Vector control motor.docx
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Vector control motor.docx
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Vectorcontrolmotor
Vectorcontrol,alsocalled field-orientedcontrol (FOC),isa variable-frequencydrive (VFD)controlmethodwherethe stator currentsofa three-phase ACelectricmotor areidentifiedastwoorthogonalcomponentsthatcanbevisualizedwithavector.Onecomponentdefinesthemagneticfluxofthemotor,theotherthetorque.Thecontrolsystemofthedrivecalculatesfromthefluxandtorquereferencesgivenbythedrive'sspeedcontrolthecorrespondingcurrentcomponentreferences.Typically proportional-integral(PI)controllers areusedtokeepthemeasuredcurrentcomponentsattheirreferencevalues.The pulse-widthmodulation ofthevariable-frequencydrivedefinesthe transistor switchingaccordingtothestatorvoltagereferencesthataretheoutputofthePIcurrentcontrollers.[1]
FOCisusedtocontrolthe AC synchronous and inductionmotors.[2] Itwasoriginallydevelopedforhigh-performancemotorapplicationsthatarerequiredtooperatesmoothlyoverthefull speed range,generatefull torque atzerospeed,andhavehighdynamicperformanceincludingfast acceleration anddeceleration.However,itisbecomingincreasinglyattractiveforlowerperformanceapplicationsaswellduetoFOC'smotorsize,costand powerconsumption reductionsuperiority.[3][4] Itisexpectedthatwithincreasingcomputationalpowerofthemicroprocessorsitwilleventuallynearlyuniversallydisplacesingle-variable scalar volts-per-Hertz (V/f)control.[5][6]
Contents
[hide]
∙1 Developmenthistory
∙2 Technicaloverview
∙3 Applicationrecap
∙4 Seealso
∙5 References
Developmenthistory[edit]
BlockdiagramfromBlaschke's1971USpatentapplication
TechnicalUniversityDarmstadt'sK.HasseandSiemens'F.Blaschkepioneered vector controlofACmotorsstartingin1968andintheearly1970s,Hasseintermsofproposingindirectvectorcontrol,Blaschkeintermsofproposingdirectvectorcontrol.[7][8] TechnicalUniversityBraunschweig'sWernerLeonhardfurtherdevelopedFOCtechniquesandwasinstrumentalinopeningupopportunitiesfor ACdrives tobeacompetitivealternativeto DCdrives.[9][10]
Yetitwasnotuntilafterthecommercializationof microprocessors,thatisintheearly1980s,thatgeneralpurposeACdrivesbecameavailable.[11][12] BarrierstouseofFOCforACdriveapplicationsincludedhighercostandcomplexityandlowermaintainabilitycomparedtoDCdrives,FOChavinguntilthenrequiredmanyelectroniccomponentsintermsofsensors,amplifiersandsoon.[13]
The Parktransformation haslongbeenwidelyusedintheanalysisandstudyof synchronous andinductionmachines.ThetransformationisbyfarthesinglemostimportantconceptneededforanunderstandingofhowFOCworks,theconcepthavingbeenfirstconceptualizedina1929paperauthoredby RobertH.Park.[14] Park'spaperwasrankedsecondmostimportantintermsofimpactfromamongallpowerengineeringrelatedpaperseverpublishedinthetwentiethcentury.ThenoveltyofPark'sworkinvolveshisabilitytotransformanyrelatedmachine'slinear differentialequationsetfromonewithtimevaryingcoefficientstoanotherwithtime invariant coefficients.[15]
Technicaloverview[edit]
OverviewofkeycompetingVFDcontrolplatforms:
VFD,withsensororsensorless
Scalarcontrol
V/f(VoltsperHertz)control
Vectorcontrol
DTC(Directtorquecontrol)
DSC(Directself-control)
SVC(Spacevectormodulation)
FOC(Field-orientedcontrol)
DirectFOC
IndirectFOC
SignalFlowGraph(SFG)forInductionMotor
SFGEquations
(d,q)CoordinateSystemSuperimposedonThree-PhaseInductionMotor[16]
SimplifiedIndirectFOCBlockDiagram [3] [17][18]
SimplifiedDirectFOCBlockDiagram [19]
SensorlessFOCBlockDiagram [20][21]
WhiletheanalysisofACdrivecontrolscanbetechnicallyquiteinvolved("Seealso"section),suchanalysisinvariablystartswithmodelingofthedrive-motorcircuitinvolvedalongthelinesofaccompanying signalflowgraph andequations.[20]
Invectorcontrol,anACinductionorsynchronousmotoriscontrolledunderalloperatingconditionslikeaseparately excited DCmotor.[22] Thatis,theACmotorbehaveslikeaDCmotorinwhichthefieldfluxlinkage and armature fluxlinkagecreatedbytherespectivefieldandarmature(ortorquecomponent)currentsare orthogonally alignedsuchthat,whentorqueiscontrolled,thefieldfluxlinkageisnotaffected,henceenablingdynamictorqueresponse.
