特征。PMLSM在低速情况下因为有多而有效的气压和低频率，电机具有抗电感能力强的根本特性。很多PMLSM具有这些特性，因为适用于PMLSM的转速和频率是有限的。通过文献【5】可以得出，适用于PMLSM的规格是一样的。电机的运转频率是6HZ，磁极距必须是30毫米。时步有限元分析法的研究为正弦PWM电压源逆变器供电的电机驱动作了依据，并且由于PWM电压源逆变器，人们对于时间步长的价值观也改变了。在文献【6】中，作者在边缘效应的根底上描述了鼓励永磁同步电机的局部动态性能。对于PMLSM驱动的启动和控制的相关方面已经有所研究。电机规格也是一样的。电阻是7.6Ω，电感是17.6mH，最大转速是2m/s。根据文献【7】显示可知，模拟电压是7V，频率是3Hz，负载驱动力是20N。电压源逆变器供电的PMLSM的动态特性的滞后性，是考虑了在合成铝板和固体回收铁中的涡电流，并通过分析时步有限元法和无线网络技术得出的。在文献【3】中，适于PMLSM的规格如下。电阻是5.2Ω，电感是2.8mH，电机驱动的转速是0.9m/s。文献【8】已经呈现出PMLSM基于正弦交流电流源，如大电感和电阻率，的稳态性能。但是，对于在低频率下的有大的电阻率和电感、半导体的SPWM逆变器操作，动态性能指标的研究在上述文献中比拟缺乏。因此，研究电机在不同负载下的动态性能是极其重要的。最近，通过精确的磁场分析，已经研究提出了电机的动态性能。其中的一种数学方法是基于有限元法的方法，它被越来越多的应用于精确探讨不对称磁场的动态性能。至于PMLSM，它有三相不平衡绕组、开放磁路、电阻率、电感系数、相位、谐波和电机电流。采用解析法和传统的有限元法客观地研究一个或两个极点的周期边界条件，是很困难的，另外考虑到连接外部SPWM变频器和磁场的问题，因此，本文就采用有限元分析法研究电机在不同负载的情况下，其暂态过程的性能，如：推力、移动速度和绕组电流。由于PMLSM靠SPWM电压源逆变器供电，电机的电流是不知道的，并且电机的电压还包括许多谐波分量，这就使有限元分析法不是很理想了。因此采用研究负荷性能时步有限元法和场耦合法就可以很好的研究该系统。这篇文章提出了使用时步有限元法和场耦合法研究电机在不同负荷情况下的性能。以下将会系统的讲解，在第二局部中，将对永磁交流同步直线电机进行描述。有限元模型在第三节中讲解。在论文第四局部将会研究PMLSM在不同负载下的性能并进行仿真和总结。在第五和第六局部，就总结实验结果并总结结论。2物理分析模型这个模型主要是由三相绕组和核心扩展插槽组成，其次是由永久性磁铁和在铁轭外表上别离出来的磁性组成。PMLSM的规格如下表1所示。其中含永磁磁铁磁化的漏磁量等。PMLSM的性能规格就在下面的表格中。PMLSM规格表型材工程材料和单位相位3匝数90主要电枢材料铁磁极距39mm槽距13mm主存材料永久性磁铁宽度27mm其次高度7mm长度120mm镶嵌外表型空隙5mm图1物理模型的方法建立的永磁直线型同步电机主要局部2—齿轮3—开槽4—绝缘磁铁材料5—永磁铁6—铁轭3PMLSM励磁电路的数学模型把SPWM电压源逆变器，电机边缘效应影响因素考虑进去，采用励磁电路方法计算电磁的暂态方程，解决向量电磁场的变化过程及电机的稳态方程，由励磁电路相结合的电磁场时步有限元方程，并说明在电枢绕组中的绕组电路电动势方程。瞬变场的控制方程，电磁场是可变的，其依据是麦克斯韦方程式。如方程式〔1〕可示：其中Az——向量电磁场中z轴方向的分量Js——电流密度Jm——磁化密度μ——磁导率在摘要中，2-d模型可以被分为三角元素构成网孔。在运用伽辽金法后，运动方程的分析模型为：其中A——未知的潜在向量电磁场I——绕组电流S,C,T——系数G——等效的矩阵磁化电流密度在外磁场作用下，磁介质磁化后出现的磁化电流要产生附加磁场。等效磁化法被用来处理永磁型场。磁化强度的符号是M0.由于电机较大的空隙特点，PMLSM的电阻和漏磁电抗没有被无视。根据欧姆定律和法拉第电磁感应定律，关于电动势和电压的产生的三相绕组式如方程【4】：其中ψ——感应电动势Ll——自感系数R——线圈电阻U——线圈电压其中N——有效的线圈匝数B——磁通密度S1——有效面积S2——有效面积适用于PMLSM的磁路和电路是不平衡的，从而固定连接器的电势不等于零域上的电势。因此电机的相位方程修改如下：其中U0——逆变器的输出电压g0——逆变器开关功能Ud——直流电压采用麦克斯韦法计算PMLSM的电磁力，其中包含了所有种类的谐波成分。电机电磁力的正弦分量计算载于公式〔9〕。电机电磁力的垂直分量计算载于公式〔10〕。其中L1——绕组的有效长度L2——积分长度Bx——x轴方向的磁通密度By——y轴方向的磁通密度FT——正弦方向上的电磁力FN——垂直方向上的电磁力PMLSM的运动方程如下：其中m——质量v——速度FL——负荷重力仿真结果仿真结果图形如下。恒定电压是30V，模块频率是2Hz，轻负载是50N，重负载是130N，电机额定同步速度是0.156m/s，这与PMLSM实验模型的参数是保持一致的。从仿真结果我们可以得到，空间磁场的功能元素及外部电路的状态作用。由于靠电压逆变器提供电压，外部条件可以忽略不计。图2是在50N负载下的三相电流的仿真图形。图3是驱动力。图4是在50N负载下的速度。图5—图7是在130N负载下的仿真图形。从图2和图5，我们可以看出在50N负载下的三相电流比在130N负载情况下的要大。因为PMLSM的磁路电枢绕组是开放的，不连续的。比拟图3和图7，我们可以看出PMLSM在130N负载下的驱动力更大。在图4和图7中可以看出，在130N负载的情况下，电机的性能更好，更稳定。如果产生的适用于PMLSM的磁阻力减少，移动速度根本上是接近同步速度的，因为有许多谐波，速度要完全相同是不可能的。〔a阶段，b阶段，c阶段〕图2在50N负载下的三相电流图3在50N负载下的驱动力图4在50N负载下不减少磁阻力时的速度图5在130N负载下的三相电流图6在130N负载下的驱动力图7在130N负载下的速度实验结果电压和电流是通过传感器来检测的。速度是通过E6B2型号的旋转编码器测得的，这个转速可以转化为电机的直线速度。数据采集系统可以通过TurboC来编辑。图8和图11分别是在50N和130N情况下的三相电流。图9和图12是分别在两种负载下的驱动力。图10和图13是在这两种负载下的速度。通过仿真和实验结果，我们可以看出，这两种情况都是可以的。图8在50N负载下的三相电流图9在50N负载下的驱动力图10在50N负载下的速度图11在130N负载下的三相电流图12在130N负载下的驱动力图13在130N负载下的速度总结在上述内容中，励磁电路耦合法中的时步有限元法和外部电路被用来分析专门适用于永磁交流同步电机在大阻力、大电感、大气隙和三相不平衡的低速度的情况下的负载性能。