CPPM混合励磁同步电动机的基本原理与特性

CPPM混合励磁同步电动机的基本原理与特性TAKAYUKIMIZUNO,KAZUTOSHINAGAYAMA,

TADASHIASHIKAGAandTADAOKOBAYASHI

日本明电舍公司(MEIDENSHACORP.)摘要永磁同步电动机在工业上得到了广泛应用。众所周知，由于不需要励磁输入，电机运行效率高。然而，由永磁材料特性决定的磁通大致保持恒定，导致永磁电机的气隙磁场难以调节。另一方面，电励磁同步电动机的气隙磁场容易调节，但在额定负载时励磁铜耗较大。为使磁通易于控制并改善传统同步电机的性能，作者提出了一种带永磁体和励磁绕组的混合励磁同步电动机(HSY),HSY的主要优点有：①无刷(免维护)，②所需的励磁容量很小(高效率)，③容易实现较强的磁场控制等。正因如此，混合励磁同步电动机在不同领域都有良好的应用前景。本文主要讨论和分析混合励磁同步电动机的基本原理与特性。SUMMARYPermanentmagnettypesynchronousmachineshavebeenwidelyusedforindustrialapplications.Itiscommonlyknownthattheyareoperatedathighefficiencysincenoexcitationinputisrequired.However,itisdifficulttocontroltheair-gapmagneticflux,becausethemagneticfluxisdeterminedbythepropertyofthepermanentmagnetandapproximatelykeptconstant.Ontheotherhand,synchronousmachineswiththefieldwindingmakeiteasytocontroltheair-gapmagneticflux.Butthecopperlossofthefieldwindingbecomeslargeattheratedload.Inordertorealizethemagneticfluxcontroleasilyandimprovetheperformanceoftheconventionalsynchronousmachine,weproposeahybridexcitationtypesynchronousmachine(HSY)withthepermanentmagnetsandthefieldwinding.AdvantagesofHSYare(1)ithasnobrushes(maintenancefree),(2)requiredexcitationinputissmall(highefficiency),(3)itiseasytogetasufficientmagneticfluxcontrol,andothers.Therefore,HSYhasagreatpossibilityofuseforvariousapplications.Inthispaper,basicprinciplesandcharacteristicsofHSYaremainlydiscussedandmadeclear.关键词同步电机，永磁，励磁绕组，混合励磁，磁场控制，有限元方法Keywords:Synchronousmachine;permanentmagnet;fieldwinding;hybridexcitation;fieldcontrol;finiteelementmethod.引言与其它旋转电机相比，永磁同步电动机(PMSY)的特点是无刷设计，并且不需要电励磁，可以实现高效率。正因如此，随着稀土永磁材料的出现，永磁同步电动机在工业领域得到了广泛应用，而且容易制造出数十千瓦的PMSY。然而，PMSY也有明显的缺点。如前述，由于永磁体特性所决定的电机气隙磁场几乎不变，绕组感应电压随转速变化，这妨碍了作为电动机使用时的恒输出运行，或作为发电机使用时的恒压运行。对于电动机，可采用具有弱磁控制的嵌入式永磁(flush-magnet)电机实现宽范围的恒输出运行。然而，若采用高性能的稀土永磁，即使在空载情况下，也需要很大的电枢电流来实现弱磁控制，这意味着电机轻载时的性能会变坏。此外，由直流电供电的PMSY需要按其额定容量选择晶闸管和逆变器,从而加大了体积。Permanentmagnetsynchronousmachines(PMSY)featurebrushlessdesign,andneednoexcitationwhichprovideshigherefficiencycomparedtoothertypesofrotatingmachines.Becauseofthis,PMSYhavefoundawideindustrialapplicationinavarietyoffields,andwiththeadventofrare-earthmagnets,PMSYofseveraltensofkilowattsareeasilymanufacturable.However,PMSYsufferfromaconsiderabledrawback.Sincemagneticfluxisdictatedbythecharacteristicsofthepermanentmagnetbeingnearlyconstant,voltageinducedinwindingsvarieswiththenumberofrevolutions,whichhindersconstant-outputoperationwhenusedasamotororconstant-voltageoperationwhenusedasagenerator.Incaseofmotors,constant-outputoperationinawiderangeisachievedbyusingflush-magnetmotorswithfield-weakeningcontrol[l,2].However,whenemployinghigh-performancemagnetssuchasrare-earthmagnets,largearmaturecurrentisrequiredforthisfield-weakeningcontrol,evenwithnoload,whichmeansdeteriorationinperformanceatlight-loadoperation[3].Besides,PMSY-baseddcpowerplants[4]requirechoppersandconverters,accordingtotheratedcapacity,withaconsequentlargesize.