Chapter5

Three-phaseACWindingandItsMagneticField車用驅動電機原理與控制基礎(第2版)PrincipleandControlFundamentalsofVehicleDriveMotors25.1BasicsofThree-phaseACCircuits

35.2TypicalACWindingStructure5.2.1ClassificationandMainDesignParametersofACWindingTypically,conductorsmadeofsurface-insulatedcopperarefirstwoundintomulti-turncoils,alsoknownascoilelements.Thesecoilsarethenplacedinsuitableslotsonthestator.Acoilconsistsofmultipleturnsofconductor,andtheportionembeddedinthecoreslotsiscalledtheeffectivesegment,whiletheportionsonbothsidesofthecorearecalledtheendportions.Thenumberofslotsspannedbyacoilelementiscalledthecoilpitch,denotedby??.Basedonsinglecoilelement,coilsfromthesamephaseunderthesamemagneticpolearefirstconnected(inseries),andthencoilsfromthesamephasebutunderdifferentmagneticpolesareconnected(eitherinseriesorinparallel)toformaphasewinding.Intermsofthenumberofphases,ACwindingscanbedividedintosingle-phaseandmulti-phasewindings.

Generally,??isusedtorepresentthenumberofphasesofthemotorstatorwinding.Accordingtothenumberofslotsperpoleperphase,itcanbedividedintointegerslotandfractionalslotwindings.Accordingtothenumberoflayersintheslot,itisdividedintosingle-layeranddouble-layerwindings.Accordingtothepitchofthecoil,itcanbedividedintoconcentratedwindinganddistributedwinding.Windingscanalsobeclassifiedintolapwindingandwavewindingbasedontheirwindingmethods.45.2.1ClassificationandMainDesignParametersofACWindingNameSymbolFormulaexpressionDefinitionPhasenumber

Thenumberofphasesofthestatoroutputterminals.Numberofpolepairs

Motormagneticfieldpolepairsnumberofslots

TotalnumberofstatorslotsCoilpitch

ThenumberofslotsspannedbythecoilelementNumberofparallelpathsThenumberofparallelbranchesperphasewindingPoledistanceNumberofstatorslotsper(rotor)magneticpoleNumberofslotsperpoleperphaseSlotareaoccupiedbyeachphaseundereachpoleSlotpitchangleSpatialelectricalangledifferencebetweentwoadjacentslotsThenumberofslotsinthestatorisrepresentedby??,where??isaninteger.Obviously,thenumberofslotsinthestatordeterminestheresolutionofthewindingspatialdiscretization.Therefore,thegeometricdimensionsofthewindingcanbeexpressedbythenumberofslots.Forexample,thecoilpitch??representsthenumberofslotsspannedbythetwoeffectivesegmentofacoilelement,whichmustbeaninteger.Thegeometricparametersoftherotorareindependentlysetfromthestator,whichmeansthatthegeometricparametersoftherotormaynotbeintegermultiplesofthenumberofslots.Thisispermissible,andinsuchcases,fractionalmultiplesofthenumberofslotsareusedforrepresentation.Onecrucialdesignvariableisthepolepitch??,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,acoilpitchof??=8ischosenforthewinding,withapolepitch??=9.Since??<??,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-pitchcoilswith??=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