分析结果外表，PMLSM在重载情况下的负载性能比轻载时好，并且电机的工作电流随着负载的增大而减小。由于止动装置的存在，PMLSM产生磁阻力的波动，同步转速范围的移动速度。如果引起的适用于PMLSM的开环控制的磁阻力降低，转动速度将相当接近于同步速度。参考文献[1]WangXudong,YuanShiying,JiaoLiucheng,etal.3-Danalysisofelectromagneticfieldandperformanceinapermanentmagnetlinearsynchronousmotor[C].IEEEInternationalElectricMachinesandDrivesConference,Cambridge,MAUSA,2001:935-938.[2]BianchiN.AnalyticalcomputationofmagneticfieldsandthrustsinatubularPMlinearservomotor[C].ConferenceRecord-IASAnnualMeeting(IEEEIndustryApplicationsSociety),Rome,Italy,2000,1:21-28.[3]BonGwanGu,KwangheeNam.AvectorcontrolschemeforaPMlinearsynchronousmotorinextendedregion[J].IEEETransactionsonIndustryApplications,2003,39(5):1280-1286.[4]GoreVC,CruiseRJ,LandyCF.Considerationsforanintegratedtransportsystemusinglinearsynchronousmotorsforultra-deeplevelmining[C].IEMD99,Seattle,Washington,USA,1999:568-570.[5]JungInSoung,HyunDongSeok.DynamiccharacteristicsofPMlinearsynchronousmotordrivenbyPWMinverterbyfiniteelementanalysis[J].IEEETransactionsonMagnetics,1999,35(5):3697-3699.[6]SangYongJung,HyunKyoJung,JangSungChun,etal.Dynamiccharacteristicsofpartiallyexcitedpermanentmagnetlinearsynchronousmotorconsideringend-effect[C].IEEEInternationalElectricMachinesandDrivesConference,Boston,USA,2001:508-515.[7]KwonByungIl,WooKyungIl,KimDuckJin,etal.Finiteelementanalysisfordynamiccharacteristicsofaninverter-fedPMLSMbyanewmovingmeshtechnique[J].IEEETransactionsonMagnetics,2000,36(4):1574-1577.[8]ShangguanXuanfeng,LiQingfu,YuanShiying.Analysisoncharacteristicsofpermanentmagnetlinearsynchronousmachineswithlargearmatureresistanceandsmallreactance[C].TheEighthInternationalConferenceonElectricalMachinesandSystems,Nanjing,China,2005,1:434-438.[9]TounziA,HenneronT,LeMenachY,etal.3-Dapproachestodeterminetheendwindinginductancesofapermanent-magnetlinearsynchronousmotor[J].IEEETransactionsonMagnetics,2004,40(2):758-761.[10]YamaguchiT,KawaseY,YoshidaM,etal.3-Dfiniteelementanalysisofalinearinductionmotor[J].IEEETransactionsonMagnetics,2001,37(5):3668-3671.[11]InSoungJung,SangBaeckYoon,JangHoShim,etal.Analysisofforcesinashortprimarytypeandashortsecondarytypepermanentmagnetlinearsynchronousmotor[J].IEEETransactionsonEnergyConversion,1999,14(4):1265-1270.外文原文资料信息[1]外文原文SiJikaiChenHaoWangXudongYuanShiyingShangguanXuanfeng[2]外文原文所在书名或论文题目：LOADPERFORMANCEOFPMLSMINLOWERSPEEDREGIONFEDBYSINUOIDALPWMINWERTER[3]外文原文来源：TRANSACTIONSOFCHINAELECTROTECHNICALSOCIETY出版社或刊物名称、出版时间或刊号、译文局部所在页码：Vol.23No.9Sep.2008网页地址：二、外文原文资料：LOADPERFORMANCEOFPMLSMINLOWERSPEEDREGIONFEDBYSINUOIDALPWMINVERTERSiJikai1,2ChenHao1WangXudong2YuanShiying2ShangguanXuanfeng2〔1.ChinaUniversityofMiningandTechnologyXuzhou221008China2.HenanPolytechnicUniversityJiaozuo454000China〕ABSTRACTForthepermanentmagnetlinearsynchronousmotor(PMLSM)fedbysinusoidalPWMvoltagesourceinverterinthelowerspeedconditionwithoutfeedbackcontrol,loadperformanceisdifferentfromthePMLSMworkinginhighspeedregion.Thepaperadoptstime-stepfiniteelementmethodandfieldcircuitcouplingmethodtoinvestigateloadperformanceofthePMLSMtodrivehorizontaltransportationsystemwithlightloadandheavyloadconditionrespectively.ItisshownthatloadperformanceofthePMLSMintheheavyloadconditionishighlybetterthanthoseinlightloadoperationconditions,andoperationcurrentbecomeslowerwithloadincreasing.Thevalidityisverifiedbycomparisonsofsimulationandexperimentalresults.Keywords:Permanentmagnetlinearsynchronousmotor(PMLSM),loadperformances,sinusoidalPWM(SPWM)inverter,time-stepfiniteelementmethod,fieldcircuitcouplingmethod1IntroductionThepermanentmagnetlinearsynchronousmotor(PMLSM)hasbeenwidelyusedinmanyapplicationsfromtransportationsystemtoofficeautomationandmilitarydevicesbecausethemotorshavelotsofmeritsashighefficient,highaccuracypositioncontrol,etc[1-4].However,itisnecessarythatloadperformanceoflowerspeedofPMLSMisprofoundlyresearched,whichhaslotsofcharacteristicstodifferentfromrotatingsynchronousmachineandPMLSMinthehighspeedregion.PMLSMinlowerspeedregionhastheessentialcharacteristicsthattherearelargeratioofthemotorresistancetoinductanceandlargeleakageinductancebecauseoflargeandeffectiveairgapandloweroperationfrequency.LotsofPMLSMshavethecharacteristicsbecausethemovingtrackofPMLSMislimitedandthemoversteadystaterunningspeedofPMLSMisfinite.IntheRef.[5],specificationsofPMLSMwereasfollow.Themotoroperationfrequencywas6Hz,thepolepitchwas30mm.IntheliteratureFEAmethodforelectricmachinesdrivenbyPWMinverterwasproposedandthevalueoftime-stepwaschangedaccordingtotheswitchinglogicofPWMinverter.IntheRef.[6],theauthorspresentedthedynamiccharacteristicsofpartiallyexcitedpermanentmagnetlinearsynchronousmotorconsideringend-effect.ThestartingandcontrolcharacteristicsrelatedtothecapabilityinPMLSMdrivingwereinvestigated.Thespecificationsofthemotorwereasfollow.Theresistancewas7.6ΩofsampleA,theinductancewas17.6mH,themaximumspeedwas2m/s.AstheRef.[7]shown,thesimulationconditionwas7V,3Hzandloadthrustwas20N.Thedynamiccharacteristicsofthehysteresiscurrentcontrolledinverter-fedPMLSMwiththeconductivesheetsecondarywasanalyzedthroughthetime-stepfiniteelementmethodandmovingmeshtechnique,whichconsideringeddy-currentsinthesecondaryaluminumsheetandsolidbackiron.IntheRef.[3],thespecificationsofPMLSMwereasfollows.Theresistancewas5.2Ω,theinductancewas2.8mH,themotorwasrunningat0.9m/s.Ref.