另一方面，通过通入励磁绕组的直流励磁电流，电励磁同步电动机(FWSY)可以容易地控制气隙磁通，于是能解决前述PMSY与磁场相关的控制问题，特别是对于基于电力供电的FWSY，采用小体积、低容量的励磁电源，可以方便地实现电压控制。然而，对于FWSY，需要额外增加如励磁绕组、电刷和光滑环，这将导致设计上的复杂、励磁损耗带来的效率恶化以及需要维护。尽管与PMSY不同，然而FWSY也有本身的问题。Ontheotherhand,field-windingsynchronousmachines(FWSY)allowforeasycontrolofmagneticfluxbymeansofdcfieldcurrentflowingthroughfieldwinding,thusalleviatingtheaforementionedproblemsofPMSYrelatedtothefieldcontrol.Particularly,itiscommonknowledgethatwithFWSY-basedpowerplants.Voltagecontrolcaneasilybeperformedbyasmall-sizelow-capacityexciter.IncaseofFWSY,however,additionalpartsarerequiredsuchasfieldwindings,brushesandsliprings.Thisresultsincomplicateddesign,deteriorationofefficiencyduetomagneticloss,andtheneedformaintenance.Thus,FWSYhavetheirownproblems,eventhoughdifferentfromthoseofPMSY.于是可以说，同步电动机可能的应用范围主要取决于其励磁方案。也就是说，如果在拟开发的同步电机中结合PMSY和FWSY的优点，同步电动机的应用范围将被极大拓宽。本文中，我们提出一种带有永磁励磁和直流励磁绕组励磁的混合励磁同步电动机(以下简称为HSY)，并从理论和试验两方面讨论它的运行原理、基本特性以及应用。Therefore,wecansaythatthepossiblerangeofapplicationofsynchronousmachinesdependsheavilyonexcitationschemes,andthatuseofsynchronousmachinescouldbewidenedsignificantlyifasynchronousmachinewasdevelopedthatcombinesadvantagesofpermanentmagnetsandfieldwindings.Inthiscontext,wehaveproposedahybridexcitationsynchronousmachinefeaturingbothpermanentmagnetsanddcfieldwindings[5,6](belowreferredtoasHSY),anddiscusseditsoperatingprincipleandbasiccharacteristicsintheoreticalandexperimentalterms,aswellaspossibleapplications.首先，本文介绍了带有永磁极和励磁绕组HSY的基本结构、采用直流励磁电流对气隙磁通有效控制以及与其它同步电机相比较的优缺点。HSY的显著特点是它的永磁极磁路和励磁绕组磁路基本上相互独立，并可以用较小的励磁安匝实现对气隙磁通的合理调节。因此，HSY在能提供免维护运行的同时还可以确保高效率的磁控制。本文研究了基于有限元分析的一个实用二维有限元模型，并分析了样机的空载和负载特性。为了建立实际系统中有限元计算结果和控制性能之间的关系，电压方程和转矩公式用于负载特性分析中。其次，将分析值与空载和负载的测量值进行比较，同时证明了HSY作为同步电动机和同步发电机使用的可行性。First,basicconstructionofHSYisdescribedthatusesbothpermanentmagnetsandfieldwindings,andensurescontrolofairgapmagneticfluxbymeansofdcfieldcurrent,aswellasitsoperatingprincipleandcomparativeprosandconsagainstothersynchronousmachines.ThedistinctivefeatureofHSYisthatmagneticcircuitsofpermanentmagnetsandfieldwindingsbasicallyareindependentofeachother,andappropriateregulationofthegapmagneticfluxcanbeperformedwithasmallmmfoffieldwinding.Hence,HSYensureshigh-efficiencymagneticcontrolwhileprovidingformaintenance-freeoperation.Apracticabletwo-dimensionalmodelwasdevelopedforfiniteelementanalysis,andbothloadandno-loadcharacteristicsoftheprototypemachinewereanalyzed.VoltageequationsandatorqueformulawereemployedinloadcharacteristicsanalysistoestablishtherelationbetweenFEMresultsandcontrolperformanceinanactualsystem.Further,measuredvaluesofloadandno-loadcharacteristicswerecomparedtoanalyticalresults,andthefeasibilityofusingHSYasasynchronousmotor[7]orasynchronousgenerator[8]wasproved.HSY的基本结构和原理2.1基本结构HSY的基本结构如图1所示，图1(a)、(b)分别为HSY的定子和转子。HSY的电枢与单极同步电机(homopolarsynchronousmachine)基本相同，电枢铁心分成两部分，在铁心的中间嵌放了励磁绕组，在励磁绕组中通入直流励磁电流可以有效地控制气隙磁通。通过导磁机壳将两部分铁心进行机械和磁路上的耦合。定子铁心槽内安放传统的三相交流绕组。