电机学（第七版）（修订版）课件 Chapter-6-Polyphase-Induction-Machines

Chapter6PolyphaseInductionMachines7/10/2024PolyphaseInductionMachines1IntroductionRotorrotationisnotsynchronouswiththemagneticfieldsetupbythearmaturewindingsInductionmachinesarealsocalledasynchronousmachinesAnalysisissimilartothatofatransformer,sincestatorandrotorwindingsaresimilartoprimaryandsecondarywindings,butwithrotationRotorconstructionisusuallyasquirrel-cagedesign7/10/2024PolyphaseInductionMachines27/10/2024PolyphaseInductionMachines3(a)Therotorofasmallsquirrel-cagemotor.(b)Thesquirrel-cagestructureaftertherotorlaminationshavebeenetchedawayRotorcurrentshavefrequencyofsfe

whichproducefluxwaverotatingatsnsr/minfasterthantherotorspeedWithrespecttothestator,therotorfluxwaverotatesatsynchronousspeed:7/10/2024PolyphaseInductionMachines4Boththestatorfluxwaveandtherotorfluxwaverotateatsynchronousspeed,sotheycaninteracttoproducetorque7/10/2024PolyphaseInductionMachines5Typicalinduction-motortorque-speedcurveforconstant-voltage,constant-frequencyoperationAtnormalload,theslipisabout2to10%RotorelectricalfrequencyislowAstheslipincreases,thespeeddropsandthetorqueincreasesTorqueisnearlyproportionaltoslipforloadsuptoratedtorqueMaximumtorqueorbreakdowntorqueisabouttwiceratedtorqueOnstartup,thespeedisinitiallyzeroandtheslipis1Thestartingcurrentislargeaswewillsee7/10/2024PolyphaseInductionMachines6CurrentsandfluxesininductionmotorsBothrotorandstatorcurrentssetuprotatingmmfwaveswithconstantamplitudethatrotateatsynchronousspeedTheresultantfluxwaveisduetobothstatorandrotormmf’sInteractionsareshowninthefigurebelowinadevelopment(asifthecylindricalgeometrywererolledoutflat)7/10/2024PolyphaseInductionMachines77/10/2024PolyphaseInductionMachines8Developedrotorwindingofaninductionmotorwithrotormmfandresultantfluxdensitywavesfor(a)zeroand(b)nonzerorotorleakagereactance.Noticethatthetorqueisinthedirectionofrotation,asexpectedforamotor.InductionmotorequivalentcircuitStator:Synchronouslyrotatingair-gapfluxgeneratescounteremf’sineachphaseStatorcurrentsproducevoltagedropduetoresistanceandleakagereactances7/10/2024PolyphaseInductionMachines9StatorequivalentcircuitisexactlylikethatoftheprimaryofatransformerRotorpresentsanimpedanceZ2tothestatorRotorimpedanceZrotordiffersfromZ2byaturnsratio(likethetransformer)andbyaspeeddifference(therotorrotateswhilethestatordoesnot)7/10/2024PolyphaseInductionMachines10Notethatthesubscript2sindicatesthatthequantityisslipfrequency,whiletherotorleakagereactanceX2isthevalueatstatorfrequency:7/10/2024PolyphaseInductionMachines11Next,weneedtoreferthisimpedancetostatorfrequencyusingAmpere’sandFaraday’slaws7/10/2024PolyphaseInductionMachines12TheimpedanceZ2isreferredtothestatorfrequencyandcompletestheequivalentcircuitAnalysisoftheequivalentcircuit7/10/2024PolyphaseInductionMachines13Numberofphases=qPowertransferredacrosstheairgap=PgapRotorI2Rloss=ProtorElectromagneticpower=Pmech7/10/2024PolyphaseInductionMachines14Alternativeformofpolyphaseinductionmotorequivalentcircuitdisplaystherotorresistanceseparatedintotwoseriesresistances:7/10/2024PolyphaseInductionMachines15ElectromagnetictorqueTmechcorrespondingtoPmechis:Corelossesmaybeneglectedorlumpedwithrotationalloss,simplifyingthecircuit7/10/2024PolyphaseInductionMachines16UseofThevenin’stheoremUseThevenin’stheoremata-binthesimplifiedequivalentcircuit:7/10/2024PolyphaseInductionMachines177/10/2024PolyphaseInductionMachines18Torque-slipcurveofinductionmotorshowingbraking,motor,andgeneratorregions.Normalmotoroperationisjustbelowsynchronousspeed.7/10/2024PolyphaseInductionMachines19Themaximumtorque,orbreakdowntorque,occursatmaximumair-gappower7/10/2024PolyphaseInductionMachines20Torque-slipcurvesforseveraldifferentvaluesofrotorcircuitresistance.Thisisexploitedtocontrolthespeedofwound-rotormotorsbyinsertingexternalresistanceinserieswiththerotorterminals.7/10/2024PolyphaseInductionMachines21ParameterdeterminationfromtestsNo-loadtestgivesrotationalloss(friction,windageandcoreloss)excitingcurrentProcedurediscussedinthetextallowsaccuratecomputationofcorelossesandXmApproximatevalue:Xm

Xnl

=V1,nl/I1,nlBlocked-rotortestgivesleakagereactancesProcedurediscussedinthetextallowsaccuratecomputationofX1+X2andR2

R1isfoundfromdcmeasurementsTable6.1givesanempiricaldistributionofleakagereactances7/10/2024PolyphaseInductionMachines227/10/2024PolyphaseInductionMachines23Table6.1Empiricaldistributionofleakagereactances(IEEEStd.112)FractionofX1+X2MotorClassDescriptionX1X2ANormalstartingtorque,normalstartingcurrent0.50.5BNormalstartingtorque,lowstartingcurrent0.40.6CHighstartingtorque,lowstartingcurrent0.30.7DHighstartingtorque,highslip0.50.5WoundrotorPerformancevarieswithrotorresistance0.50.5RotorcircuitparametervariationAsthemotorstarts,therotorcircuitparametersR2andL2mayvarywithslipfrequencyduetotheskineffectThiseffectispronouncedinmanydesignsthatutilizedeepbarordouble-cagerotorsR2mayincreasebyafactorof3fromdcto60HzRotorfrequencywillvaryfromthestatorfrequencyatstart-updowntoafewpercentofstatorfrequencyatnormalrunningconditionsTheseeffectsmeanthatonesetofparametersmaynotbesuitabletoanalyzebothstartingandrunningconditions7/10/2024PolyphaseInductionMachines24Typicaltorque-speedcurvesfor1800r/mingeneral-purposeinductionmotors(NEMAdesignclasses)ClassBmotorsareoftenusedforgen