Theory
for Electrical Machines : Principles and Practice Ming Cheng
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GeneralAirgapFieldModulationTheoryforElectricalMachines
IEEEPress
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AdamDrobot
Peter(Yong)Lian
AndreasMolisch
SaeidNahavandi
JeffreyReed
ThomasRobertazzi
DiomidisSpinellis
AhmetMuratTekalp
GeneralAirgapFieldModulationTheory
forElectricalMachines
PrinciplesandPractice
MingCheng
SoutheastUniversity
Nanjing,China
PengHan Ansys,Inc.
Irvine,USA
YiDu
JiangsuUniversity
Zhenjiang,China
HonghuiWen
SoutheastUniversity Nanjing,China
Copyright©2023byTheInstituteofElectricalandElectronicsEngineers,Inc.Allrights reserved.
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Contents
Preface xi
AbouttheAuthors xv
AbouttheCompanionWebsite xvii
1Introduction 1
1.1ReviewofHistoricalDevelopmentofElectricalMachines 1
1.2LimitationsofClassicalElectricalMachineTheories 7
1.2.1FragmentationofElectricalMachineTheories 7
1.2.2LimitationsinAnalysisofOperatingPrinciples 8
1.2.3LackofUniformityinPerformanceAnalysis 9
1.3OverviewofMagneticFieldModulationMachinesandtheir Theories 11
1.4ScopeandOrganizationoftheBook 14 References 16
2AirgapMagneticFieldModulationPhenomenainElectrical Machines 23
2.1TraditionalElectricalMachines 23
2.1.1BrushedDirectCurrentMachines 24
2.1.2InductionMachines 26
2.1.3SynchronousMachines 29
2.2FieldModulationMagneticGears 33
2.2.1ConstructionandOperatingPrinciple 34
2.2.2AirgapMagneticFieldModulationBehaviors 36
2.2.3OtherMGTypes 42
2.3MagneticallyGearedMachines 45
2.3.1EvolutionofMGMs 46
2.3.2AirgapMagneticFieldModulationBehaviors 48
2.4PMVernierMachine 50
2.4.1MachineConstruction 50
2.4.2AirgapMagneticFieldModulationBehaviors 50
2.5LinearPMVMachine 52
2.5.1MachineConstruction 53
2.5.2AirgapMagneticFieldModulationBehaviors 54
2.6Flux-switchingPMMachine 57
2.6.1MagneticFieldModulationMechanismofPMField 58
2.6.2MagneticFieldModulationMechanismofArmature Field 62
2.7Doubly-FedMachines 66
2.7.1ClassificationandOperatingPrinciples 67
2.7.2CascadedType 70
2.7.3ModulationType 71
2.7.4CommonalitiesandDifferencesofExistingBrushless Doubly-fedMachines 78
2.8UniformityofMachineOperatingPrinciples 79 References 82
3ThreeKeyElementsModelforElectricalMachines 87
3.1Introduction 87
3.2ClassicalWindingFunctionTheoryandItsLimitations 89
3.2.1WindingMMF 89
3.2.2ClassicalWindingFunctionTheory 92
3.2.3LimitationsofClassicalWindingFunctionTheory 95
3.3ThreeKeyElements 99
3.3.1SourceofExcitation 101
3.3.2Modulator 101
3.3.3Filter 103
3.4MathematicalRepresentationofThreeKeyElements 103
3.4.1SourceMMF 104
3.4.2ModulationOperator 108
3.4.3Filter 120
3.4.4UnifiedAirgapModel 121
3.4.5DualityBetweenElectricalMachinesandSwitchingPower Converters 124
3.5TorqueDecomposition 129
3.5.1GeneralTorqueEquation 129
3.5.2Wound-FieldSalient-PoleSM 132
3.5.3SynRM 135
3.5.4Squirrel-CageIM 135
3.5.5BDFRM 136
3.5.6BDFIM 138
3.5.7FSPMMachine 139
3.5.8PMVMachine 151
3.5.9Axial-FluxPMVMachine 155 References 158
4AnalysisofMagneticFieldModulationBehaviors 163
4.1Introduction 163
4.2MagneticFieldModulationBehaviorsandTorqueComponents 163
4.2.1AsynchronousandSynchronousModulation Behaviors 164
4.2.2AsynchronousandSynchronousTorqueComponents 166
4.3CharacterizationofModulationBehaviorsinTypicalMachine Topologies 167
4.3.1BrushedDCM 168
4.3.2Wound-FieldSalient-PoleSM 168
4.3.3Wound-FieldNon-Salient-PoleSMandSlip-Ring Doubly-FedInductionMachine 169
4.3.4SquirrelCageIMandBDFIM 170
4.3.5SynchronousReluctanceMachineandBrushless Doubly-FedReluctanceMachine 171
4.3.6Surface-MountedPMSMandFRPMMachine 173
4.3.7InteriorPMSMandFSPMMachine 174
4.3.8SwitchedReluctanceMachineandVernierMachine 175
4.3.9Magnetically-GearedMachineandPMVernier Machine 176
4.4TorqueCompositionofTypicalMachineTopologies 177
4.4.1CaseStudyI–BDFIM 179