[8]hadpresentedthesteady-stateperformanceofPMLSMbasedonsinusoidalaccurrentsourcesuchaslargerratioofresistanceandinductance,andthemoverinandouttheprimary.Unfortunately,asforthePMLSMfedbySPWMinverteroperatedinloweroperationfrequencyregionwithlargerratioofresistanceandinductanceandlargerleakageinductance,thestudyofdynamicperformanceispoorinabove-mentionedliteraturesanditisimportanttoinvestigatethemotordynamicperformanceindifferenceloadsconditions.Recently,manynumericalmethodshavebeenproposedtoinvestigatemotor’sdynamicperformancethroughaccuratemagneticfieldanalysis.Oneofthenumericalmethodsbasedonthefiniteelementmethod,whichismoreandmoreusedtoaccuratelyinvestigatedynamiccharacteristicsofspecifyandnewmachinesstructuresorasymmetrymagneticfield,canconsidergeometricdetailsandthenonlinearofmagneticcircuit[9-11].AsforPMLSM,ithasthreephasewindingsunbalance,magneticcircuitopening,biggerratioofresistanceandinductanceofthephasewindings,andtimeharmonicforthemotorcurrentexistence.ItisdifficulttostudythemotorperformancesadoptingtheanalyticalmethodandtheconventionalFEMwithobjectiveofoneortwopolesconsideringperiodboundaryconditions,additionallyconsideringthelinkagequestionsofouterSPWMinverterandmagneticfield,thus,thepaperusestotalmodelofthemotorFEAtoattaintransientprocessperformancessuchasthrust,themoverspeedandwindingscurrentindifferentloadconditions.DuetothePMLSMfedbySPWMvoltagesourceinverter,thecurrentsofthemotorareunknownandvoltageincludeslotsofharmoniccomponents,theeffectofusingonetooloffiniteelementmethodisnotideal.Thustime-stepfiniteelementmethodandcouplingfieldcircuitmethodisadoptedtoinvestigateloadperformancesofthemotordrivinghorizontaltransportationsystem.Thepaperpresentssimulationtools,whichusingtime-stepfiniteelementmethodandfieldcircuitcouplingmethodandexperimenttoinvestigatethemotorperformancesintwoloadsconditions,lightloadandheavyload.Thepaperisorganizedasfollows.InsectionⅡ,theprototypePMLSMisdescribed.FEMmodelisestablishedinsectionⅢ.InsectionⅣsimulationresultsofPMLSMloadperformancesareattainedanddiscussed.InsectionⅤexperimentalresultsarepresented.Lastly,insectionⅥsomeconclusionsaredrawn.2AnalysismodelTheprimaryiscomposedofthree-phasewindingsandcoreopenedslot,andthesecondaryconsistsinpermanentmagnetsandtheseparatedmagnetismpiecewhichplacedonthesurfaceoftheironyoke.SinglesidetypeshortprimaryandsurfacemountedPMLSMareshowninFig.1,inwhichpermanentmagnetmagnetizationisunanimoustoairgapfluxaxis,leakagefluxinpolesintervallowerandcraftworksimple.ThespecificationsofPMLSMareshowninTable.TablePMLSMspecificationsFig.1PhysicalmodelofsurfacepermanentmagnetlinearsynchronousmotorTheprimary2—Tooth3—Slot4—Materialofinsulatingmagnet5—Permanentmagnet6—Thesecondaryyoke3Field-circuitcouplingmathematicmodelofPMLSMTotakecircuitfedbySPWMvoltagesourceinverterandthemotorendeffectsintoaccount,thepaperadoptsfield-circuitcouplingmethodtocalculateelectromagnetictransientprocess,solveequationvariablesofmagneticvectorpotentialandthemotorphasecurrent,whicharecombinationofelectromagneticfieldtime-stepfiniteelementEqu.andthreephasewindingscircuitequations.byelectromotiveforceinthearmaturewindings.Transientfieldgoverningequations.inwhichAzdenotesmagneticvectorpotentialisvariableareshowninEq.