Performance-of-BDFM-as-generator-and-motor

PerformanceofBDFMasgeneratorandmotorR.A.McMahon,P.C.Roberts,X.WangandP.J.TavnerAbstract:Theperformanceofthebrushlessdoubly-fedmachine(BDFM)isanalysedusingaper-phaseequivalentcircuit.Anexpressionfortheratingofthemachineasafunctionofmagneticandelectricloadingsisdeveloped,andtheratingiscomparedtothoseofthedoubly-fedinductionmachineandcascadedinductionmachines.AsthemagneticfieldinaBDFMiscomplex,themagneticloadingisconsideredindetailandanewgeneralisedloadingisderived.TheBDFMsuffersareductionratingofaboutone-quarterincomparisontocomparableconventionalmachines,arisingfrompenaltiesinmagneticandelectricloadingsconsequentonthepresenceoftwostatortorotorcouplings.Thehandlingofreactivepowerhasanimportanteffectonthemachineperformanceandthispointisillustratedwithexperimentalresultsfromaframesize180BDFM.Thetestswerecarriedoutatmodestfluxdensitiestoavoidtheeffectsofsaturation,buttheimplicationsofsaturationareconsidered.ListofsymbolsX1,X2,Xr,Xcindicatingastator1,2,rotororcoremodelquantityXfXg,IfXg,jXjdenotesreal,imaginarypart,mag-nitudeofcomplexXffðXÞargumentofcomplexX,i.e.arctan¼IfXg=fXgðÞN,nwindingturns,turnsratio(real)R,Lresistance,selfinductance(real)X0indicatesanapparent(referred)quantityS,Q,Papparentpower,reactivepower(real),realpower(real)V,Icomplexvoltage,currentp1,p2statorwindingpolepairsorBDFMrotationalshaftspeedsslip(real)jffiffiffiffiffiffiffi1pfphaseangleofcurrent(real)dloadangleinsynchronousmode(real)Ingeneral,symbolsdenotecomplexquantities.1IntroductionDoubly-fedmachinesareattractiveasvariablespeeddrivesorgeneratorsbecausetheassociatedinverteronlyneedsafractionalratingcomparedtothatofthemachine.Potentialapplicationsincludegenerationfromwindpower[1,2]andintegrateddrives[3].Thispaperisconcernedwithonetypeofdoubly-fedmachine,thebrushlessdoubly-fedmachine(BDFM).TheBDFMhastwostatorwindings,eachproducinganairgapfieldofadifferentpolenumber,chosentoavoidtransformercouplingbetweenthestatorwindings.Therotorisspeciallydesignedtocoupletobothairgapfields.AcomparisonoftheBDFMwithothertypesofdoubly-fedsystemshasbeengivenbyHopfenspergerandAtkinson[4].RecentworkontheBDFMincludesthegeneralisedanalysispublishedbyWilliamsonetal.[5],studiesofpowerflowthroughthemachine[6,7]andtheequivalentcircuitapproachproposedbyRobertsetal.[8].However,thereremainsaneedtoconsidertheoperationofthemachinefromtheperspectiveofterminalquantities.InthispaperweshowhowtheuseoftheequivalentcircuitforthemachineleadstoanunderstandingofoperatingconditionsandhencehowtheratingofaBDFMcanbeestablished.[5,9].2BasicconfigurationABDFMcanoperateinseveralwaysbutthesynchronous,doubly-fed,modeisusedforcontrolledvariable-speedoperation[5,9].Inthisarrangement,onewinding,thepowerwinding,isconnecteddirectlytothegrid.Theotherwinding,thecontrolwinding,issuppliedwithvariablevoltageatvariablefrequencyfromaconverteralsoconnectedtothegrid.Statorandrotorquantitiesareshownforthesynchro-nousmodeinFig.1.Theshaftangularvelocityisgivenby:or¼o1þo2p1þp2ð1Þandslipsforthetwowindingscanbedefinedas:s19o1p1oro1¼or1o1ð2Þs29o2p2oro2¼or2o2ð3ÞE-mail:[e-mail]gDepartment,UniversityofCambridge,TrumpingtonStreet,CambridgeCB21PZ,UKP.C.RobertsiswithScientificGenericsLtd.,HarstonMill,Harston,CambridgeCB25GG,UKP.J.TavneriswithSchoolofEngineering,UniversityofDurham,DurhamDH13LE,UKrIEE,2006IEEProceedingsonlineno.20050289doi:10.1049/ip-epa:20050289Paperfirstreceived11thJulyandinfinalrevisedform10thNovember2005IEEProc.-Electr.PowerAppl.,Vol.153,No.2,March2006289Thefrequenciesofthefieldsduetostator1andstator2intherotorreferenceframeare:or1¼o1p1orð4Þor2¼o2p2orð5ÞAfurtherrelationshipfortheangularvelocityattheso-called‘natural’speed,thatisthesynchronousspeedwhenthecontrolwindingisfedwithDCðo2¼0Þ,isgivenby:on¼o1p1þp2ð6ÞInthesynchronousmode,from(1),(4)and(5)or1¼or2.Hencefrom(2)and(3):s2s1¼o1o2ð7Þ3EquivalentcircuitsforBDFMAper-phaseequivalentcircuitfortheBDFMbasedontwoinductionmachineswithconnectedrotorsisgivenin[8].Asitwasnotpossibletodeterminealltheparametersexplicitlyfrommeasurements,anelectricallyequivalentcircuitforwhichallparameterscouldbefoundwasproposed.Thiscircuit,showninFig.2,isusedinthispaper;themachineistakentobethree-phase.Parametersareshownreferredtothepowerwindingandironlossesareneglected.Thecircuitisvalidforallmodesofoperation,includingthesynchronousmode.Theparameters,intheunreferredform,aredefinedinTable1.Inthisformoftheequivalentcircuit,thestatorleakageinductancesarenotshownexplicitlyandthevaluesofthemagnetisinginductancesandturnsratiosforthetwowindingsthereforehaveslightlymodifiedvalues.Thereferredandactualstator2supplyvoltagearerelatedby:V002¼n1n2V2ð8ÞTosimplifyfurtheranalysis,wecannowconsideranequivalentcircuitfortheinnercoreofaBDFM,obtainedbyomittingthemagnetisingreactancesandthestatorandrotorresistances.However,inrotordesignsreportedtodate,therotorleakagereactanceisrelativelylargeandcannotbeneglected[8].Asignificantportionoftheleakageinductanceintheserotorsisduetothehighspatialharmoniccontentoftherotorfield.Theequivalentcircuit,againreferredpowerwindin