4.4.2CaseStudyII–BDFMwithaHybridRotor 183
4.4.3CaseStudyIII–FSPMMachine 186
4.5MagneticFieldModulationBehaviorsofVariousModulators 188
4.5.1SalientReluctancePoleModulator 188
4.5.2MultilayerFluxBarrierModulator 197
4.5.3Short-CircuitedCoilModulator 202
4.6InterchangeabilityofModulators 213
4.6.1ComparisonofThreeBasicModulatorTypes 213
4.6.2InfluenceofModulatorsonMachinePerformance 217 References 225
5PerformanceEvaluationofElectricalMachinesBasedon
GeneralAirgapFieldModulationTheory 227
5.1Introduction 227
5.2Squirrel-CageIM 227
5.2.1AirgapMagneticFieldAnalysis 229
5.2.2InductanceandTorqueCharacteristics 231
5.3BrushlessDoubly-fedMachines 234
5.3.1StatorWindingMMF 235
5.3.2AirgapMagneticFieldandInductances 238
5.3.3QuantitativeAnalysisof4/2BDFRM 250
5.3.4QuantitativeAnalysisof4/2BDFIM 264
5.4SynRM 272
5.4.1Inductances 272
5.4.2TorqueCharacteristic 274
5.5FRPMMachine 276
5.5.1MagneticFieldModulationBehavior 276
5.5.2InfluenceofKeyTopologicalParameters 279
5.5.3ExperimentalValidation 280
5.6ComparisonofRepresentativeMachineTopologies 284 References 288
6InnovationofElectricalMachineTopologies 293
6.1InnovationMethods 293
6.1.1ChangeofSourceMMF 294
6.1.2ChangeofModulator 296
6.1.3ChangeofFilter 296
6.1.4ChangeofRelativePositionofThreeKeyElements 297
6.1.5ChangeofRelativeMotionofThreeKeyElements 297
6.2DSPMMachinewith Π-ShapedStatorCore 298
6.2.1MachineConstructionandOperatingPrinciple 299
6.2.2PerformanceAnalysisandComparison 308
6.2.3PrototypeandExperimentalResults 310
6.3Stator-PMVariableReluctanceResolver 313
6.3.1MachineConstructionandOperatingPrinciple 315
6.3.2Odd-PoleIssueandSolutionsBasedonGAFMT 318
6.4FRPMMachine 322
6.4.1OperatingPrinciple 324
6.4.2AnalysisofOpen-CircuitBack-EMFBasedonGAFMT 330
6.5FSPMMachinewithFull-PitchWindings 332
6.5.1MachineConstructionandOperatingPrinciple 334
6.5.2InfluenceofKeyGeometricParameters 336
6.5.3ComparativeStudy 340
6.6Rotor-PMFSPMMachine 341
6.6.1MachineConstructionandOperatingPrinciple 342
6.6.2WindingConsistencyandComplementarity 345
6.6.3FundamentalElectromagneticPerformance 347
6.7Dual-RotorMagnetically-GearedPowerSplitMachine 359
6.7.1MachineConstructionandOperatingPrinciple 360
6.7.2ModesofOperation 362
6.7.3AsymmetryinMagneticCircuits 365
6.7.4ComplementaryMGPSMandExperimentalValidation 370
6.8StatorField-ExcitationHTSMachines 383
6.8.1StatorField-ExcitationHTSFlux-SwitchingMachine 385
6.8.2Double-StatorFieldModulationSuperconductingExcitation Machine 387
6.8.3TechnicalChallengesandOutlookofFieldModulationHTS Machines 391
6.9BrushlessDoubly-FedReluctanceMachinewithanAsymmetrical CompositeModulator 393
6.9.1PhaseShiftPhenomenonofModulatedHarmonics 394
6.9.2AsymmetricalCompositeModulator 398
6.9.3ExperimentalVerification 400 References 402
7OtherApplicationsofGeneralAirgapFieldModulation Theory 409
7.1Introduction 409
7.2AnalysisofRadialForcesinBrushlessDoubly-fedMachines 410
7.2.1ElectromagneticVibrationandNoiseinElectrical Machines 410
7.2.2AnalysisofRadialForces 410
7.2.3CalculationofRadialForces 411
7.2.4Pole-PairCombinationsWithoutUMP 422
7.3DesignofSuspensionWindingsforBearinglessHomopolarand ConsequentPolePMMachines 423
7.3.1DesignPrincipleofPole-ChangingWindings 424
7.3.2Solution1:CoilSpany = 4 427
7.3.3Solution2:CoilSpany = 5 427
7.4LossCalculation 427
7.4.1StrayLoadLossCalculationforIMs 432
7.4.2ComputationallyEfficientCoreLossCalculationforFSPM MachinesSuppliedbyPWMInverters 449
x Contents
7.5OptimizationofSalientReluctancePoleModulatorsforTypicalField ModulationElectricalMachines 472
7.5.1TypicalSalientReluctancePoles 473
7.5.2OptimizationforMagnetically-GearedPMMachine 477
7.5.3OptimizationforFRPMMachine 482
7.5.4GeneralGuidelines 487
7.6Airgap-Harmonic-OrientedDesignOptimizationMethodology 488
7.6.1Airgap-Harmonic-OrientedDesignOptimization Concept 490
7.6.2SensitivityAnalysis 495
