Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)2024/3/28Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)StatorRevolvingMagneticFieldMagneticPolePairsrotateatSynchronousSpeedThreePhaseACVoltageExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)SynchronousRotorDCinputtotherotorcreateselectromagneticpolespairsPolesofdifferentpolarityarecreatedbywindingaroundthepoleindifferentdirectionsExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)SynchronousMotorRotor“Locked”intopowersupply,rovlovesatsynchronousspeedExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PhasorsandPhasorDiagramsTheconceptofPhasorsisrelatedtosinusoidalwaveformsthataredistributedinspaceandvarywithtime.Phasorsarecomplex(asincomplexnumbers)quantitiesusedforsimplifiedcalculationoftimevaryingandtravelingwaveforms.Themagnitudeandphaserelationshipbetweenthevectorsandcanbeshownsimplyinphasordiagrams.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PhasorDiagramExampleConsiderthesimpleRL(resistiveinductive)circuitV=Vmsin(ωt)Voltagefunctionoftime.Currentfunctionoftimeanddisplacedbyangle

VI

LMagneticFluxinInductor90°outofphasewithvoltagewaveformi90°Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PhasorDiagramCont.

VIFLФLRecall:

B:MagneticFluxDensitydenoteФ

H:MagneticFluxIntensityormmfdenoteF

o:Constantofpermeabilityoffreespace

r:Constantofpermeabilityofelectricalsteel

Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)CylindricalRotorSynchronousMachine:Duetotheevenairgap,theformulationsforbasicmachinequantitiesissimplified.Wewillconsiderthecylindricalmachinetheoryfirstandthenextendtheanalysistothesalientpolecase.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)AxisofFieldAxisofPhaseA90°lagArmaturecurrentmmfFarResultantmmfFrFieldmmfFfRotorRotationStatorRotorNSStatorI.D.RotorO.D.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)IaVtIaraEintEaΦar

-Φar

fΦf

RjIaxAjIax1Φr-

ar

arErExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)CylindricalRotorPhasorDiagramForSynchronousGeneratorVt: 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: ReactivevoltagedropofreactanceofArmaturereactionExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)FromthediagramitisevidentthatEr,thevoltageinducedinthestatorbytheeffectofthearmaturereactionflux,isinphasewithIaXl.ThesummationofErandIaXlgivesthetotalreactivevoltageproducedinthearmaturecircuitbythearmatureflux.TheratioofthistotalvoltagetoarmaturecurrentisdefinedasXsorthesynchronousreactance.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)SalientPoleSynchronousMachinesExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)SalientPoleSynchronousMachineExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)TwoReactionTheoryOneoftheconceptsusedincylindricalrotortheorywasthesummationofbothfluxandmmfwaveforms.

r=f+arandFr=Ff+FarThisisallowedsince

B=o

rHandthemagneticpermeabilityoftheairgapisconstantaroundtherotorHoweverforsalientpolemachines,thepermeabilityofthefluxpathvariessignificantlyastheratioofairgaptosteelchanges.Thereforer

f+ar

Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)SalientPoleSynchronousMachineWithasalientpolemachine,asinusoidaldistributionoffluxcannotbeassumedintheairgapduetothevariationinmagneticpermeancealongtheairgap.However,owingtothesymmetryofasalientpolemachinealongthedirectandquadratureaxis,asinusoidaldistributionofmmfcanbeassumedalongeachaxis.BreakthemmfofthearmaturecurrentAarintotwocomponents,AdandAq.AdisthecomponentofAarthatworksalongthedirectaxisandAqisthecomponentofAarcenteredonthequadratureaxis.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)TwoReactionTheory:IntroductionIfyouacceptthatAarcanbebrokenintotwocomponentsAdandAq,itfollowsthatforeachmmfwaveform,aemfwaveformexists90degreesoutofphasewithit.SoAdhasanassociatedEd,andAqhasanassociatedEq.ThesevoltagedropscanbethoughofhasbeingcreatedbyafictitiousreactancedropEd=XadIdandEq=XaqIq

