THESISFORTHEDEGREEOFLICENTIATEOFENGINEERING Electric machine control for energy efficient electric drive systems ANDREASANDERSSON DepartmentofEnergyandEnvironment DivisionofElectricPowerEngineering CHALMERSUNIVERSITYOFTECHNOLOGY Göteborg,Sweden2015 Electricmachinecontrolforenergyefficientelectricdrivesystems ANDREASANDERSSON ©ANDREASANDERSSON,2015. LicentianteThesisattheGraduateSchoolinEnergyandEnvironment DepartmentofEnergyandEnvironment DivisionofElectricPowerEngineering ChalmersUniversityofTechnology SE–41296Göteborg Sweden Telephone+46(0)31–7721000 ChalmersBibliotek,Reproservice Göteborg,Sweden2015 iii iv Electricmachinecontrolforenergyefficiencyelectricdrivesystems ANDREASANDERSSON DepartmentofEnergyandEnvironment ChalmersUniversityofTechnology Abstract Pure electric vehicles and hybrid electric vehicles are of increasing interest in theautomotiveindustry,muchduetochallengessuchasemissionlevellegislationsand the environmentalimpact of the transportation sector. When continuously striving for better performing and more energy efficient electric powertrains, with high drivability andredundancy,thereisaneverincreasingneedforfurtherresearchanddevelopmentin theareasofcontrols,designandsystemleveloptimization. Over the past decade, noise and vibrationsfrom electric driveshas increasingly becomean area of attentionfor both academiaand industry. The absence of the broad bandnoisefromtheinternalcombustionenginebringsnewnoise, vibrationandharsh- ness (NVH) challengesforelectric propulsionapplications. Magneticnoise fromelec- tricalmachinesisofparticularinterestinautomotiveapplications. Itisnotonlyrelated to the physicaldesignand mountingof the electricalmachinebutalso to the choiceof controlapproachandvoltagemodulationstrategy. This thesis is focused on energy efficiency enhancements in the electric drive system,primarilyonthecontrolofthethreephaseinverter.Inadditiontotheenergyeffi- ciencyperspective,alsotheappearanceofelectromagneticforcesandNVH-perspectives areconsidered. Alternativemodulationtechniquesareinvestigated,wherethesocalled discontinuouspulse width modulationis is provento decrease the inverter losses, sub- stantially. Theappearanceofelectromagneticforcesisinvestigatedextensively,withfocus onradialforcesactingasattractiveorrepulsiveforcesbetweentherotorandthestator.Its influenceonstatordeformations,andconsequentlynoiseandvibrations,isinvestigated wherealsoinfluenceofmachinedesign,modulationtechniquesandperceivedannoyance oftheradiatedsoundareincluded. The scientific contribution can be summarized with two parts. Firstly, the in- terdisciplinary research where energy efficiency enhancements are coupled to NVH- performance. Secondly, the cause and effect of electromagnetic forces as the link be- tweenmachinedesign,controlsandNVH-perspectives. ItisproventhatwhenusingdiscontinuousPWM(DPWM)insteadofsynchronous v PWM(SPWM),theinverterlossescanbedecreasedwithupto-17percent.Whilecom- plementingthemodulationwithrandomizationoftheswitchingfrequencytheincreasein perceivedannoyance,duetoincreasedradiatednoisewhenusingDPWM,issignificantly decreased. Atrotationalspeedsabovebasespeed,nodifferenceinperceivedannoyance betweenDPWMandSPWMcouldstatisticallybeensuredwhenrandomizationisused. Ata randomizationlevelwithavarianceofs =1000Hzthe noiseiscomparablewith the magnitude of the harmonics themselves, hence further randomization in terms of increasedvarianceiswithoutanygain. IndexTerms: Energyefficiency,modulationtechniques,noiseassessment,permanent magnetsynchronousmachine(PMSM). vi Acknowledgements First and foremost I would like to thank Professor Torbjörn Thiringer, my aca- demic supervisor and examiner, for his continuous and consistent support during the work. I wouldalso liketo thankDr. StefanLundberg,myacademicco-supervisor,for his time and contributions,especially with the extensivesupportwith the experimental work.AspecialthanksgoestoDr.JonnLantzatVolvoCarGroup,myindustrialsupervi- sor,forhistimeandsupportaswellastheindustrialcontributions.Theworkisfounded byVolvoCarGroupandtheSwedishEnergyAgency,botharegratefullyacknowledged forthefinancialsupport. Manypeople,bothatVolvoCarsandatChalmers,havebeeninvolvedtovarying degreesandby theirsupport,knowledgeandhelpfulnessinfluencedthe work. I would liketothankthemall,especiallymycolleaguesattheDivisionofElectricPowerEngi- neeringatChalmersandtheDepartmentofElectricPropulsionSystemsatVolvoCars. AndreasAndersson Göteborg,Sweden Autumn,2015 vii viii Contents Abstract v Acknowledgements vii Contents ix 1 Introduction 1 1.1 Problembackground . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Purposeofthethesisandcontributions . . . . . . . . . . . . . . . . . . 2 1.3 Thesisoutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Electricdrivesystem 5 2.1 Salient-polePMSMmodelling . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Equivalentcircuitmodel . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 PMSMcontrol . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3 Maximumtorqueperamperewithvariableinductances . . . . . 8 2.2 Three-phasevoltagesourceinverter . . . . . . . . . . . . . . . . . . . 10 2.3 Pulsewidthmodulationtechniques . . . . . . . . . . . . . . . . . . . . 12 2.3.1 SPWMwiththirdharmonicinjection . . . . . . . . . . . . . . 14 2.3.2 DiscontinuousPWM . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.3 RandomPWM . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Losscalculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Corelosscalculations . . . . . . . . . . . . . . . . . . . . . . 19 2.4.2 Inverterlosses. . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Longitudinalvehicledynamicsmodelling . . . . . . . . . . . . . . . . 21 ix Contents 3 ElectromagneticforcesinrelationtoNVHforaPMSM 23 3.1 Modalanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 Airgapfluxdensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.1 Appearanceoffluxdensity . . . . . . . . . . . . . . . . . . . . 26 3.2.2 Effectsofstatorslots . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Electromagneticforces . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.4 Radialandtangentialcomponents . . . . . . . . . . . . . . . . . . . . 35 3.5 Statordynamicresponseandradiatedsoundpower . . . . . . . . . . . 38 4 Experimentalsetup 43 4.1 Testingequipment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.1 Inverterandelectricalmachine . . . . . . . . . . . . . . . . . . 44 4.1.2 Noisemeasurements . . . . . . . . . . . . . . . . . . . . . . . 46 4.1.3 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 Testprocedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5 Finiteelementmodelling 51 5.1 2DANSYSMaxwellmodel . . . . . . . . . . . . . . . . . . . . . . . 52 5.1.1 Machineparameteridentification . . . . . . . . . . . . . . . . 52 5.1.2 Harmonicsininducedvoltage . . . . . . . . . . . . . . . . . . 53 5.2 SensitivityofMaxwell2D-model. . . . . . . . . . . . . . . . . . . . . 55 5.2.1 Sensitivityanalysisofmeshsize . . . . . . . . . . . . . . . . . 56 5.2.2 Sensitivityanalysisoftimestepsize . . . . . . . . . . . . . . . 58 5.3 VoltageexcitedFEmodellinginANSYSMaxwell . . . . . . . . . . . 60 5.3.1 Derivationofinducedvoltage . . . . . . . . . . . . . . . . . . 61 5.3.2 Statorwindingresistancehandling . . . . . . . . . . . . . . . . 62 5.3.3 Initialphasecurrent. . . . . . . . . . . . . . . . . . . . . . . . 62 5.3.4 ProposedsimulationsequenceinANSYSMaxwell . . . . . . . 63 5.4 ANSYSmulti-physicssimulations . . . . . . . . . . . . . . . . . . . . 67 5.4.1 Simulationsetup . . . . . . . . . . . . . . . . . . . . . . . . . 67 6 Theoreticalanalysisofelectromagneticfluxandforcedensity 69 6.1 Influenceofstatorslots . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.1.1 Closedstator . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.1.2 Variationofstatorslotopeningwidth . . . . . . . . . . . . . . 72 6.2 Inverterswitchinginfluenceonforcedensityharmonics . . . . . . . . . 77 x