7.6.3Multi-ObjectiveOptimization 498
7.6.4OptimizationResultsandExperimentalValidation 501 References 508
AppendixADerivationofModulationOperators 513
A.1DerivationofModulationOperatorforShort-circuitedCoils 513
A.2DerivationofModulationOperatorforSalientReluctancePoles 514
A.3DerivationofModulationOperatorforMultilayerFluxBarriers 516
AppendixBMagneticForceofCurrent-CarryingConductorsinAirgapandin Slots 521
References 524
AppendixCMethodsforForceandTorqueCalculation 525
C.1MaxwellStressTensorMethod 525
C.2PrincipleofVirtualWork 530
C.2.1TorqueDerivedfromMagneticStoredEnergyandVirtual Displacement 530
C.2.2TorqueDerivedfromCo-energyandVirtual Displacement 532
References 533
Index 535
Preface
Electricalmachinesaredevicesthatconvertmechanicalenergyintoelectrical energyorviceversa.Theywereinventedinthe1800sandhaveahistoryof nearly200years.Otherinventionsofsimilarages,suchastheWattsteam engine,telegraph,incandescentlightbulb,etc.,havebeenoutdatedbyemerging technologies.Bycontrast,theelectricalmachineshowsgreattenacityandvitality, becomingalivingfossiloftheIndustrialRevolution.
Demandforhigh-performanceelectricalmachinesisincreasingdaybyday withtherapiddevelopmentofoursocialeconomy.Applicationareasofelectrical machineshaveextendedfromconventionalindustrialdrivetoaerospace,transportation,numericalcontrolmachinetools,robots,andotherhigh-techfields, rangingfromdeepbelowthesurfaceoftheearthtodeepspace,fromthefurthest depthsoftheoceantothesurfacesoflandandsea.
Thediversityinperformancerequirementsfordifferentapplicationsleadsto theinventionofnovelelectricalmachinetopologieswithdifferentperformance advantages,especiallythosehavingmultipleworkingspatialharmonics,such asthemagneticallygearedmachine(MGM),permanentmagnetvernier(PMV) machine,brushlessdoublyfedmachines,justtonameafew.
Thesenewmachinetopologiesshowsignificantmagneticfieldmodulation effects,posinggreatchallengestoexistingtheoriesfortheanalysisofelectrical machines.Theoperationofsomeemergingelectricalmachines,suchasthe PMVmachinewithdissimilarnumbersofstatorwindingpolepairsandmagnet polarities,canhardlybeexplaineddirectlybythewell-establishedtheoryfor inductionmachinesandsynchronousmachines.Inaddition,mosttheoriesand methodsfortheanalysisofelectricalmachinesweredevelopedandtherefore validforonlycertainmachinetypes.
Basedontheextensivescientificandindustrialresearchforhigh-performance electricalmachinesanddrivetechnologiesconductedbytheJiangsuElectrical Machines&PowerElectronicsLeague(JEMPEL),SoutheastUniversity,Nanjing, China,overthepastdecades,theauthorsnoticedthegeneralityofairgapmagnetic
fieldmodulationphenomenainelectricalmachinesanditsinstrumentalrolein improvingperformanceofelectricalmachines.Thediscoverieswerefurtherexaminedagainstalmostalltheknownelectricalmachinetopologies,andthentheorizedtodevelopthegeneralairgapfieldmodulationtheory.
Thebookisorganizedintosevenchaptersandthreeappendices,asoutlined below:
● Chapter1reviewsthehistoricaldevelopmentofelectricalmachinesandtheir theories.
● Chapter2analyzestheairgapmagneticfieldmodulationphenomenaincommonmachinetopologies,aimingtorevealtheubiquityofmagneticfieldmodulationphenomenainelectricalmachines.
● Chapter3abstractsaunitmachinewithonestator,onerotorandonelayerof airgapasacascadeofthreekeyelements,basedonwhichgeneralizedmathematicalmodelsforthethreeelementsareproposed,formingthegeneralairgap fieldmodulationtheoryframeworkforelectricalmachines.
● Chapter4analyzestherelationshipbetweendifferentmodulationbehaviorsand theirtorquecompositions.
● Chapter5appliesthegeneralairgapmagneticfieldmodulationtheorytomultiplerepresentativemachinetopologiestoshowitsapplicationinqualitative analysisandquantitativecalculationofmachineperformance.
● Chapter6coverstheinnovationofmachinetopologywiththeguidanceofthe generalairgapfieldmodulationtheory.
