电机学（第七版）（修订版）课件 Chapter-5-Synchronous-Machines、Chapter-6-Polyphase-Induction-Machines

Chapter5SynchronousMachines7/10/2024SynchronousMachines1IntroductionTheDCfieldisnormallyontherotorandACarmaturewindingisonthestatorDCfieldcurrentsetsupmainair-gapfluxandACarmaturehandlestheelectricalpowerRotorrotatesinsynchronismwiththemagneticfieldsetupbythearmaturewindingsRotorspeedisproportionaltothefrequencyofthearmaturecurrentsinsteadystate7/10/2024SynchronousMachines2Stator-rotormutualinductanceis

Laf

cos(qme)Insteadystate

qme=wet+de0Open-circuitarmaturevoltageis 7/10/2024SynchronousMachines3Simplifiedthree-phasesynchronousmachineStatormutualinductanceis Lab=Laa0cos(120˚)=-½Laa0Statorselfinductanceis La=Laa0+Lal

Balancedthree-phasecurrentsia+ib+ic=0 7/10/2024SynchronousMachines47/10/2024SynchronousMachines5Motorsignconventionsimplymeansthereferencedirectionsarechosenfornormalmotoroperation7/10/2024SynchronousMachines6Synchronous-machineequivalentcircuits:(a)motorreferencedirectionand(b)generatorreferencedirection.7/10/2024SynchronousMachines7IaVa(Ra+jXs)IaEafIaEaf(Ra+jXs)IaVaSynchronousmotorandgeneratorphasordiagramsbothhavinglaggingpowerfactorattheterminals(IalaggingVa)MotorGenerator5.3Open-andShort-CircuitCharacteristicsTheopen-circuitarmaturevoltageandshort-circuitarmaturecurrent,bothplottedversusthefieldcurrent,allowcomputationofthesynchronousreactanceXsOpen-circuitcharacteristicwillshowsignificantsaturationandisoftencalledopen-circuitsaturationcurveShort-circuitcharacteristic(plotteduptoslightlyaboveratedcurrent)willnot,sincetheexcitationislowtheseconditions7/10/2024SynchronousMachines87/10/2024SynchronousMachines9Open-andshort-circuitcharacteristicsshowingequivalentmagnetizationlineforsaturatedoperatingconditions7/10/2024SynchronousMachines10SaturatedandunsaturatedvaluesofXs:SaturatedandunsaturatedvaluesofXsinperunit:Inlargesynchronousmachines,thearmatureresistanceismuchsmallerthanthesynchronousreactance.5.4Steady-StatePower-AngleCharacteristic7/10/2024SynchronousMachines11(a)Impedanceinterconnectingtwovoltages(b)phasordiagramMaximumpowerdeliveredbyasynchronousmachineisaspecialcaseofpower-anglecharacteristicforpowertransferthroughaseriesimpedanceZ=R+jX,fromE1toE2ForsimplicityZjX7/10/2024SynchronousMachines125.5Steady-StateOperatingCharacteristics7/10/2024SynchronousMachines13Constructionusedforderivationofasynchronousgeneratorcapabilitycurve.7/10/2024SynchronousMachines14ThisequationgivesthefieldheatinglimitThearmatureheatinglimitissimplythemachinevolt-ampererating(ratedcurrentatratedterminalvoltage)7/10/2024SynchronousMachines15Phasordiagramforconstant-poweroperationatconstantterminalvoltage.NotethatlesslaggingormoreleadingcorrespondstosmallerexcitationvoltagemagnitudeEafandsmallerfieldcurrentIfIa3VajXsIa2Eaf1Ia2Ia1Eaf3Eaf2jXsIa3jXsIa17/10/2024SynchronousMachines16SynchronousGeneratorVCurves5.6EffectsofSalientPolesIntroductiontosynchronouslyrotatingdqaxistheoryResolvearmaturephasorsintodandqaxiscomponentsDirect(d)axisisalignedwithfieldpoles,quadrature(q)axisismidwaybetweenpoles7/10/2024SynchronousMachines177/10/2024SynchronousMachines18Inductanceisfluxlinkageperunitampere:Thed-axiscurrentproducesMMFthatseesashortairgap(acrosspolefaces)sothed-axisinductanceislargeTheq-axiscurrentproducesMMFthatseesalongairgap(interpolarregion)sotheq-axisinductanceisrelativelysmallSalient-polemachinesareanalyzedwithaphasordiagramrepresentingd-andq-axisquantitiesseparately:IdseesXdandIqseesXqwhereXd>XqNosimpleequivalentcircuitisavailable7/10/2024SynchronousMachines197/10/2024SynchronousMachines20Phasordiagramforasalient-polesynchronousgenerator.7/10/2024SynchronousMachines21Phasordiagramillustratingthetechniqueforlocatingthequadratureaxisgivenarmatureterminalvoltage,currentandpowerfactorPermanent-MagnetACMachinesPolyphasesynchronousmachineswithpermanent-magnetrotorsareuseful,withmanyapplicationsparticularlyasmotorsTheanalysisissimilartothatalreadydiscussed,excepttheexcitationisnotadjustablePermanent-magnetmotorsareusuallyoperatedfromvariable-frequencymotordrives7/10/2024SynchronousMachines227/10/2024SynchronousMachines23Schematicdiagramofthree-phasepermanent-magnetacmachine.Thearrowindicatesthedirectionofrotormagnetization.Thismachinecanbeanalyzedasifitwereawound-fieldmachinewithconstantfieldcurrent.Thecontrolofapermanent-magnetacmotoroftenusesarotorpositionsensor.SummaryThesynchronousmachineisanalyzedundersteady-stateoperatingconditionsPolyphasecurrentsonthestatorproducearotatingMMFthatinteractswiththatoftherotatingfieldwindingtoproduceasteadytorqueTheequivalentcircuitandthephasordiagramareusefulforperformancecalculationsunderawidevarietyofoperatingconditions7/10/2024SynchronousMachines24Chapter6PolyphaseInductionMachines7/10/2024PolyphaseInductionMachines25IntroductionRotorrotationisnotsynchronouswiththemagneticfieldsetupbythearmaturewindingsInductionmachinesarealsocalledasynchronousmachinesAnalysisissimilartothatofatransformer,sincestatorandrotorwindingsaresimilartoprimaryandsecondarywindings,butwithrotationRotorconstructionisusuallyasquirrel-cagedesign7/10/2024PolyphaseInductionMachines267/10/2024PolyphaseInductionMachines27(a)Therotorofasmallsquirrel-cagemotor.(b)Thesquirrel-cagestructureaftertherotorlaminationshavebeenetchedawayRotorcurrentshavefrequencyofsfe

whichproducefluxwaverotatingatsnsr/minfasterthantherotorspeedWithrespecttothestator,therotorfluxwaverotatesatsynchronousspeed:7/10/2024PolyphaseInductionMachines28Boththestatorfluxwaveandtherotorfluxwaverotateatsynchronousspeed,sotheycaninteracttoproducetorque7/10/2024PolyphaseInductionMachines29Typicalinduction-motortorque-speedcurveforconstant-voltage,constant-frequencyoperationAtnormalload,theslipisabout2to10%RotorelectricalfrequencyislowAstheslipincreases,thespeeddropsandthetorqueincreasesTorqueisnearlyproportionaltoslipforloadsuptoratedtorqueMaximumtorqueorbreakdowntorqueisabouttwiceratedtorqueOnstartup,thespeedisinitiallyzeroandtheslipis1Thestartingcurrentislargeaswewillsee7/10/2024PolyphaseInductionMachines30CurrentsandfluxesininductionmotorsBothrotorandstatorcurrentssetuprotatingmmfwaveswithconstantamplitudethatrotateatsynchronousspeedTheresultantfluxwaveisduetobothstatorandrotormmf’sInteractionsareshowninthefigurebelowinadevelopment(asifthecylindricalgeometrywererolledoutflat)7/10/2024PolyphaseInductionMachines317/10/2024PolyphaseInductionMachines32Developedrotorwindingofaninductionmotorwithrotormmfandresultantfluxdensitywavesfor(a)zeroand(b)nonzerorotorleakagereactance.Noticethatthetorqueisinthedirectionofrotation,asexpectedforamotor.InductionmotorequivalentcircuitStator:Synchronouslyrotatingair-gapfluxgeneratescounteremf’sineachphaseStatorcurrentsproducevoltagedropduetoresistanceandleakagereactances7/10/2024PolyphaseInductionMachines33StatorequivalentcircuitisexactlylikethatoftheprimaryofatransformerRotorpresentsanimpedanceZ2tothestatorRotorimpedanceZrotordiffersfromZ2byaturnsratio(likethetransformer)andbyaspeeddifference(therotorrotateswhilethestatordoesnot)7/10/2024PolyphaseInductionMachines34Notethatthesubscript2sindicatesthatthequantityisslipfrequency,whiletherotorleakagereactanceX2isthevalueatstatorfrequency:7/10/2024PolyphaseInductionMachines35Next,weneedtoreferthisimpedancetostatorfrequencyusingAmpere’sandFaraday’slaws7/10/2024PolyphaseInductionMachines36TheimpedanceZ2isreferredtothestatorfrequencyandcompletestheequivalentcircuitAnalysisoftheequivalentcircuit7/10/2024PolyphaseInductionMachines37Numberofphases=qPowertransferredacrosstheairgap=PgapRotorI2Rloss=ProtorElectromagneticpower=Pmech7/10/2024PolyphaseInductionMachines38Alternativeformofpolyphaseinductionmotorequivalentcircuitdisplaystherotorresistanceseparatedintotwoseriesresistances:7/10/2024PolyphaseInductionMachines39ElectromagnetictorqueTmechcorrespondingtoPmechis:Corelossesmaybeneglectedorlumpedwithrotationalloss,simplifyingthecircuit7/10/2024PolyphaseInductionMachines40UseofThevenin’stheoremUseThevenin’stheoremata-binthesimplifiedequivalentcircuit:7/10/2024PolyphaseInductionMachines417/10/2024PolyphaseInductionMachines42Torque-slipcurveofinductionmotorshowingbraking,motor,andgeneratorregions.Normalmotoroperationisjustbelowsynchronousspeed.7/10/2024PolyphaseInductionMachines43Themaximumtorque,orbreakdowntorque,occursatmaximumair-gappower7/10/2024PolyphaseInductionMachines44Torque-slipcurvesforseveraldifferentvaluesofrotorcircuitresistance.Thisisexploitedtocontrolthespeedofwound-rotormotorsbyinsertingexternalresistanceinserieswiththerotorterminals.7/10/2024PolyphaseInductionMachines45ParameterdeterminationfromtestsNo-loadtestgivesrotationalloss(friction,windageandcoreloss)excitingcurrentProcedurediscussedinthetextallowsaccuratecomputationofcorelossesandXmApproximatevalue:Xm

Xnl

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

R1isfoundfromdcmeasurementsTable6.1givesanempiricaldistributionofleakagereactances7/10/2024PolyphaseInductionMachines467/10/2024PolyphaseInductionMachines47Table6.1Empiricaldistributionofleakagereactances(IEEEStd.112)FractionofX1+X2MotorClassDescriptionX1X2ANormalstartingtorque,normalstartingcurrent0.50.5BNormalstartingtorque,lowstartingcurrent0.40.6CHighstartingtorque,lowstartingcurrent0.30.7DHighstartingtorque,highslip0.50.5WoundrotorPerformancevarieswithrotorresistance0.50.5RotorcircuitparametervariationAsthemotorstarts,therotorcircuitparametersR2andL2mayvarywithslipfrequencyduetotheskineffectThiseffectispro