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Chapter5
Three-phaseACWindingandItsMagneticField车用驱动电机原理与控制基础(第2版)PrincipleandControlFundamentalsofVehicleDriveMotors25.1BasicsofThree-phaseACCircuits
35.2TypicalACWindingStructure5.2.1ClassificationandMainDesignParametersofACWindingTypically,conductorsmadeofsurface-insulatedcopperarefirstwoundintomulti-turncoils,alsoknownascoilelements.Thesecoilsarethenplacedinsuitableslotsonthestator.Acoilconsistsofmultipleturnsofconductor,andtheportionembeddedinthecoreslotsiscalledtheeffectivesegment,whiletheportionsonbothsidesofthecorearecalledtheendportions.Thenumberofslotsspannedbyacoilelementiscalledthecoilpitch,denotedby𝑦.Basedonsinglecoilelement,coilsfromthesamephaseunderthesamemagneticpolearefirstconnected(inseries),andthencoilsfromthesamephasebutunderdifferentmagneticpolesareconnected(eitherinseriesorinparallel)toformaphasewinding.Intermsofthenumberofphases,ACwindingscanbedividedintosingle-phaseandmulti-phasewindings.
Generally,𝑚isusedtorepresentthenumberofphasesofthemotorstatorwinding.Accordingtothenumberofslotsperpoleperphase,itcanbedividedintointegerslotandfractionalslotwindings.Accordingtothenumberoflayersintheslot,itisdividedintosingle-layeranddouble-layerwindings.Accordingtothepitchofthecoil,itcanbedividedintoconcentratedwindinganddistributedwinding.Windingscanalsobeclassifiedintolapwindingandwavewindingbasedontheirwindingmethods.45.2.1ClassificationandMainDesignParametersofACWindingNameSymbolFormulaexpressionDefinitionPhasenumber
Thenumberofphasesofthestatoroutputterminals.Numberofpolepairs
Motormagneticfieldpolepairsnumberofslots
TotalnumberofstatorslotsCoilpitch
ThenumberofslotsspannedbythecoilelementNumberofparallelpathsThenumberofparallelbranchesperphasewindingPoledistanceNumberofstatorslotsper(rotor)magneticpoleNumberofslotsperpoleperphaseSlotareaoccupiedbyeachphaseundereachpoleSlotpitchangleSpatialelectricalangledifferencebetweentwoadjacentslotsThenumberofslotsinthestatorisrepresentedby𝑍,where𝑍isaninteger.Obviously,thenumberofslotsinthestatordeterminestheresolutionofthewindingspatialdiscretization.Therefore,thegeometricdimensionsofthewindingcanbeexpressedbythenumberofslots.Forexample,thecoilpitch𝑦representsthenumberofslotsspannedbythetwoeffectivesegmentofacoilelement,whichmustbeaninteger.Thegeometricparametersoftherotorareindependentlysetfromthestator,whichmeansthatthegeometricparametersoftherotormaynotbeintegermultiplesofthenumberofslots.Thisispermissible,andinsuchcases,fractionalmultiplesofthenumberofslotsareusedforrepresentation.Onecrucialdesignvariableisthepolepitch𝜏,whichreferstothenumberofstatorslotscorrespondingtoeachmagneticpole(oftherotor).
Thecombinationofthenumberofpolesontherotorandthenumberofslotsonthestatorhasasignificantimpactonthemotor'sperformance.Thisiscommonlyreferredtoasthe“pole-slotcombinationproblem”.5
5.2.1ClassificationandMainDesignParametersofACWinding6
5.2.1ClassificationandMainDesignParametersofACWinding75.2.2TheDesignofThree-phaseDistributedWindingNameSymbolValuePhasenumber3Numberofpolepairs1Numberofslots6Coilpitch3Polepitch3Numberofslotsperpoleperphase1Slotpitchangle60°Parameterstablefora3-phase,1-pair-pole,6-slotsingle-layerdistributedstatorwindingFig.4-46-slotsingle-layerwindingwiringdiagramandwindingexpansiondiagram(m=3,Z=6,p=1,q=1,y=6)PhasebandAZBXCYSlotnumber123456Table:Slotallocationforeachphaseband(60-degreephaseband)8
5.2.2TheDesignofThree-phaseDistributedWindingFig.4-46-slotsingle-layerwindingwiringdiagramandwindingexpansiondiagram(m=3,Z=6,p=1,q=1,y=6)9
5.2.2TheDesignofThree-phaseDistributedWindingPhasebandAZBXCYSlotnumber1,23,45,67,89,1011,12Table:Slotallocationforeachphaseband(60-degreephaseband)105.2.2TheDesignofThree-phaseDistributedWinding
11