● Chapter7presentsmoreapplicationexamplesofthedevelopedtheory.
● AppendixAshowsthemathematicalderivationofthethreetypicalmodulation operators.
● AppendixBclarifiestherelationshipbetweenelectromagneticforces/torques onconductorsplacedintheairgapandin-slotconductors.
● AppendixCpresentstheMaxwellStressTensormethodandprincipleofvirtual work,whicharethebasisofforce/torqueanalysisusingthegeneralairgapfield modulationtheory.
Thecontentspresentedinthisbookareaselectedcollectionofscientificand industrialresearchworkconductedbytheJEMPELanditsextendedresearch groupsduringthepastdecades.TheauthorsareverygratefultoalltheJEMPEL members,especiallyProf.XiaoyongZhu,Prof.YubinWang,Dr.LeSun,Dr.Xinkai Zhu,Dr.JingxiaWang,Dr.YuZengfortheirdedicatedassistanceinpreparingthe manuscript,andDr.GanZhang,Mr.ZhengzhouMa,Ms.ChenchenZhaofortheir tremendoushelpinthepreparationofmainfigures.
TheauthorswouldalsoliketoexpresstheirsinceregratitudetoProf.WeiHua, Prof.JianzhongZhang,Prof.WenxiangZhao,Prof.XianglinLi,Dr.QiangSun, Dr.HongyunJia,Dr.FengYu,Dr.FengLi,Dr.LingyunShao,Dr.PengSu,
Preface
Dr.MinghaoTong,Dr.XiaofengZhuandDr.PeixinWangfortheirexcellent researchoutcomes,whichareessentialingredientsofthisbook.
Wearedeeplyindebtedtoourcolleaguesandfriendsworldwidefortheir continuoussupport,encouragement,anddiscussiononthesubjectmatterover theyears,especiallyProf.AymanEL-Refaie,Prof.C.C.Chan,Prof.DanM.Ionel, Prof.HosseinTorkaman,Prof.IonBoldea,Prof.IqbalHusain,Prof.JamesKirtley, Prof.JianguoZhu,Prof.K.T.Chau,Prof.LongyaXu,Prof.W.N.Fu,Prof.Ying Fan,Prof.Z.Q.Zhu,Prof.ZheChen,Prof.ZhengWang,Dr.ArijitBanerjee, Dr.BaoyunGe,Dr.HaoHuang,Dr.JianningDong,Dr.KaiyuanLu,Dr.MingXu, Dr.SaZhu,Dr.ShengyiLiu,Dr.YingPang,Ms.XiaopingLi,fortheirvaluable feedbackonthistheory.
Wealsomuchappreciatethereviewersofthisbookfortheirthoughtfuland constructivecomments,andEditorsofJohnWiley&Sonsfortheirprofessional andtimelysupportinthereviewandproductionprocess.
Lastbutnotleast,wethankourfamiliesfornurturingandunconditionallysupportingthewritingofthisbook.
AbouttheAuthors
MingCheng receivedhisB.Sc.andM.Sc.degreesfromSoutheastUniversity, Nanjing,China,in1982and1987,respectively,andhisPh.D.degreefromthe UniversityofHongKong,HongKong,in2001,allinelectricalengineering.Since 1987,hehasbeenwithSoutheastUniversity,whereheiscurrentlyanEndowed ChairProfessorattheSchoolofElectricalEngineeringandtheDirectorofthe ResearchCenterforWindPowerGeneration.
HeisaFellowoftheInstituteofElectricalandElectronicsEngineers(IEEE) andtheInstitutionofEngineeringandTechnology(IET)andwasaDistinguished LectureroftheIEEEIndustryApplicationsSocietyfor2015/2016.Hehasserved aseditor-in-chief,editorandeditorialboardmemberofvariousinternational journals,aswellaschairandorganizingcommitteememberofmanyinternationalconferences,especiallyintheareaofElectricalMachinesandPower Electronics.
Histeachingandresearchinterestsincludeelectricalmachines,motordrives forEV,renewableenergygeneration,andservomotor&control.Intheseareas, hehaspublishedover500refereedtechnicalpapersand7booksandholdsover 150inventionpatents.
Hehasreceivedmanyawards,includingSecondPrizeintheStateTechnological InventionAwards(givenbytheStateCouncilofthePeople’sRepublicofChina); FirstPrizeinChina’sMinistryofEducation’sNaturalScienceAwards;FirstPrize inJiangsuProvincialGovernment’sScienceandTechnologyAward;theIET AchievementAward;andtheEnvironmentalExcellenceinTransportationAward forEducation,Training,andPublicAwarenessbySAEInternational.
PengHan receivedB.Sc.andPh.D.degreesinelectricalengineeringfromthe SchoolofElectricalEngineering,SoutheastUniversity,Nanjing,China,in2012 and2017,respectively.