,whereId: DirectaxiscomponentofarmaturecurrentIq:QuadratureaxiscomponentofarmaturecurrentXad:DirectaxisarmaturereactionreactanceXaq:QuadratureaxisarmaturereactionreactanceExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)IaVtIaraEintEaΦarθjIaxAAjIax1IdxldIqxlqIdxAdIqxAqForCylindricalRotor:Ia2=Id2+Iq2Xld=XlqXAd=XAqExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)TwoReactionDiagramSinceforaCylindricalRotor:Ia2=Id2+Iq2and(IaXs)2=(IdXd)2+(IqXq)2Xld=XlqXAd=XAqXs=Xd=XqItisnotnecessarytousetworeactiontheorytodescribethequantitiesofacylindricalrotormachine.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)EaIqIaIdΦfΦrΦaqΦadΦarPhasorDiagramofaSalientPoleSynchronousGeneratorExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)IaVtIdEint

IqK1EintIdxadIqxaqEaIaraIaxlIa:StatorcurrentVt:StatorterminalVoltageIra:VoltageofstatorresistanceIxl:VoltageofstatorleakagereactanceEint:InternalairgapvoltageK1Eint:Extrammfrequiredtoovercomestatorsaturation,K1issaturationfactorIdxad:reactivevoltagedropdirectaxisIdxaq:ReactivevoltagedropquadratureaxisEa:Totalsumofdirectaxisvoltage,airgap voltage,opencircuitvoltage?εδId=Iasin(

+δ)Iq=Iasin(

+δ)Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign-MagneticFieldsThemmfwaveofarmaturereactionandthemmfwaveofthepolearecreatedontwodifferentsidesoftheairgapbutmustbecombinedtodeterminearesultantmmf.Todothiswemustdetermineconversionfactorstoconvertanstatorsidemmftoandequivalentrotorsidemmf.90°lagArmaturecurrentmmfFarResultantmmfFrFieldmmfFfRotorRotationStatorRotorNSExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign–MagneticFieldsC1:Ifpeakofthefundamentalisunity,thenC1ispeakofacutalwaveform.NotethatWiesemancallsthisA1No-Load:motorisexcitedbythefieldwindingonlyExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign–MagneticFieldCd1:Ifpeakofthefundamentalisunity,thenCd1ispeakofacutalwaveform.NotethatWiesemancallsthisAd1ArmaturemmfSinewavewhoseaxiscoincideswiththepolecenterExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign–MagneticFieldCq1:Ifpeakofthefundamentalisunity,thenCq1ispeakofacutalwaveform.NotethatWiesemancallsthisAq1ArmaturemmfSinewavewhoseaxiscoincideswiththegapbetweenpolesExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)ListofPoleConstantsCd1–RatioofthefundamentaloftheairgapfluxproducedbythedirectaxisarmaturecurrenttothatwhichwouldbeproducedwithauniformgapequaltotheeffectivegapatthepolecenterCq1–RatioofthefundamentaloftheairgapfluxproducedbythequadratureaxisarmaturecurrenttothatwhichwouldbeproducedwithauniformgapequaltotheeffectivegapatthepolecenterC1–Theratioofthefundamentaltotheactualmaximumvalueofthefieldformwhenexcitedbythefieldonly(no-load)Cm–Ratiooffundamentalairgapfluxproducedbythefundamentalofarmaturemmftothatproducedbythefieldforthesamemaximummmf.Thisisthearmaturereactionconversionfactorforthedirectaxis.Cm=Cd1/C1K

–Fluxdistributioncoefficient;theratiooftheareaoftheactualnoloadfluxwavetotheareaofitsfundamentalExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleConstantsWhatfollowsaregraphsthatrelatethephysicalgeometryofthepoletothepoleconstants.ThesegraphscanbefoundintheappendixofEngineeringNote106.Thegraphsintheengineeringnoteareidenticaltographsthatfirstappearedina1927AIEEpapertitledGraphicalDeterminationofMagneticFieldsbyRobertWieseman.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleConstantsWiesemanusedhandplottingtechniquestoplotthefluxfieldsofseveralhundredsofpoleshapestocomeupwiththegraphs.Duetotheintensivenatureofthework,thegraphsareplottedforalimitedrangeofpolegeometry:Polearc/Polepitch=0.5to.75 Gmax/Gmin=1.0to3.0 Minimumgap/polepitch=.005to.05 SincethesecurvesareusedbySMDStocalculatemotorperformance,SMDSwillnotrunwithanyoneofthesethreevariablesoutsideofthegivenrange.Thereisnoreason,besidesthelimitationsoftheoriginalcurves,whyvariablesoutsidetherangeslistedabovecouldn’tbeused.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign–MagneticFieldsDeterminationofK

Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign–MagneticFieldsDeterminationofC1Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign–MagneticFieldsDeterminationofCq1Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign–MagneticFieldsDeterminationofCd1Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)PoleFaceDesign–MagneticFieldsPolefacedesignscomeintwoflavors,singleradiusanddoubleradius.Thereasonforthisistheshapeofthepoleheadrelativetothestatorboreradiushasalargeinfluenceoftheshapeofthefieldfluxwaveform.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)ReactanceCalculationsXad=ReactanceofarmaturereactiondirectedalongthedirectaxisXaq=ReactanceofarmaturereactiondirectedalongthequadratureaxisT=CommonReactanceFactor

a=PermeanceFactorCd1=PoleConstantCq1=PoleConstantExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)T=CommonReactanceFactorm=#phasesL=StatorCoreLengthf=frequencyZ=SeriesConductorsperPhaseKw=WindingfactorStatorP=#PolesReactanceCalculationsExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)

a=PermeanceFactorD=DiameterofStatorBoreP=#PolesKg=Carter’sGapCoefficeintgmin=MinimumairgapatcenterofpoleReactanceCalculationsExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)ArmatureLeakageReactanceisdeterminedusingamethodologyidenticaltotheinductionmachine.SynchronousReactancesXd=Xl+XadXq=Xl+XaqExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)ExcitationCalculations1.CalculatetotalMagneticFlux2.ConvertarmaturemagneticFluxtoFieldEquivalent3.CalculateEintbyaddingarmatureresistanceandleakagereactancedropstoterminalvoltage.4.Usingstep2,calculatetheamphereturnsrequiredtomagnitizetheairgap.5.UsingstepEintfromstep3andelectricalsteelmagnitizationcurvescalculatetheampereturnsrequiredtomagnitzethestatorcoreandairgap.6.Usingtheresultsof4and5calculatethesaturationfactor.7.Usingtheresultsof3and5calculatethedirectaxiscomponentofmmf.8.Calculatethedirectaxiscomponentofarmaturereaction9.Usingtheresultsof6and7calculatethemmfrequirementsatthepoleface10.Calculatethepolesaturationmmf11.Totaldirectaxisexcitationisthesumof8and9Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)ExcitationCalculationsStepOne:TotalfundamentalfluxperpoleEph: PhasevoltageatstatorterminalsKp: PitchFactorKd: DistributionFactorFreq: FrequencyNSPC: ArmatureseriesturnsperphasepercircuitExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)ExcitationCalculation Step2:CalculatetotalfluxperpoleonopencircuitK

relatesfundamentalfluxperpoletototalfluxperpoleusingfactors.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)ExcitationCalculationCont.Step3:Calculatetotalairgapfluxperpoleatthespecificvoltageandloadofinterest.ThisvoltagewasshownonthepreviousphasordiagramasEint.Step3a:CalculatethestatorleakagereactanceusingsameformulasderivedfortheInductionmotorstator.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)FieldExcitationCont.PortionofthepreviousphasordiagramisredrawnFromdiagramitisevidentthat:IaxlIaraIaVtIdEint

Iq

Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)IaVtEint

IqK1EintIdxadIqxaqIaxaqIaraIaxlαεδIdK1Eintsin(α)Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)FieldExcitationCont.Step4:Calculatetheampereturnsneededtomagnetizetheairgapatratedvoltage:Fg.Samegapfactorusedfrominductionmotortheory(i.e.Carter’scoefficient)Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)FieldExcitationCont.Step5:Calculatethestatorcore+statorteethampereturnsatthevalueoffluxcorrespondingtoEint.Ac:AreaofstatorcoreAt:AreaofstatorteethBCmax:maximumvalueoffluxdensityinstatorcoreBTmax:maximumvalueoffluxdensityinstatorteethExcitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)FieldExcitationCont.UsingB-Hcurvesformagneticsteelusedforstatorlaminations,readoffavalueofmmfinamphereturnsforthevalueofBCmaxandBTmaxcalculatedinprevioussteps.Makesureunitsmatch.Excitation研發(fā)培訓(xùn),設(shè)計培訓(xùn)FieldExcitationCont. Step6:CalculatethecomponentmmfinthedirectaxiscorrespondingtoK1eintStep6a:CalculatesaturationfactorK1fromB-Hcurveforelectricalsteel.Statormmf:ActualvalueofampereturnscorrespondingtoEintvalueoffluxfromst