(1)accordingtoMaxwellequations.whereAz——z-axiscomponentofmagneticvectorpotentialJs——CurrentdensityoftheprimarywindingsJm——Equivalentmagnetizingsurfacecurrentdensityofpermanentmagnetμ——ThepermeabilityInthepaper,the2-Dmodelissubdividedintosmalltriangleelementstoformameshthatcoverstheentireregionadoptingn-orderunitbasicfunctionandlinearinterpolation.AfterapplyingtheGalerkinmethod,thegoverningequations.fortheanalysismodelisexpressedaswhereA——Unknownmagneticvectorpotential(AisusedinEq.(1)withdifferentmeaning)I——CurrentinthewindingsS,C,T——CoefficientrespectivelyG——CorrespondingmatrixofequivalentmagnetizationcurrentdensityEquivalentmagnetizingsurfacecurrentmethodisadoptedtodealwithNdFeBtypepermanentmagnet,whichisuniformitymagnetization,regulationshape,andlineardemagnetization.IntensityofmagnetizationsignisM0.PMLSMresistanceandleakagereactanceisnotneglectedduetothemotorwithlargeairgapcharacteristic.AccordingtoOhmlawandFaradayelectromagneticinductionlaw,relationofelectromotiveforceandvoltageproducedtheprimarythree-phasewindingsisshowninEq.(4).whereψ——ThewindingsfluxlinkageLl——ThemotorleakageinductanceR——WindingsresistanceU——WindingsphasevoltagewhereN——WindingeffectiveturnsB——FluxdensityS1——WindingeffectiveareaintheslotS2——CoupledeffectiveareaoftheprimaryandthesecondaryToPMLSMmagneticcircuitandelectriccircuitareunbalance,thuselectricpotentialoftheconnectorofstarpointisnotequaltozeroandthemotorphaseequations.shouldbechangedasfollows.WhereU0——Outputvoltageoftheinverterg0——Theinverterswitchon-offfunctionUd——DirectvoltageofbuslinkMaxwell’sstresstensorisadoptedtocalculatePMLSMelectromagneticforce,whichincludesallkindsofharmonicscomponentelectromagneticforce.ThemotorelectromagneticforcetangentialcomponentisshowninEq.(9).ThemotorelectromagneticforcenormalcomponentisshowninEq.(10).whereL1——WindingeffectivelengthL2——IntegralspaceBx——x-axisfluxdensitycomponentintheairgapfieldBy——y-axisfluxdensitycomponentintheairgapfieldFT——ElectromagneticthrustforceFN——NormalelectromagneticforceMovementequationofPMLSMisshowninEq.(11).wherem——Massv——ThemotormovervelocityFL——Loadforce4SimulationresultsThesimulationconditionsareasfollows.Linevoltageis30V,modulefrequencyis2Hz,lightloadis50Nandhighloadis130N,themotorratedsynchronousspeedis0.156m/s,whichareidenticaltoexperimentalPMLSMparameters.Thesimulationresultsareattainedfromcosimulationoffiniteelementfunctionofmagneticfieldandspacestatefunctionofoutercircuit.Themotorvoltageresultsareneglectedbecausethevoltageinverterisnotalmostaffectedbytheouterconditions.Fig.2showssimulationresultsofthreephasecurrentinload50Ncondition.Fig.3displayssimulationresultofthrustforce.InFig.4,themoverspeedsinload50Nconditionareshown.Shortdashlinedenotesthemoverspeedinload50NconditionundereliminationofPMLSMdetentforcebychangingendshape.Fig.5～Fig.7showrespectivelysimulationresultsofthree-phasecurrent,thrustforce,speedofthePMLSMinload130Ncondition.FromFig.2andFig.5,itisshownthatthethree-phasecurrentsofthePMLSMinload50Nconditionarelargerthanthoseofinload130Ncondition,accordingtoeveryloadconditionthemotorphasecurrentisunbalancethataphasecurrentvalueisalmostclosetobphasecurrent,butbothislargerthancphasecurrentvaluebecausethePMLSMmagneticcircuitisopenandarmaturewindingsarediscontinuous.IntermsofcomparisonwithFig.3andFig.6,wecanknowthatthetendencyofthethrustforceofthePMLSMinload130Nconditionisfavorable.AsshowninFig.4andFig.7,inload130Ncondition,thestaringperformanceofthemotoriswellandthereislittleundulation.IfthedetentforceproducedarmaturecorelengthofPMLSMisreduced,themoverspeedisbasicallyclosetothesynchronousspeed,butitisimpossiblethatitisabsolutelysameassynchronousspeedbecausetherearelotsofharmoniccomponentsincurrentfedfromSPWMvoltageFig.2Three-phasecurrentinload50NconditionFig.3Thrustforceinload50NconditionFig.4Speedwithandwithoutreducingdetentforceinload50Nconditioninverterandairgapfieldisunsinuso-idalevenifdrivensystemiswithfeedbackcontrol.Fig.5Three-phasecurrentinload130NconditionFig.6Thrustforceinload130NconditionFig.7Speedinload130Ncondition5ExperimentalresultsExperimentalinvertertypeisFR-A241E-55KinverterofMitsubishicorp.Voltageandcurrenthallsensorsareusedtodetectsigns.ThemoverspeedisattainedbytherotatingencoderforE6B2type,whoserotatingspeedcanbeconvertedintothemotorlinespeed.SoftwareofthedatacollectionsystemiseditedthroughTurboClanguage.Fig.8andFig.11showthree-phasecurrentinload50Nand130Ncondition,respectively.ThrustforceofthemotorintwoloadsconditionisshowninFig.9andFig.12.FromFig.10andFig.13,itisshownthattherearetwospeedcurvesinload50Nand130Ncondition.Bycomparisonsofsimulationandexperimentresults,wecanseethatbotharehighlycompatible.Fig.8Three-phasecurrentinload50NconditionFig.9Thrustforceinload50NconditionFig.10Speedinload50NconditionFig.11Three-phasecurrentinload130NconditionFig.12Thrustforceinload130NconditionFig.13Speedinload130Ncondition6ConclusionsInthepaper,field-circuitcouplingmethodofthetime-stepfiniteelementmethodandouterelectricpowercircuitisutilizedtoanalyzespecialloadperformancesoflowerspeedofPMLSMwithlargeratiooftheresistancetotheinductance,largeairgapandthree-phaseunbalance.AnalysisresultsshowthatloadperformancesofthePMLSMintheheavyloadconditionarehighlybetterthanlightloadoperationconditions,andoperationcurrentbecomeslowerwithloadincreasingbecauseofthelargeratiooftheresistancetotheinductanceandlargeairgap.Duetoexistenceofdetentforce,thePMLSMmoverspeedfluctuatesintherangeofthesynchronousspeed.IfthedetentforceofPMLSMwithopenloopcontrolisreduced,themoverspeedisquiteclosetosynchronousspeed.Refrerence[1]WangXudong,YuanShiying,JiaoLiucheng,etal.3-Danalysisofelectromagneticfieldandperformanceinapermanentmagnetlinears