FromNovember2014toNovember2015,hewasaGuestPh.D.studentat theDepartmentofEnergyTechnology,AalborgUniversity,Aalborg,Denmark, wherehefocusedonbrushlessdoublyfedmachines’applicationinwindenergy
conversionandhigh-powerdrives.HeiscurrentlywithAnsys,Inc.,USA,as aSeniorApplicationEngineer.BeforejoiningAnsys,hewasaPostdoctoral ResearcherwiththeCenterforHighPerformancePowerElectronics(CHPPE) DepartmentofElectricalandComputerEngineering,TheOhioStateUniversity, andlatertheSPARKLaboratory,DepartmentofElectricalandComputerEngineering,UniversityofKentucky.Hiscurrentresearchinterestsincludeelectrical machines,machinedrives,powerelectronics,andrenewableenergy.
HeisanIEEESeniorMemberandanAssociateEditorforIEEETransactionson IndustrialElectronics,IEEETransactionsonIndustryApplicationsandJournal ofPowerElectronics.Hereceivedtwobestpaper/posterawardsfromIEEE conferences,andThirdPrizeintheIEEEIASStudentThesisContestin2018.
YiDu receivedB.Sc.andM.Sc.degreesinelectricalengineeringfromJiangsu University,Zhenjiang,China,in2002and2007,respectively,andaPh.D.degree inelectricalengineeringfromSoutheastUniversity,Nanjing,China,in2014.
HehasbeenwithJiangsuUniversitysince2002,whereheiscurrentlya ProfessorintheSchoolofElectricalandInformationEngineering.From2018to 2019,hewasaVisitingProfessorwiththeDepartmentofElectronic&Electrical Engineering,TheUniversityofSheffield,Sheffield,UK.Hisresearchinterests includedesignandanalysisofelectricalmachinesystemswithlow-speedand high-torqueoutputs,andwithwide-speedrange.
HonghuiWen receivedB.Sc.andPh.D.degreesinelectricalengineeringfrom theSchoolofElectricalEngineering,SoutheastUniversity,Nanjing,China,in2016 and2021,respectively.
SinceJanuary2022,hehasbeenwiththeCollegeofElectricalandInformationEngineering,HunanUniversity,Changsha,China,whereheiscurrentlyan AssistantProfessor.Histeachingandresearchinterestsincludethedesign,analysis,andoptimizationofmagneticfieldelectricalmachines.Intheseareas,hehas publishedonebookandover10peer-reviewedtechnicalpapers.
AbouttheCompanionWebsite
Thisbookisaccompaniedbyacompanionwebsite: www.wiley.com/go/genairgapfieldmodulationtheory
Thewebsiteincludesmodelsandscripts.
1.1ReviewofHistoricalDevelopmentofElectrical Machines
Electricalmachinesareelectromagneticdevicestoachieveelectromechanical energyconversion.SinceJacobiinventedtheDCmachine(DCM)in1834 andTeslainventedtheinductionmachine(IM)in1880s,electricalmachine technologyhasdevelopedrapidly,anditsapplicationhasbecomemoreand moreextensive.Electricalmachineshavebecomeoneofthemostimportant energyandpowertechnologiestosupportthenationaleconomy.Varioustypes ofmachineswithpowerlevelsrangingfromseveralmilliwattstohundredsof megawatts,especiallythethreetraditionalmachinetopologies,namelytheDCM, ACinduction(asynchronous)machine,andACsynchronousmachine(SM),have madegreatcontributionstothedevelopmentofhumansociety[1,2].
Itisworthmentioningthatthesteamengine,telegraph,incandescentlamp, etc.,whichappearedatvirtuallythesametimeaselectricalmachines,havebeen replacedbyemergingtechnologiesandhavegraduallyfadedintodisuse.Bycontrast,theelectricalmachinepresentsatenaciousvitality,andcanbeconsidereda survivingfossilofthemodernindustrialrevolution,onewhichconstantlyrenews itslife.Correspondingly,thedevelopmentandinnovationofelectricalmachine theoriesandtechnologieshaveneverstopped.
Withtheproliferationofelectrificationandautomationtechnologies,the applicationofelectricalmachineshasexpandedfromconventionalindustrial drivetoaerospace,transportation,CNCequipment,roboticsandotherhigh-tech fields,andfromgroundtodeepspace,deepsea,anddeepearth.Theperformance requirementsofmachinesfordifferentapplicationsareconstantlyrefined, andthetraditionalbrushedDCMs,IMs,andSMsaredifficulttomeetthe demandingrequirementsofnewfieldsandapplications.Meanwhile,therapid developmentofmaterialtechnology,processingandmanufacturingtechnology, andcontroltechnology,combinedwithnewapplicationrequirements,hasgiven
GeneralAirgapFieldModulationTheoryforElectricalMachines:PrinciplesandPractice, FirstEdition.MingCheng,PengHan,YiDu,andHonghuiWen. ©2023TheInstituteofElectricalandElectronicsEngineers,Inc.Published2023byJohnWiley&Sons,Inc. Companionwebsite:www.wiley.com/go/genairgapfieldmodulationtheory
risetovariousnewelectricalmachineswithdifferentconstructions,different workingprinciples,anddifferentperformanceadvantages,suchas:synchronous reluctancemachines(SynRMs)[3–5],permanentmagnet(PM)brushless machines[6,7],verniermachines[8],brushlessdoubly-fedinductionmachines (BDFIMs)[9–11],brushlessdoubly-fedreluctancemachines(BDFRMs)[12,13], transversefluxmachines[14],switchedreluctancemachines(SRMs)[15,16], stator-PMbrushlessmachines[17–20],PMvernier(PMV)machines[21,22], magnetically-gearedmachines(MGMs)[23–26],dual-mechanical-port(DMP) machines[27,28],etc.