Fig4-7Slotelectromotiveforcestardiagramofthree-phasedouble-layerwinding5.2.2TheDesignofThree-phaseDistributedWinding12
phasebandAZBXCY1,2,34,5,67,8,910,11,1213,14,1516,17,1819,20,2122,23,2425,26,2728,29,3031,32,3334,35,365.2.2TheDesignofThree-phaseDistributedWindingTable:Slotallocationforeachphaseband(60-degreephaseband)135.2.2TheDesignofThree-phaseDistributedWinding
Connectionof12coilsinthephaseAwinding(onebranch)Connectionof12coilsinthephaseAwinding(twobranches)14Oncetheslotnumbersaredetermined,wiringandconnectionscanbemadebasedonthecoilpitch.TakingthephaseAwindingasanexample,solidlinesrepresentthesegmentsoftheupperlayercoils,anddashedlinesrepresentthesegmentsofthelowerlayercoils,andeachcoiliscomposedofonesolidandonedashedline.Thecoilnumberisindicatedbytheslotnumberoftheupperlayersegment,markedatthetopofthecoil.Inthisdesign,acoilpitchof𝑦=8ischosenforthewinding,withapolepitch𝜏=9.Since𝑦<𝜏,itisashort-pitchwinding.Thecoilswithineachpolephasegroupareconnectedinseries.Coilgroups1,2,3,andcoilgroups10,11,12areconnectedinseriestoformtheA1andX1phasebandsunderthefirstpairofmagneticpoles.Twocoilgroupsareconnectedinanti-directiontoformthefirstbranch(polephasegroup).Coilgroups19,20,21,andcoilgroups28,29,30areconnectedinseriestoformtheA2andX2phasebandsunderthesecondpairofmagneticpoles.Thetwophasebandsareconnectedinanti-directiontoformthesecondbranch.Fig.4-8ExpandedviewofthephaseAwindinginthethree-phasedouble-layeredwinding(Z=36,p=2,m=3,y=8,twopole-phaseisconnectedinseries)5.2.2TheDesignofThree-phaseDistributedWindingFig.4-12Thepole-phasegroupcomposedoffull-pitchcoilswith𝑞=3hasthreecoilsdistributedsuccessivelyinthreeadjacentslots,formingafull-pitchdistributedwinding.Byaddingtherectangularmagnetomotiveforcewavesproducedbyeachwhole-pitchcoilpointbypoint,thecompositemagnetomotiveforceofthispole-phasegroupcanbeobtained.Thecompositemagneticfluxwaveformisastaircasewaveform.155.3.1MagnetomotiveForceofSingle-phaseWinding
16ElectromotiveForceofSinusoidalCurrent-excitedSingle-phaseWindingFig.4-11electromotiveforceofsinglecoilFull-pitchandshort-pitchcoil
17a)Themagneticfieldgeneratedbythefull-pitchcoil
5.3.1MagnetomotiveForceofSingle-phaseWindingb)WavefunctionofmagnetomotiveforceforfullpitchcoilFig.4-11Themagnetomotiveforceofsingle-phasecoil
185.3.2The(Pulsating)MagnetomotiveForceofaSingle-phaseWindingUnderCosineCurrentExcitation19Fig.4-13Thefundamentalpulsatingmagnetomotiveforcewave(standingwave)ofasingle-phasewindingatdifferentinstants
5.3.2The(Pulsating)MagnetomotiveForceofaSingle-phaseWindingUnderCosineCurrentExcitation20Fig.4-14Spatialdistributionofharmonicmagnetomotiveforce
5.3.2The(Pulsating)MagnetomotiveForceofaSingle-phaseWindingUnderCosineCurrentExcitation21Three-phaseWindingsandTheirCompositeMagnetomotiveForce22Three-phaseWindingsandTheirCompositeMagnetomotiveForce23Three-phaseWindingsandTheirCompositeMagnetomotiveForce245.3TheMagnetomotiveForceofSymmetricalThree-phaseWindingExcitedbySymmetricalThree-phaseCurrent255.3TheMagnetomotiveForceofSymmetricalThree-phaseWindingExcitedbySymmetricalThree-phaseCurrent
Fig.4-15Statorwindingsoftwo-polethree-phaseACmotors
265.3.3TheSpaceVectorExpressionofPlanarRotatingMagnetomotiveForce
Fig.4-19Shaftcoilanditsschematicdiagram,correspondingspacevectordrawingmethod27Thecurrentvectorsofthestatorandrotorareequivalenttothe“axiscoil”.5.3.3TheSpaceVectorExpressionofPlanarRotatingMagnetomotiveForce285.3.3TheSpaceVectorExpressionofPlanarRotatingMagnetomotiveForce
295.4StatorVoltage,Current,andFluxLinkageVectors
305.4.1StatorCurrentVectorandVoltageVector
315.4.1StatorCurrentVectorandVoltageVectorFig.4-21Thestatorandrotorcurrentvectorsareequivalenttothe"shaftcoil"
325.4.2StatorFluxLinkageVector
Fig.4-22CosinedistributedmagneticfieldgeneratedbyA-phasewindinga)Cosinedistributedmagnetomotiveforcewave
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