BasicconstructionoftheproposedHSYisshowninFig.1.Specifically,Figs.1(a)and(b)showthecrosssectionofHSYandthedesignoftherotor,respectively.HSY'sarmatureisbasicallythesameasthatofahomopolarsynchronousmachine[9].Thearmaturecoreisdividedintwo,andfieldwindingismountedinaspaceinthecentralpartofthecore.Passingdccurrent(fieldcurrent)throughthiswindingensuresappropriateregulationofthegapmagneticflux.Thetwoarmaturecoresarecoupled,mechanicallyandmagnetically,throughanexternalbackyoke.Also,slotsareprovidedinthearmaturecoretolayconventionalthree-phaseacwindings.交流绕组 定子铁心(a)定子 (b)转子图1HSY的基本结构类似，转子部分也分成两段。为简化起见，图中转子左边和转子右边分别称之为N极边和S极边。在N极边，气隙由交替的永磁极和铁心叠片的凸极部分构成，以下由永磁极构成的极简称为磁极，由铁心构成的极简称为铁极。S极边的极配置是这样安排的，即S极边的磁极与N极边的铁极同轴，反之亦然。同样，通过转子内部磁轭将两段转子铁心进行机械和磁路上的耦合起来。Similarly,therotorunitalsoisdividedintwo.Forthesakeofsimplicity,theleft-handsideandtheright-handsideinthediagramwillbereferredtoasN-polesideandS-poleside,respectively.AttheN-poleside,theairgapisformedwithalternatepermanentmagnetpoles,andsalientpartsofthelaminatedcore.Below,thepoleswithmagnetswillbereferredtoasmagnetpoles,andthepolesformedbythecorewillbereferredtoascorepoles.ThepoleconfigurationattheS-polesideisarrangedsothatS-sidemagnetpolesarecoaxialtoN-sidecorepoles,andviceversa.Also,bothrotorcoresarecoupledmechanicallyandmagneticallythroughtheinternalbackyoke.2.2运行原理由于永磁体的高磁阻，在图1(a)电枢中间的励磁绕组中通入励磁电流，几乎所有的磁通都走铁极。这样所产生直流磁通的路径为：导磁机壳-S极边电枢铁心-S极边铁极-转子轭—N极边铁极—S极边电枢铁心—导磁机壳。改变励磁电流的大小和方向可以控制直流磁通的大小和方向。WhenfieldcurrentflowsthroughthefieldwindinginthecentralpartofthearmatureasshowninFig.l(a),almostallthemagneticfluxcomesthroughthearmaturecorepolesbecausethepermanentmagnetsshowahighreluctance.Thus,demagneticfluxisgeneratedinthecircuitof(armaturebackyoke—S-sidearmaturecore—S-sidecorepole—rotorbackyoke—N-sidecorepole—N-sidearmaturecore—maturebackyoke).Themagnitudeanddirectionofthismagneticfluxcanbecontrolledinagreementwiththemagnitudeanddirectionofthefieldcurrent.另一方面，如果永磁体具有大矫顽力，如采用稀土永磁材料，某些外部磁场作用下不会出现退磁问题，在磁极方向上产生几乎为恒值磁通，并确认是安全的。因此，不考虑励磁电流的漏磁通及其它漏磁通，可以大致认为从N极边磁极出来的磁通通过导磁机壳进入S极边的磁极。Ontheotherhand,ifpermanentmagnetswithlargecoerciveforce,suchasrare-earthmagnets,areemployed,thereisnoproblemofdemagnetizationunderapplicationofsomeexternalmagneticfieldwhichmakesitsafetobelievethatnearlyconstantfluxisgeneratedinthedirectionofthemagnetpolarity.Therefore,ignoringthemagneticfluxproducedbyfieldcurrent,andallowingforsomeleakageflux,itmaybasicallybeconsideredthatthefluxthatgoesoutfromtheN-sidemagnetentersintotheS-sidemagnetviathearmaturebackyoke.于是，可以认为励磁磁通和永磁磁通走相互独立的路径，然而实际上这二个磁通合成构成气隙磁通，通过励磁电流控制实现对气隙磁通的合理调节，分别讨论如下：Thus,magneticfluxoffieldwindingandthatofthepermanentmagnetmaybeconsideredasgoingalongindependentroutes.Inpractice,however,thesefluxescombine,andappropriateadjustmentoftheair-gapfluxcanbeperformedthroughfieldcurrentcontrol,aswillbeshownbelow.无励磁情况(励磁电流If=0)这种情况下，气隙磁通由永磁材料的特性和电机磁路，即仅由永磁极决定。转子旋转时，电枢绕组切割N极边，或S极边下的磁通，在绕组中感应电流。此时磁通的方向如图2(a)所示(图中磁通的路径是示意的，没有画出电枢铁心和导磁机壳)。