Inordertoprovideanoverviewoftherelevantresearchonelectricalmachines,a bibliometricanalysiswasperformedinIEEEXploredigitallibrarydatabaseatthe endof2021.TheresultssummarizedinFigure1.1showthediversityofmachine topologiesandsoaringnumbersofpublicationsonthese“unconventional” machines.
● Asrepresentativetraditionalelectricalmachines,IMsandwound-field salient-poleSMshaveexperiencedthelongesthistoryofresearch.Considerable researchworkhadbeendonebeforethefield-orientedcontrol(FOC)method wasinventedbyF.Blaschkein1971.ResearchonIMsgrowssteadilyand peakedat2014–2015.Incontrast,researchonwound-fieldsalient-poleSMs wasinterruptedinthe1970sand1980sandresumedlater,butitismuchless popularthanthatofIMs.
Figure1.1 Numberofpublicationson“unconventionalmachines”indexedbyIEEE Xploredigitallibrarydatabase.DS/DRM–Dual-stator/dual-rotormachine,FSPM–Flux-switchingPM,VM–Verniermachine,DSPM–Doubly-salient-polePM, VFRM–Variablefluxreluctancemachine,FRPM–Flux-reversalPM.
● High-energy-productPMmaterialswereintroducedintothemanufacturingand performanceimprovementofelectricalmachinesinthelate1970s,afterwhich theresearchonPMbrushlessmachinesbegantogrowsteadily,withadramatic increasein2010.Afterwards,theresearchonPMmachinesdecreasedduetothe largepricefluctuationofPMmaterials,butstillstayedatahighlevel.
● InadditiontoIMsandPMSMs,researchonSRMshascontinuedtogrowsteadily sinceitsrevivalin1980.Bycontrast,researchonSynRMshasbeenmorestable, withadramaticgrowthin2014and2015.Itwasprobablycausedbythelarge pricefluctuationofPMmaterials,whichledtotheconceptsof“PM-free”and “less-PM”electricalmachines.
● Theso-called“stator-PMmachines”inventedinthe1990swhichmainlyinclude doubly-salient-polePMmachines,flux-switchingPMmachines(FSPMs)and flux-reversalPMmachinesstartedtogaintheirpopularityafter2005.Compared todoubly-salient-polePMmachinesandflux-reversalPMmachines,FSPMs weremoreattractivetoresearchersinbothacademiaandindustry.Research onFSPMswitnessedadramaticincreasein2014andpeakedin2014–2015.
● ResearchonBDFIMsandBDFRMsdatesbacktoearly1970s.Ithasbeen increasingsincethe1990sandpeakedin2014–2015.
● ResearchonMGMsandverniermachinesstartedintheearly1990sbutdidnot receivemuchattentionuntil2010.Itwashardlyaffectedbythepricefluctuation ofPMmaterials.
● Dual-stator/dual-rotormachinetopologiesstartedtogainpopularityafter2004 andkeepincreasingsteadilyafterwards,peakingin2014–2015.
Atthesametime,theoriesforelectricalmachineshavealsobeenenrichedand improved.Inadditiontothebasicphysicallaws(suchasthelawofelectromagnetic inductionandthelawofelectromagneticforce)followedbyelectricalmachines, avarietyoftheoriesandanalysismethodshaveemergedaccordinglytoconduct theperformanceanalysisandcalculationofdifferentmachines.
Forexample,toaddressthedifficultiescausedbytheunequaldirect-axis(d-axis) andquadrature-axis(q-axis)reluctanceofthesalient-poleSMinarmaturereactioncalculation,A.Blondelproposedthetwo-reactiontheory[29,30].Whenthe axisofthearmaturemagnetomotiveforce(MMF) F a coincidesneitherwiththe d-axisnorwiththe q-axis, F a canbedecomposedintothe d-axiscomponent F ad andthe q-axiscomponent F aq ,asshowninFigure1.2.Thenthe d-axisand q-axis armaturereactionmagneticfieldscanbecalculatedseparately,andfinallytheyare superimposed.Ithasbeenprovedthatsatisfactoryresultscanbeobtainedbyusing thetwo-reactiontheorywhenthemagneticcircuitsaturationisnottakeninto account.Afterthat,R.H.Parkfurthergeneralizedandextendedthetwo-reaction theoryandproposedthefamousParktransformation,therebyestablishinggeneralcalculationformulaforthecurrent,voltage,powerandtorqueofSMsunder
Figure1.2 DecompositionofarmatureMMFofwould-fieldsalient-poleSMinto d -axis and q-axiscomponents.
steadyandtransientstates[31],whichbringsgreatconveniencetotheanalysis andcalculationofSMs.
