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)Voltagefunctionoftime.CurrentfunctionoftimeanddisplacedbyangleLMagneticFluxinInductor90°outofphasewithvoltagewaveformi90°PhasorDiagramCont.VIFLФLRecall:B:MagneticFluxDensitydenoteФH:MagneticFluxIntensityormmfdenoteFo:Constantofpermeabilityoffreespacer:ConstantofpermeabilityofelectricalsteelCylindricalRotorSynchronousMachine:Duetotheevenairgap,theformulationsforbasicmachinequantitiesissimplified.Wewillconsiderthecylindricalmachinetheoryfirstandthenextendtheanalysistothesalientpolecase.StatorI.D.RotorO.D.IaVtEaΦar-ΦarfΦf-ararErCylindricalRotorPhasorDiagramForSynchronousGeneratorVt: TerminalVoltageIa: StatorCurrentLagsterminalVoltagebyAngleEa: AirGapVoltage,thevoltageinducedintothearmaturebythe fieldvoltageactingalone,the“opencircuit”voltageEr: ReactivevoltageproducedbyarmaturefluxEint: ResultantVoltageintheAirGapar: FluxfromArmaturecurrent(ArmatureReaction)f: Fluxduetofieldcurrentr: Resultantfluxar+fFf: mmfofFieldAar: mmfofArmatureCurrent(ArmatureReaction)FR: Resultantmmf,thesumofF+AIara: Voltagedropofarmatureresistance Iaxl: ReactivevoltagedropofArmatureleakagereactanceIaxA: ReactivevoltagedropofreactanceofArmaturereactionFromthediagramitisevidentthatEr,thevoltageinducedinthestatorbytheeffectofthearmaturereactionflux,isinphasewithIaXl.ThesummationofErandIaXlgivesthetotalreactivevoltageproducedinthearmaturecircuitbythearmatureflux.TheratioofthistotalvoltagetoarmaturecurrentisdefinedasXsorthesynchronousreactance.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:QuadratureaxisarmaturereactionreactanceIaVtIaraEintEaΦarθjIaxAAjIax1ForCylindricalRotor:Ia2=Id2+Iq2Xld=XlqXAd=XAqTwoReactionDiagramSinceforaCylindricalRotor:Ia2=Id2+Iq2and(IaXs)2=(IdXd)2+(IqXq)2Xld=XlqXAd=XAqXs=Xd=XqItisnotnecessarytousetworeactiontheorytodescribethequantitiesofacylindricalrotormachine.EaIaΦfPhasorDiagramofaSalientPoleSynchronousGeneratorIaIa:StatorcurrentVt:StatorterminalVoltageIra:VoltageofstatorresistanceIxl:VoltageofstatorleakagereactanceEint:InternalairgapvoltageK1Eint:Extrammfrequiredtoovercomestatorsaturation,K1issaturationfactorIdxad:reactivevoltagedropdirectaxisIdxaq:ReactivevoltagedropquadratureaxisEa:Totalsumofdirectaxisvoltage,airgap voltage,opencircuitvoltageId=Iasin(+δ)Iq=Iasin(+δ)PoleFaceDesign-MagneticFields Themmfwaveofarmaturereactionandthemmfwaveofthepolearecreatedontwodifferentsidesoftheairgapbutmustbecombinedtodeterminearesultantmmf.Todothiswemustdetermineconversionfactorstoconvertanstatorsidemmftoandequivalentrotorsidemmf.lagArmaturecurrentmmfFarResultantmmfFrFieldmmfFfRotorRotationStatorRotorNSPoleFaceDesign–MagneticFieldsC1:Ifpeakofthefundamentalisunity,thenC1ispeakofacutalwaveform.NotethatWiesemancallsthisA1No-Load:motorisexcitedbythefieldwindingonlyPoleFaceDesign–MagneticFieldCd1:Ifpeakofthefundamentalisunity,thenCd1ispeakofacutalwaveform.NotethatWiesemancallsthisAd1ArmaturemmfSinewavewhoseaxiscoincideswiththepolecenterPoleFaceDesign–MagneticFieldCq1:Ifpeakofthefundamentalisunity,thenCq1ispeakofacutalwaveform.NotethatWiesemancallsthisAq1ArmaturemmfSinewavewhoseaxiscoincideswiththegapbetweenpolesListofPoleConstants