Inthiscase,thegapfluxisgovernedbycharacteristicsofpermanentmagnetsandmagneticcircuit,thatis,itdependsonmagnetpolesonly.Whentherotorisrotating,however,thearmaturewindingcutsacrossmagneticfluxateithertheN-pole,orS-poleside,andcurrentisinducedinthewinding.Hence,thedirectionofmagneticfluxisasshowninFig.2(a).(Inthediagram,themagneticfluxrouteisshownschematically;thearmaturecoreandbackyokeareomitted.)(a)无励磁电流(b)(a)无励磁电流(b)去磁励磁电流(c)增磁励磁电流图2HSY运行原理去磁情况(励磁电流If<0)这里励磁电流的方向如图2(b)所示，永磁体产生的磁通与情况(1)相同，并与励磁磁通相叠加。如前所述，几乎所有的励磁磁通全部走铁极，但S极边与N极边的磁通方向相反，于是在电枢绕组中感应一个反向电压分量，这意味着感应电压比无励磁电流情况低。因此，气隙磁通相应减小。此时的合成磁通(永磁极磁通和励磁磁通产生的)路径相当复杂，特别地，永磁极磁通和铁极磁通相等时的磁场分布如图2(b)所示。Here,thedirectionoffieldcurrentisasshowninFig.l(a).Thefluxproducedbythemagnetsisthesameaswithcase(l),whilethefluxproducedbyfieldwindingissuperimposed.Aswasstatedintheforegoing,almostallthefluxproducedbyfieldwindinggoesthroughcorepoles.However,magneticfluxesattheS-poleandN-polesidesareopposingeachother,andareversecomponentarisesinthevoltageinducedinthearmaturewinding,whichmeansthattheinducedvoltageislowercomparedtothecaseofzerofieldcurrent.Therefore,thegapmagneticfluxbecomesweakenedaccordingly.Thedistributionoftheresultingmagneticflux(producedbymagnets,andfieldwinding)israthercomplicated.Particularly,whenfluxesofcorepolesandofmagnetpolesareofthesamemagnitude,thisdistributionisasshowninFig.2(b).增磁情况(励磁电流If>0)励磁电流方向与如图2(c)方向相反。此时在N极边和S极边的磁通方向相同，电枢绕组中感应电压高于励磁电流为零时的情况。图2(c)显示这种情况下的磁通分布，图中永磁极和铁极的磁通相等。上述原理表明，通过改变直流励磁电流，可以连续地控制HSY的气隙磁通和绕组感应电压。Here,thedirectionoffieldcurrentisoppositecomparedtoFig.1(a).Inthiscase,magneticfluxesattheS-poleandN-polesidesareofthesamedirection,andthevoltageinducedinthearmaturewindingishighercomparedtothecaseofzerofieldcurrent.Therefore,thegapmagneticfluxbecomesweakenedaccordingly.ShowninFig.2(c)isthefluxdistributioninthecasethatfluxesofcorepolesandofmagnetpolesareofthesamemagnitude.TheaboveprinciplesuggeststhatthegapfluxandthevoltageinducedinarmaturewindingofHSYcanbecontrolledadequatelyandcontinuouslybyvaryingdcfieldcurrent.2.3HSY的优缺点上面介绍了HSY的结构和运行原理，其优点和缺点总结如下：(1)电机体积对于HSY来说，为了产生励磁磁场，需要励磁绕组和导磁机壳，因此，若电机容量相等,HSY的体积要比PMSY的大。然而，直流励磁可以使HSY的气隙磁密比PMSY的大，同时可用机座作为导磁机壳，这样可使HSY与PMSY的体积设计得大致相当；另一方面，与FWSY相比，HSY消除了转子绕组、电刷和滑环，因此减小了电机体积。WithHSY,fieldwindingandbackyokesarerequiredtogeneratedcmagneticfield.Thus,itmaybethoughtthat,generally,HSYwillbeoflargersizethanPMSY,withthecapacitybeingequal.However,dcmagneticfieldmakesitpossibletoincreasethegapmagneticfluxdensitycomparedtoPMSY,whileframescanbeemployedasbackyokes.Nevertheless,itseemspossibletodesignHSYofthesamesizeasPMSY.Ontheotherhand,ifcomparedtoFWSY,theproposedHSYeliminatesrotorwindings,brushesandsliprings,whichcontributestosmallerdesign.(2)控制单元HSY作为电动机使用时，由于需要直流磁场，与普通PMSY的驱动单元相比，应额外增加一个励磁电路。如前所述，HSY所需要的励磁容量很小，这样一个微小的励磁电路可放在电动机的驱动电路中，与PMSY相比，电路体积并没有明显增加；从控制效率方面讲,由于新型HSY采用励磁绕组进行磁场控制取代了传统的弱磁控制，控制效率大为改善；此外，HSY作为发电机使用时仅需要一个小的励磁电路，这意味着控制单元很小，而PMSY则需要控制芯片和开关管。与FWSY相比，HSY用永磁提供所需的励磁安匝，降低了励磁输入，从而减小了控制单元体积。