AnotherexampleisthatG.Kronproposedaunifiedtheoryforanalyzingelectricalmachines[32],whichraisedthetheoryofelectricalmachinestoanewlevel.He analyzedmachinecharacteristicsfromtheperspectiveofenergyforthefirsttime. Accordingtothelawofenergyconservation[33],therearefourformsofenergy inelectricalmachines:electricalenergy,mechanicalenergy,electromagneticfield storageenergyandthermalenergy.Accordingtothemotorconvention,theenergy equationcanbewrittenas
Inaddition,theconceptofmagneticco-energywasproposed,andtherelationshipbetweenmagneticco-energyandmagneticenergyis:
where W m isthemagneticenergy, W ′ m themagneticco-energy, i1 thewinding current,and �� 1 themagneticfluxlinkage.Whenrepresentedgraphically,themagneticco-energyistheareaoftheverticallyshadedpartinFigure1.3.Therateof changeofthemagneticco-energytothemechanicaldisplacementistheelectromagnetictorque:
Figure1.4 Two-axisprimitivemachine.
where T em istheelectromagnetictorqueand �� themechanicaldisplacementangle ofelectricalmachines.
Again,B.Adkinsetal.proposedthegeneraltheoryofACmachines.Any electricalmachinescanbeequivalenttoaprimitivemachinemodelbycoordinate transformation,asshowninFigure1.4.Basedonthisprimitivemachinemodel,a setofvoltageequationsrepresentingtherelationshipbetweenvoltageandcurrent oftheprimitivemachineandtorqueequationsrepresentingtherelationship betweentorqueandcurrentcanbederivedandthensolvedusingaunified approach[34].
Cellswithsolid-linebordersinTable1.1listtypicalelectricalmachinetheoriesinthehistoryofmachinedevelopmentaswellastheirapplications,authors andotherinformation,whichtogetherconstitutetheclassicalelectricalmachine theoryandlayasolidtheoreticalfoundationforthedevelopmentofmachinetechnologyrepresentedbyDCMs,IMs,andSMs.
Figure1.3 Magneticenergy W m andmagneticco-energy W m ’
Table1.1 Typicaltheoriesforelectricalmachines.
YearNameoftheoryTypicalapplicationsAuthors
1913Two-reaction theory[29,30]
1925Rotatingmagnetic fieldtheory[35]
1926Cross-fieldtheory [36]
1929Park transformation [31]
1930Generalized theoryof electrical machinery[32]
1954Symmetrical components[37]
1959Spacevector theoryfor transientanalysis [38]
1973Generaltheory usingequivalent magneticcircuit [39]
1975Thegeneral theoryofAC machines[34]
1965Windingfunction theory[40,41]
1992Spiralvector theory[42]
1994Unifiedtheoryof torqueproduction [43]
2017Generalairgap fieldmodulation theory[44]
Wound-fieldsalient-pole SMsandSynRMs
ACelectricalmachines withsinusoidal back-electromotiveforce (back-EMF)
ACelectricalmachines withsinusoidalback-EMF
ACelectricalmachines withsinusoidalback-EMF
Electromechanicalenergy conversiondevices
A.Blondel(France)
K.L.Hansen(United States)
H.R.West(United States)
R.H.Park(United States)
G.Kron(UnitedStates)
ACelectricalmachines withsinusoidalback-EMF
W.V.Lyon(United States)
IMsandSMsPákK.Kovács (Hungary)
SMsandDCMsJ.Fienne(United Kingdom)
ACelectricalmachinesB.Adkins(United Kingdom)
IMsandSMsN.L.Schmitzand D.W.Novotny(further improvedbyT.A.Lipo) (UnitedStates)
ACcircuitsandmachinesS.Yamamura(Japan)
AllelectricalmachinesD.A.Staton,T.J.E. Miller,etal.(United Kingdom)
AllelectricalmachinesM.Cheng,P.Han, W.Hua(China)
1.2LimitationsofClassicalElectricalMachine Theories
Althoughtheclassicalelectricalmachinetheoryhasbroughtgreatconvenience totheanalysisoftraditionalDC,inductionandsynchronousmachines,itstill seemstobeinadequateinanalyzinglargenumbersofnewmachinetopologies. Insummary,limitationsoftheclassicalelectricalmachinetheorymainlyliein thefollowingthreeaspects.
