Excitation研发培训,设计培训

SynchronousMachines-ReactanceandExcitationCalculationMarkFanslowTecoWestinghouseEngineeringTrainingNov.2005StatorRevolvingMagneticFieldMagneticPolePairsrotateatSynchronousSpeedThreePhaseACVoltageSynchronousRotorDCinputtotherotorcreateselectromagneticpolespairsPolesofdifferentpolarityarecreatedbywindingaroundthepoleindifferentdirectionsSynchronousMotorRotor“Locked”intopowersupply,rovlovesatsynchronousspeedPhasorsandPhasorDiagramsTheconceptofPhasorsisrelatedtosinusoidalwaveformsthataredistributedinspaceandvarywithtime.Phasorsarecomplex(asincomplexnumbers)quantitiesusedforsimplifiedcalculationoftimevaryingandtravelingwaveforms.Themagnitudeandphaserelationshipbetweenthevectorsandcanbeshownsimplyinphasordiagrams.PhasorDiagramExampleConsiderthesimpleRL(resistiveinductive)circuitV=Vmsin(ωt)22)sin(rLtVimVoltagefunctionoftime.CurrentfunctionoftimeanddisplacedbyangleVILMagneticFluxinInductor90°outofphasewithvoltagewaveformi90°PhasorDiagramCont.VIFLФLRecall:HBroB:MagneticFluxDensitydenoteФH:MagneticFluxIntensityormmfdenoteFo:Constantofpermeabilityoffreespacer:ConstantofpermeabilityofelectricalsteelCylindricalRotorSynchronousMachine:Duetotheevenairgap,theformulationsforbasicmachinequantitiesissimplified.Wewillconsiderthecylindricalmachinetheoryfirstandthenextendtheanalysistothesalientpolecase.AxisofFieldAxisofPhaseA90°lagArmaturecurrentmmfFarResultantmmfFrFieldmmfFfRotorRotationStatorRotorNSStatorI.D.RotorO.D.IaVtIaraEintEaΦar-ΦarfΦfRjIaxAjIax1Φr-ararErCylindricalRotorPhasorDiagramForSynchronousGeneratorVt:TerminalVoltageIa:StatorCurrentLagsterminalVoltagebyAngleEa:AirGapVoltage,thevoltageinducedintothearmaturebythefieldvoltageactingalone,the“opencircuit”voltageEr:ReactivevoltageproducedbyarmaturefluxEint:ResultantVoltageintheAirGapar:FluxfromArmaturecurrent(ArmatureReaction)f:Fluxduetofieldcurrentr:Resultantfluxar+fFf:mmfofFieldAar:mmfofArmatureCurrent(ArmatureReaction)FR:Resultantmmf,thesumofF+AIara:VoltagedropofarmatureresistanceIaxl:ReactivevoltagedropofArmatureleakagereactanceIaxA:ReactivevoltagedropofreactanceofArmaturereactionFromthediagramitisevidentthatEr,thevoltageinducedinthestatorbytheeffectofthearmaturereactionflux,isinphasewithIaXl.ThesummationofErandIaXlgivesthetotalreactivevoltageproducedinthearmaturecircuitbythearmatureflux.TheratioofthistotalvoltagetoarmaturecurrentisdefinedasXsorthesynchronousreactance.lAalarsXXIXIEXSalientPoleSynchronousMachinesSalientPoleSynchronousMachineTwoReactionTheoryOneoftheconceptsusedincylindricalrotortheorywasthesummationofbothfluxandmmfwaveforms.r=f+arandFr=Ff+FarThisisallowedsinceB=orHandthemagneticpermeabilityoftheairgapisconstantaroundtherotorHoweverforsalientpolemachines,thepermeabilityofthefluxpathvariessignificantlyastheratioofairgaptosteelchanges.Thereforerf+arSalientPoleSynchronousMachineWithasalientpolemachine,asinusoidaldistributionoffluxcannotbeassumedintheairgapduetothevariationinmagneticpermeancealongtheairgap.However,owingtothesymmetryofasalientpolemachinealongthedirectandquadratureaxis,asinusoidaldistributionofmmfcanbeassumedalongeachaxis.BreakthemmfofthearmaturecurrentAarintotwocomponents,AdandAq.AdisthecomponentofAarthatworksalongthedirectaxisandAqisthecomponentofAarcenteredonthequadratureaxis.TwoReactionTheory:IntroductionIfyouacceptthatAarcanbebrokenintotwocomponentsAdandAq,itfollowsthatforeachmmfwaveform,aemfwaveformexists90degreesoutofphasewithit.SoAdhasanassociatedEd,andAqhasanassociatedEq.ThesevoltagedropscanbethoughofhasbeingcreatedbyafictitiousreactancedropEd=XadIdandEq=XaqIq,whereId:DirectaxiscomponentofarmaturecurrentIq:QuadratureaxiscomponentofarmaturecurrentXad:DirectaxisarmaturereactionreactanceXaq:QuadratureaxisarmaturereactionreactanceIaVtIaraEintEaΦarθjIaxAAjIax1IdxldIqxlqIdxAdIqxAqForCylindricalRotor:Ia2=Id2+Iq2Xld=XlqXAd=XAqTwoReactionDiagramSinceforaCylindricalRotor:Ia2=Id2+Iq2and(IaXs)2=(IdXd)2+(IqXq)2Xld=XlqXAd=XAqXs=Xd=XqItisnotnecessarytousetworeactiontheorytodescribethequantitiesofacylindricalrotormachine.EaIqIaIdΦfΦrΦaqΦadΦarPhasorDiagramofaSalientPoleSynchronousGeneratorIaVtIdEintIqK1EintIdxadIqxaqEaIaraIaxlIa:StatorcurrentVt:StatorterminalVoltageIra:VoltageofstatorresistanceIxl:VoltageofstatorleakagereactanceEint:InternalairgapvoltageK1Eint:Extrammfrequiredtoovercomestatorsaturation,K1issaturationfactorIdxad:reactivevoltagedropdirectaxisIdxaq:ReactivevoltagedropquadratureaxisEa:Totalsumofdirectaxisvoltage,airgapvoltage,opencircuitvoltageßεδId=Iasin(+δ)Iq=Iasin(+δ)PoleFaceDesign-MagneticFieldsThemmfwaveofarmaturereactionandthemmfwaveofthepolearecreatedontwodifferentsidesoftheairgapbutmustbecombinedtodeterminearesultantmmf.Todothiswemustdetermineconversionfactorstoconvertanstatorsidemmftoandequivalentrotorsidemmf.90°lagArmaturecurrentmmfFarResultantmmfFrFieldmmfFfRotorRotationStatorRotorNSPoleFaceDesign–MagneticFieldsC1:Ifpeakofthefundamentalisunity,thenC1ispeakofacutalwaveform.NotethatWiesemancallsthisA1No-Load:motorisexcitedbythefieldwindingonlyPoleFaceDesign–MagneticFie