SinceHSYrequiresdcmagneticfield,anexciterwithcontrolcircuitryisneededinadditiontotheconventionalPMSYdriveunitwhenemployedasamotor.However,aswasexplainedabove,HSYrequiresrelativelysmallexcitation,andaminiatureexcitercanbebuiltintothedriveunitofthemotorwithoutsignificantincreaseinsizecomparedtoPMSY.Speakingintermsofefficientcontrol,thenewHSYoffersconsiderableimprovement,becauseinadditiontomagneticfieldcontrolwithfieldwinding,aconventionalcontrolschemeusingarmaturecurrentsuchasfield-weakeningcontrol[l,2]canbeimplementedaswell.Ontheotherhand,whenusedasagenerator,PMSYcallsforchoppersandconverters[4],whileHSYrequiresonlyasmall-sizelow-capacitysimpleexciter[8],whichmeansaconsiderablysmallercontrolunit.IfcomparedtoFWSY,muchoftherequiredmmfisprovidedbypermanentmagnets,whichimplieslowerexcitationinput,andsmallersizeofcontrolunit.（3）励磁输入和效率事实上，HSY额定负载运行时励磁损耗相当大，与PMSY相比效率下降。然而，HSY需要的励磁容量相当小（样机只需要160W）,总效率并没有明显下降。特别地，当电机轻载实现弱磁控制时，HSY的励磁损耗可忽略不计，与此同时，PMSY采用电枢电流弱磁控制的铜损耗则很大，效率下降。因此，可使用HSY改善电机轻载时的效率。与FWSY相比，HSY需要的励磁输入很小，总效率会有所提高。ThefactisthatwhenHSYisoperatedatratedload,magneticlossisratherhigh,andefficiencydropscomparedtoPMSY.However,sincemagneticfieldrequiresrelativelylowpower（atmost160Wwithprototypemachinetobedescribedbelow）,theoverallefficiencyisnotlikelytobedegradedsignificantly.Particularly,whenperformingfield-weakeningcontrolunderlightloads,magneticlossisnegligiblewithHSY,whereasincaseofPMSY,copperlossduetothearmaturecurrentperformingweakening-fieldcontrolprevailsandefficiencydrops[3].Therefore,theuseofHSYisassumedtoimproveefficiencyinthelight-loadarea.ComparedtoFWSY ,theproposedHSYrequiressmallerexcitationinput,andtheoverallefficiencyisexpectedtoimprove.可用不同的方式考察HSY的优缺点，取决于比较的角度。总的来说,HSY结合了PMSY和FWSY两种电机的特性，是一种中间的解决方案，适用于有磁场控制需求的场合。Thus,prosandconsofHSYmightbeconsideredindifferentwaysdependingonthebasisofcomparison.Onthewhole,HSYcanbeclassifiedasanintermediatesolutioncombiningcharacteristicsofbothPMSYandFWSYthatisappropriateforapplicationscallingforactivemagneticcontrol.2.4样机样机的主要技术数据见表1。分析原理时，作为例子讨论的是6极电机，但电机设计时极数是可以灵活选择的。综合考虑电机的额定功率、电源频率和每极的磁体尺寸，样机采用了8极方案。与文献[6]所报告的结果一样，磁体型式、励磁绕组的匝数和其它一些参数作了修正。BriefspecificationsoftheprototypemachinearelistedinTable1.Whenexplainingtheoperationsprinciple,

额定功率20kW频率200Hz额定电压200V极数8电枢铁心外径195mm电枢铁心内径135mm定子导磁机壳厚12.5mm电枢铁心全长175mm气隙长0.65mm定子槽数36（每极每相槽数1.5）电枢绕组型式双层分布叠绕组励磁绕组匝数176匝永磁体Nd-Fe-B,Br=1.1T表1 样机的主要技术数据a6-polemachinewasconsideredbywayofexample,butdesignsarefeasiblewithanarbitrarynumberofpoles.Withtheprototypemachine,an8表1 样机的主要技术数据HSY的特性表1样机磁场的有限元分析如下。对于HSY，磁通的路径是三维的，这需要精确的三维分析。然而，从实用的角度出发，这里采用二维非线性分析。DescribedbelowisFEManalysisofthemagneticfieldsystemoftheprototypemachineasspecifiedinTable1.WithHSY,therouteofmagneticfluxisthree-dimensional,whichcallsforstrict3-Danalysis.Forthesakeofpracticability,however,atwo-dimensionalnonlinearanalysiswasperformed.3.1分析模型与假定在HSY中，磁极和铁极是交替排列的，且样机为分数槽电枢绕组，应考虑选择一个一对极区域的分析模型；此外，励磁绕组产生的磁动势绝大部分作用于气隙，故近似认为该磁动势是仅作用在气隙处的一个等效磁动势。基于上面假定，可以采用二维模型完成下面的分析。