1.2.1FragmentationofElectricalMachineTheories
Amongexistingelectricalmachinetheories,thetwo-reactiontheorywasprimarilyusedtoanalyzeSMs[29–31].Therotatingmagneticfieldtheory[35] andcross-fieldtheory[36]weresuitableforACmachineswithsinusoidal back-electromotiveforces(EMFs).Theunifiedtheoryoftorqueproduction basedonmagneticfluxlinkage-currenttrajectorieswasemployedtoanalyzeall electricalmachinesbynumericalmethods[43].Thewindingfunctiontheorywas mainlyforIMsandSMs[41].ThegeneraltheoryofACmachinesbasedonthe two-axisprimitivemachine[34]andgeneraltheoryusingequivalentmagnetic circuits[39]weremainlyappliedtoIMsandSMs,thoughtheycanalsobefurther extendedforDCMs.Itcanbeconcludedthattheexistingtheoriesareonlyvalid forcertainmachinetopologiesandnoneofthemareapplicabletoallmachine types.
Inaddition,sometheoriescanonlybeusedastoolsforquantitativeanalysisof machineperformance,butfailtointerpretthephysicsbehindthemachineoperation,orviceversa.Forinstance,thegeneraltheoryofACelectricalmachines developedbyB.Adkinsetal.basedonthetwo-axisidealizedmachineorprimitive machinemodel[34]isonlyvalidforconventionalACmachineswithexplicitdirect andquadratureaxesandDCMs.Thegeneraltheoryusingequivalentmagnetic circuitsdevelopedbyJ.Fienneetal.[39]canbeusedforbothACmachinesand DCMs,butitcanonlybeusedforperformancecalculationsandcannotrevealthe internalmechanismandphysicalnatureofelectromechanicalenergyconversion.
Ontheotherhand,machineswiththesameorsimilarstructurescanbe treatedasdifferentmachinetypesfromdifferentperspectives.Forexample, bothmachinesshowninFigures1.5and1.6havethreelayersfromtheinside totheoutsideinthemechanicalstructure,namely,theinnermostPMlayer,the salient-polerotorlayerinthemiddle,andtheoutermostwindinglayer.However, themachineshowninFigure1.5waswellknownasaMGM[45],whiletheone showninFigure1.6wasconsideredasapartitioned-statorFSPMmachine[46].
Figure1.5 Dual-rotorMGMAdaptedfrom[45].
Figure1.6 Partitioned-statorFSPMmachine[46].
1.2.2LimitationsinAnalysisofOperatingPrinciples
Forsomenew/specialmachines,theclassicalelectricalmachinetheoryisno longerfullyapplicable.Inotherwords,itisdifficulttodirectlyusetheclassical theorytointerprettheworkingprincipleandanalyzetheperformanceofthese machines.Forexample,accordingtotheclassicalelectricalmachinetheoryand thebasicprinciplesofelectromechanicalenergyconversion[1,2],thenumbers ofpolepairsofthestatorwindingandrotorfieldarerequiredtobeidentical soastoachievecontinuouselectromechanicalenergyconversion.However,for thePMVmachine[21]showninFigure1.7,thearmaturefieldcreatedbythe armaturewindinghasonepolepair,buttherotorhas34PMpoles.Obviously,the numbersofstatorandrotorpolepairsareunequal,sointuitively,themachine willnotbeabletooperate.EvenifthewindingMMFharmonicsareconsidered, the17-pole-pairMMFharmonicisofaverylowamplitudeandthecorresponding torquecomponentisalmostnegligible.Therefore,thistypeofmachineseems tobeofnopracticalvalueaccordingtotheclassicaltheory.However,research resultsshowthatthismachinetypecannotonlyrealizeelectromechanicalenergy
Figure1.7 PMVmachine,(a)cross-sectionalview,(b)linearwindingpattern.
Figure1.8 12/10FSPMmachine. conversion,butalsooffershighertorquedensitythanconventionalPMmachines [47],thereasonofwhichwillbeexplainedlaterinthisbook.
FSPMmachinesareanotherexample.Figure1.8showsa12-slotstatorand 10-polerotor(12/10)FSPMmachine[48,49]withboththearmaturewindings andPMslocatedinthestatorandasimplesalient-polerotor.Thismachinehas 12PMsonthestatorandadjacentmagnetsaremagnetizedinoppositedirections, formingastationarymagneticfieldwith6pairsofpoles,and10salientpoleson therotor.Theequivalentnumberofmainpolepairsobtainedaccordingtoits speedandcurrentfrequencyis4,whichneitherequalstothenumberofpolepairs ofthestatorPMfieldnorthenumberofsalientpolesoftherotor.Itisdifficultto explainthismismatchbydefinitionsofpolepairsintheclassicalmachinetheory.
1.2.3LackofUniformityinPerformanceAnalysis
Theanalysisofdifferenttypesofmachinesisisolatedfromeachotherandlacks internaluniformityduetothefragmentationofelectricalmachinetheories. EvenforIMsandSMs,thoughbothofthemareACmachines,theanalyses
Table1.2 ComparisonofanalysismodelsforIMsandSMs.
Electricalequivalentcircuit(per-phase)
Phasordiagram(per-phase)
Torqueequation
Torquecharacteristic
SM(takingthe non-salient-poletypeasanexample)