Cd1–Ratioofthefundamentaloftheairgapfluxproducedbythedirectaxisarmaturecurrenttothatwhichwouldbeproducedwithauniformgapequaltotheeffectivegapatthepolecenter Cq1–Ratioofthefundamentaloftheairgapfluxproducedbythequadratureaxisarmaturecurrenttothatwhichwouldbeproducedwithauniformgapequaltotheeffectivegapatthepolecenter C1–Theratioofthefundamentaltotheactualmaximumvalueofthefieldformwhenexcitedbythefieldonly(no-load) Cm–Ratiooffundamentalairgapfluxproducedbythefundamentalofarmaturemmftothatproducedbythefieldforthesamemaximummmf.Thisisthearmaturereactionconversionfactorforthedirectaxis.Cm=Cd1/C1 K–Fluxdistributioncoefficient;theratiooftheareaoftheactualnoloadfluxwavetotheareaofitsfundamentalPoleConstants Whatfollowsaregraphsthatrelatethephysicalgeometryofthepoletothepoleconstants.ThesegraphscanbefoundintheappendixofEngineeringNote106.Thegraphsintheengineeringnoteareidenticaltographsthatfirstappearedina1927AIEEpapertitledGraphicalDeterminationofMagneticFieldsbyRobertWieseman.PoleConstantsWiesemanusedhandplottingtechniquestoplotthefluxfieldsofseveralhundredsofpoleshapestocomeupwiththegraphs.Duetotheintensivenatureofthework,thegraphsareplottedforalimitedrangeofpolegeometry:Polearc/Polepitch=0.5to.75 Gmax/Gmin=1.0to3.0 Minimumgap/polepitch=.005to.05 SincethesecurvesareusedbySMDStocalculatemotorperformance,SMDSwillnotrunwithanyoneofthesethreevariablesoutsideofthegivenrange.Thereisnoreason,besidesthelimitationsoftheoriginalcurves,whyvariablesoutsidetherangeslistedabovecouldn’tbeused.PoleFaceDesign–MagneticFieldsDeterminationofKPoleFaceDesign–MagneticFieldsDeterminationofC1PoleFaceDesign–MagneticFieldsDeterminationofCq1PoleFaceDesign–MagneticFieldsDeterminationofCd1PoleFaceDesign–MagneticFieldsPolefacedesignscomeintwoflavors,singleradiusanddoubleradius.Thereasonforthisistheshapeofthepoleheadrelativetothestatorboreradiushasalargeinfluenceoftheshapeofthefieldfluxwaveform.ReactanceCalculationsXad=ReactanceofarmaturereactiondirectedalongthedirectaxisXaq=ReactanceofarmaturereactiondirectedalongthequadratureaxisT=CommonReactanceFactora=PermeanceFactorCd1=PoleConstantCq1=PoleConstantT=CommonReactanceFactorm=#phasesL=StatorCoreLengthf=frequencyZ=SeriesConductorsperPhaseKw=WindingfactorStatorP=#PolesReactanceCalculationsa=PermeanceFactorD=DiameterofStatorBoreP=#PolesKg=Carter’sGapCoefficeintgmin=MinimumairgapatcenterofpoleReactanceCalculationsArmatureLeakageReactanceisdeterminedusingamethodologyidenticaltotheinductionmachine.SynchronousReactancesXd=Xl+XadXq=Xl+XaqExcitationCalculations1.CalculatetotalMagneticFlux2.ConvertarmaturemagneticFluxtoFieldEquivalent3.CalculateEintbyaddingarmatureresistanceandleakagereactancedropstoterminalvoltage.4.Usingstep2,calculatetheamphereturnsrequiredtomagnitizetheairgap.5.UsingstepEintfromstep3andelectricalsteelmagnitizationcurvescalculatetheampereturnsrequiredtomagnitzethestatorcoreandairgap.6.Usingtheresultsof4and5calculatethesaturationfactor.7.Usingtheresultsof3and5calculatethedirectaxiscomponentofmmf.8.Calculatethedirectaxiscomponentofarmaturereaction9.Usingtheresultsof6and7calculatethemmfrequirementsatthepoleface10.Calculatethepolesaturationmmf11.Totaldirectaxisexcitationisthesumof8and9ExcitationCalculationsStepOne:TotalfundamentalfluxperpoleEph: PhasevoltageatstatorterminalsKp: PitchFactorKd: DistributionFactorFreq: FrequencyNSPC: ArmatureseriesturnsperphasepercircuitExcitationCalculation Step2:CalculatetotalfluxperpoleonopencircuitKrelatesfundamentalfluxperpoletototalfluxperpoleusingfactors.ExcitationCalculationCont.Step3:Calculatetotalairgapfluxperpoleatthespecificvoltageandloadofinterest.ThisvoltagewasshownonthepreviousphasordiagramasEint. Step3a:CalculatethestatorleakagereactanceusingsameformulasderivedfortheInductionmotorstator.FieldExcitationCont.PortionofthepreviousphasordiagramisredrawnFromdiagramitisevidentthat:IaαεδK1Eintsin(α)FieldExcitationCont.Step4:Calculatetheampereturnsneededtomagnetizetheairgapatratedvoltage:Fg.Samegapfactorusedfrominductionmotortheory(i.e.Carter’scoefficient)FieldExcitationCont.Step5:Calculatethestatorcore+statorteethampereturnsatthevalueoffluxcorrespondingtoEint.Ac:AreaofstatorcoreAt:AreaofstatorteethBCmax:maximumvalueoffluxdensityinstatorcoreBTmax:maximumvalueoffluxdensityinstatorteethFieldExcitationCont. UsingB-Hcurvesformagneticsteelusedforstatorlaminations,readoffavalueofmmfinamphereturnsforthevalueofBCmaxandBTmaxcalculatedinprevioussteps.Makesureunitsmatch.FieldExcitationCont. Step6:CalculatethecomponentmmfinthedirectaxiscorrespondingtoK1eint Step6a:CalculatesaturationfactorK1fromB-Hcurveforelectricalsteel.Statormmf:ActualvalueofampereturnscorrespondingtoEintvalueoffluxfromstep5.FgEint:ValueofmmfthatwouldresultbyextendingthestraitportionofB-Hcurve.Fgwascalculatedinstep4.mmfeintFieldExcitationCont.Step7:K1eld=K1EintcosßK1eld:Componentofmmfinthedirectaxis correspondingtoK1EintK1:SaturationFactorfromstep6Eint:Voltageintheairgapfromstep4ß:AnglebetweenFieldExcitationVoltageand Eint.:ß=-FieldExcitationCont.Step8:Calculatethedirectaxiscomponentofarmaturereaction:Idxad Xadcalculatedinreactancesection Id=Iasin(ε)FieldExcitationCont.Step9:Addingtheresultsfromstep7andstep6,yougetthemmfrequirementsatthepolefaceFPF.FPF=K1Eintcos(ß)+IdxadTheunitsofFPFareampereturns.FieldExcitationCont.Step10:Calculatethepolesaturationmmf.Usingtheresultsofthenextlecture,calculatethepoleleakagefactorKLTherotorfluxperpoleisthenKLxEintxFReadthevalueofmmfperpolefromthepolesteelB-HCurve.FieldExcitationFinishThetotalexcitationrequiredalongthedirectaxisisthesumofsteps9and10.Theresultisinunitsofampere-turns.Dividetheampere-turnsbythenumberofturnsperpoletoarriveatFullLoadFieldAmps.THEEND Questions?