文献［6］给出了一个可接受的空载特性分析模型，即一个一对极定子区域，转子处于任意位置，通入电流流过气隙两端以等效励磁绕组磁动势。上面的方法不能用于负载特性分析，原因在于不能确定周期性的边界条件。SincemagnetpolesandcorepolesarelocatedalternatelyinHSY,whilethearmaturewindingoftheprototypemachineisfractionatedbyslots,ananalyticalmodelshouldbeconsideredintermsof2-polefragment.Besides,themmfproducedbyfieldwindingactsmostlyinthegap,andcanbeapproximatedwiththeequivalentforceappliedinthegaponly.Withtheaboveassumptionsmade,adequateanalysiscanbeperformedusingatwo-dimensionalmodel.Asshownin[6],acceptableanalysisofno-loadcharacteristicscanbeconductedprovidedthecrosssectionofthe2-polefragmentisconsideredatanarbitrarylocationontherotor,whilepassingelectriccurrentthroughbothendsofthegaptoobtainmmfofthefieldwinding.However,thisapproachcannotbeusedforanalysisofloadcharacteristicsbecauseitprovesimpossibletospecifyperiodicboundaryconditions.为此，引入二个分离模型，一个是含N边、S边的磁极模型，另一个是仅含铁极模型，如图3(a)、(b)所示。这样气隙磁通可从两个模型分析结果合成得到，并用于电机特性的计算，无论电机是否加负载。这种方法是合理的假设：即磁通从N极边磁极通过导磁机壳流向S极边磁极；与此同时，磁通从S极边铁极流向N极边铁极。实际上，不能用图(3)所示的模型合理计算通过电枢和转子轭的磁通，这个模型可以视为导磁机壳足够厚，磁路不易饱和。Asaresult,twoseparatemodelswereprovidedinvolvingN-sideandS-sidemagnetpoles,andcorepoles,respectively,asshowninFigs.3(a)and(b).Asaresult,thegapmagneticfluxwasfoundbycombininganalyticalresultstobethenusedincalculationofcharacteristicsnomatterwhatloadwasapplied.ThismethodisjustifiedassumingthatthefluxoutflowingfromtheN-sidemagnetpolegoestoanS-sidemagnetpoleviabackyoke,

whilesimilarly,thefluxoutflowingfromtheS-sidecorepolegoestotheN-sidecorepole.Actually,magneticfluxgoingthroughthearmatureandrotorbackyokecannotbeaccountedforproperlyintermsofthemodelshowninFig.3.Thismodel,however,mayberecognizedasacceptablesincethebackyokeisthickenough,andnotsusceptibletomagneticsaturation.LmEsiii.肚吋日耻却poles■Ihlhhdelor«c*epciks.图3二维有限元分析模型如图所示，等位周期性边界条件施加在边界线上，零磁位的约束条件施加在铁心内外圆周上。另外，用两极之间的电流表示励磁绕组磁动势，对应于各极之间磁场的大小和方向。对于空载下的两个模型，这些电流假定为在各自槽内的电枢电流。事实上，N极边和S极边由相同的励磁绕组励磁,这意味着模型中的磁动势只是实际磁动势的一半。在下面的讨论中，为了避免在模型和样机涉及励磁电流和磁动势之间发生混淆，所有的值都转换为用样机的值来表示。Asshowninthediagram,periodicboundaryconditionsofequalpotentialareimposedattheboundarylines,whilelimitingconditionsofzeropotentialareimposedalongtheinnerandoutercircumferencesofthecore.Also,mmfofthefieldwindingisrepresentedaselectriccurrentsinthegapbetweenpoles,withregardtomagnitudeanddirectionofmagneticfieldatrespectivepoles.Thesecurrentsareassumedtobearmaturecurrentsinrespectiveslotsforbothmodelsunderno-loadoperation.Infact,however,theN-polesideandtheS-polesideareexcitedthroughthesamefieldwinding,whichmeansthatthismodelshowsmmfthatisonlyhalftheactualvalue.Therefore,toavoidconfusionbetweenthemodelandtheprototypemachineinthefollowingconsiderationsinvolvingfieldcurrentandmmf,allthevalueswillbeconvertedintermsoftheprototypemachine.3.2空载特性分析图4空载磁场分布作为图3所示空载模型分析结果的例子，图4画出了励磁电流10A时的磁力线分布图。由于空载，永磁极和励磁绕组所产生的电动势共同作用于所有的磁极,两个模型中所画的磁通几乎相同。在电机空载运行条件下，磁通的大小随励磁电流而变，然而所画的磁通模型却保持不变。正是由于这个原因，本文省去了不同励磁电流下的磁场分布图。图4空载磁场分布ShowninFig.4aremagneticfluxplotsatthefieldcurrentof10A,asexamplesofanalyticalresultsobtainedforthemodelsshowninFig.3underno-loadoperation.Withno-load,electromagneticforcesproducedbypermanentmagnetsandfieldwindingareapplieduniformlyatallpoles,andthefluxplotsarenearlythesameforbothmodels.Also,incaseofno-loadoperation,themagnitudeofmagneticfluxvarieswithfieldcurrent,butthepatternofmagneticfluxplotremainsunchanged.Forthisreason,fluxplotsfordifferentfieldcurrentshavebeenomittedfromthispaper.采用有限元方法计算了励磁电流为-5A、0、5A时电机的气隙磁密，计算结果见图5,从左列至右列分别为磁极模型和铁极模型的气隙磁密分布。所有磁密分布只考虑一个周期,起点从模型的左边端点开始。FEManalysiswasperformedforfieldwindingundercurrentsof-5,0and5Atofindfluxdensitydistributionintheairgap.TheresultsaregiveninFig.5,wheretheleftandrightcolumnspertaintofluxdensitydistributionforthemodelsofmagnetpolesandcorepoles,respectively.Withallfluxdensitydistributions,oneperiodwasconsideredstartingfromtheleftendofthemodel.对于实际电机，N极边磁极与S极边铁极对齐，反之亦然。正由于此，电枢绕组的感应电压正比于磁通密度（图中左列和右列）的合成值（平均值），这一合成值的基波分量称之为等效气隙磁密，此等效气隙磁密也在图5中给出了。Withtheactualmachine,N-sidemagnetpolesareinlinewiththeS-sidecorepoles,andviceversa.Becauseofthis,thevoltageinducedinarmaturewindingisdirectlyproportionaltotheresultantvalue（averagevalue）ofthefluxdensitiesgivenintheleftandrightcolumnsinthediagram.Thefundamentalcomponentofthisresultantvaluewillbereferredtoasequivalentgapfluxdensity.ThevaluesofthisequivalentgapfluxdensityaregiveninFig.5aswell.显而易见，当励磁电流变化时，永磁极下的磁密几乎不变，而铁极处的磁密则是变化的。这表明，合成磁密，即等效气隙磁密是可控的。AsisevidentfromFig.5,whenvaryingfieldcurrentmagneticfluxremainsnearlyunchangedatmagnetpoleswhilechangingatcorepoles,whichmeansthattheresultingvalue,thatisequivalentgapfluxdensitycanbecontrolled.F'-.IdMacinttpoleCutepoleFluxdkruity.T[peakof3A/■■■'.fT'U'.九/JurtAc pal亡Al pule].IE4-0.R52AL.R.Jl./ii・EUuiluniwaJx(1.厲电□\出Ar pole1.LODG、Al potIlII脚aLJ1-K.ZREiiiklLintvaluu-.一..II沾1d.Xr" ■■ ~"At].II驚Alc^rcpafc0跖2上匚..一\l-JT-Jl-/ftisultanlvalue:'9-141;lAV•jn’EJVTAAlnia.gncLpcikAehmc[KileI.22D10HH3图5空载分析结果图6给出了不同励磁电流时上述分析的结果，一个等效气隙磁密曲线。由图显见，等效气隙磁密正比于励磁电流，尔后达到在最大电流时的极限值，那是由于电枢铁心凸极部分磁

饱和所引起的。PresentedinFig.6areresultsoftheaboveanalysiswithvaryingfieldcurrent,intheformofanequivalentfluxdensitycurve.Asisobviousfromthediagram,theequivalentgapfluxdensityvarieslinearlywithfieldcurrent,butthenreachesitslimitatlargecurrents,whichisattributabletomagneticsaturationatthearmaturecore'ssalientparts.图6等效气隙磁密图6等效气隙磁密、yokefluxdmficy(T)1小-5■0—1-0 F 1—. I i图7导磁机壳磁密另一方面，气隙N极边和S极边的合成磁通是环绕导磁机壳的直流磁通。这个磁通值可以容易地从图5中永磁极的磁密和铁极磁密之间的差值和气隙面积求出。也就是说，导磁机壳的磁通密度可以由该磁通和导磁机壳的截面积计算得到。图7给出了导磁机壳磁密与励磁电流的关系曲线。由图可见，通过导磁机壳的直流磁密随着等效气隙磁密的增加而下降,反之亦然。励磁电流为零时，导磁机壳的磁密为1.2T。由于导磁机壳磁饱和的原因，实际样机气隙磁密的有效控制区间是If>0o因此，为了进一步降低气隙磁密，从考虑磁饱和的角度出发，应合理选择导磁机壳的厚度。Ontheotherhand,resultingfluxattheN-sideorS-sideofthegapisadcfluxcirculatingthroughthebackyoke.ThevalueofthisfluxcaneasilybededucedfromthedifferencebetweenfluxdensitiesatmagnetpolesandcorepolesshowninFig.5,andthegaparea.Also,thefluxdensityatthebackyokecanbefoundfromthisflux,andthebackyokecross-sectionarea.Thefluxdensitycurvevs.fieldcurrentisshowninFig.7forthearmaturebackyoke.Asmaybeseenfromthediagram,dcfluxgoingthroughthebackyokedecreaseswithincreasingequivalentgapflux,andviceversa.Withzerofieldcurrent,armaturebackyokefluxdensityis1.2T.Becauseofmagneticsaturationatthebackyoke,withtheactualprototypemachine,efficientcontroloftheequivalentgapfluxisfeasibleatfieldcurrentIf>0.Therefore,iffurtherloweringofequivalentgapfluxisrequired,appropriatethicknessofthebackyokemustbeselectedwithregardtomagneticsaturation.上述计算结果是基于二维非线性分析，没有考虑导磁机壳的饱和问题。因此，与反向励磁电流区间的测量值（下面讨论）存在一个显著差异。Theabovecalculatedresultswerebasedontwo-dimensionalnonlinearanalysis,whichdidnotallowformagneticsaturationatthebackyoke.Hence,thereisasignificantdiscrepancywithmeasuredresults（tobediscussedbelow）intheareaofnegativefieldcurrent.3.3负载特性的分析方法HSY可用作电动机和发电机。然而，本文着眼于分析HSY的运行原理和基本特性，这样做有助于弄清楚电枢绕组感应电压和电流之间的相位关系。基于这个目的，重点放在分析HSY负载同步运行时的感应电压和电流。特别地，这种同步化几乎可以实现使发电机的功率因数为1,或如永磁型交流伺服电动机广泛使用的控制策略（仅通入q轴电流，以下简称

为Id=0控制)。HSYcanbeutilizedbothasmotors[7]andgenerators[8].However,thisstudyisintendedtoexplaintheoperatingprincipleandbasiccharacteristicsofHSY.Insodoing,itishelpfultospecifythephaserelationbetweenvoltageinducedinarmaturewindingandarmaturecurrent.Forthispurpose,theemphasiswasplacedonanalysisofloadoperationwiththeinducedvoltageandarmaturecurrentsynchronized.Specifically,thissynchronismisnearlyachievedincaseofageneratoroperatingatthepowerfactorof1,orwiththecontrolschemethatisusedwidely,forexample,withmagnet-typeacservomotors(whenq-axiscurrentonlyispassed;referredtobelowasId=0control).下面给出了HSY稳态运行时的电压和转矩方程，该方程可从永磁电动机公式中加入磁通项(由于励磁绕组)得到，并变换到以转子角速度旋转的同步d-q坐标系：GivenbelowarethevoltageequationandtorqueformulaforHSYsteady-stateoperation.Theexpressionswereobtainedbyaddingfluxterms(duetofieldwinding)toexpressionsforPMmotor[2],andconvertingtorotationaxesd-qsynchronizedwiththerotorangularspeed.=RI—0LIdadqqI+RI+3(A+MqddaqT二k[(A+MI)I+(L—L)II] (2)tffqdqdq式中，Vd、Vq分别为d、q轴电枢相电压分量，I『Iq分别为d、q轴电枢相电流分量，If为直流励磁电流，Ra为电枢绕组电阻，Ld、Lq分别为d、q轴电枢绕组自感分量，A为永磁体产生并与电枢绕组交链的磁链，Mf为励磁绕组与电枢绕组之间的互感，①为电源的角频率，kt为转矩常数。Here,Vd,Vqared-axisandq-axiscomponentsofarmaturephasevoltage;Id,Iqared-axisandq-axiscomponentsofarmaturecurrent;Ifisdcfieldcurrent;Raisthearmaturewindingresistance;Ld,Lqared-axisandq-axiscomponentsofarmaturewindingself-inductance;Aisthefluxlinkageinarmaturewindingduetomagnets;Mfisthemutualinductanceoffieldwindingandarmaturewinding;&isthepowersourceangularfrequency;andktisaconstant.用气隙磁密表示公式(1)、(2)，有3)二RI—3(LI+kB3)d ad Oq rq=RI+3(LI+kB)4)q aq O4)T二K(BI—BI)tdqqd(3)、(4)式中有下列关系kB二LI 、5)5)kB二A+MI+LI>rd ffaddK=kkd、d、q轴分量，Bd、Bq分别式中，L为电枢绕组的漏电感，L、L分别为电枢反应电成d aq为气隙磁通的d、q轴分量，kr、Kt分别为常数。Here.L°isthearmaturewindingleakageinductance;Lad、Laqared-axisandq-axiscomponentsofarmaturereactioninductance;Bd、Bqared-axisandq-axiscomponentsofgapflux;andkr、Ktareconstants.上式表明，如果已知d、q轴气隙磁密以及对应的电枢电流和电枢相电压，可以计算出电机的端电压和转矩。为了计算上面的气隙磁密，首先分析设置电流后的模型，然后再求气隙磁密。Theaboveexpressionssuggestthatd-axisandq-axiscomponents