Vectorcontrolaccordinglygeneratesathree-phase PWM motorvoltageoutputderivedfroma complexvoltagevectortocontrolacomplexcurrentvectorderivedfrommotor'sthree-phasemotorstatorcurrentinputthrough projections or rotations backandforthbetweenthethree-phasespeedandtimedependentsystemandthesevectors'rotatingreference-frametwo-coordinate timeinvariantsystem.[23]
Suchcomplex stator motorcurrentspacevectorcanbedefinedina(d,q)coordinatesystemwithorthogonalcomponentsalongd(direct)andq(quadrature)axessuchthatfieldfluxlinkagecomponentofcurrentisalignedalongthedaxisandtorquecomponentofcurrentisalignedalongtheqaxis.[22] Theinductionmotor's(d,q)coordinatesystemcanbesuperimposedtothemotor'sinstantaneous(a,b,c)three-phase sinusoidal systemasshowninaccompanyingimage(phasesa&bnotshownforclarity).Componentsofthe(d,q)systemcurrentvector,allowconventionalcontrolsuchasproportionalandintegral,or PI,control,aswithaDCmotor.
Projectionsassociatedwiththe(d,q)coordinatesystemtypicallyinvolve:
[20][23][24]
∙Forwardprojectionfrominstantaneouscurrentsto(a,b,c)complex stator currentspacevectorrepresentationofthethree-phase sinusoidal system.
∙Forwardthree-to-twophase,(a,b,c)-to-(
)projectionusingthe Clarke transformation.Vectorcontrolimplementationsusuallyassumeungroundedmotorwithbalancedthree-phasecurrentssuchthatonlytwomotorcurrentphasesneedtobesensed.Also,backwardtwo-to-threephase,(
)-to-(a,b,c)projectionusesspacevectorPWMmodulatororinverseClarketransformationandoneoftheotherPWMmodulators.
∙Forwardandbackwardtwo-to-twophase,(
)-to-(d,q)and(d,q)-to-(
)projectionsusingtheParkandinverseParktransformations,respectively.
However,itisnotuncommonforsourcestousethree-to-two,(a,b,c)-to-(d,q)andinverseprojections.
While(d,q)coordinatesystemrotationcanarbitrarilybesettoanyspeed,therearethreepreferredspeedsorreferenceframes:
[16]
∙Stationaryreferenceframewhere(d,q)coordinatesystemdoesnotrotate;
∙Synchronouslyrotatingreferenceframewhere(d,q)coordinatesystemrotatesatsynchronousspeed;
∙Rotorreferenceframewhere(d,q)coordinatesystemrotatesatrotorspeed.
Decoupled torqueandfieldcurrentscanthusbederivedfromrawstatorcurrentinputsforcontrolalgorithmdevelopment.[25]
WhereasmagneticfieldandtorquecomponentsinDCmotorscanbeoperatedrelativelysimplybyseparatelycontrollingtherespectivefieldandarmaturecurrents,economicalcontrolofACmotorsinvariablespeedapplicationhasrequireddevelopmentofmicroprocessor-basedcontrols[25] withallACdrivesnowusingpowerfulDSP(digitalsignalprocessing)technology.[26]
Inverterscanbeimplementedaseither open-loop sensorlessorclosed-loopFOC,thekeylimitationofopen-loopoperationbeingmimimumspeedpossibleat100%torque,namely,about0.8 Hzcomparedtostandstillforclosed-loopoperation.[9]
Therearetwovectorcontrolmethods,director feedback vectorcontrol(DFOC)andindirectorfeedforward vectorcontrol(IFOC),IFOCbeingmorecommonlyusedbecauseinclosed-loopmodesuchdrivesmoreeasilyoperatethroughoutthespeedrangefromzerospeedtohigh-speedfield-weakening.[27] InDFOC,fluxmagnitudeandanglefeedbacksignalsaredirectlycalculatedusingso-calledvoltageorcurrentmodels.InIFOC,fluxspaceanglefeedforwardandfluxmagnitudesignalsfirstmeasurestatorcurrentsand rotor speedforthenderivingfluxspaceangleproperbysummingtherotoranglecorrespondingtotherotorspeedandthecalculatedreferencevalueof slip anglecorrespondingtotheslipfrequency.[28][29]
Sensorlesscontrol(seeSensorlessFOCBlockDiagram)ofACdrivesisattractiveforcostandreliabilityconsiderations.Sensorlesscontrolrequiresderivationofrotorspeedinformationfrommeasuredstatorvoltageandcurrentsincombinationwithopen-loopestimatorsorclosed-loopobservers.[20][21]
Applicationrecap[edit]
1.Statorphasecurrentsaremeasured,convertedtocomplexspacevectorin(a,b,c)coordinatesystem.
2.Currentvectorisconvertedto(
)coordinatesystem. Transformedtoacoordinatesystem rotatingin rotor referenceframe,rotorpositionbeingderivedby integrating thespeedbymeansof speedmeasurement sensor.
3.Rotor fluxlinkage vectorisestimatedbymultiplyingthestatorcurrentvectorwithmagnetizinginductanceLm and low-passfiltering theresultwiththerotorno-load timeconstant Lr/Rr,namely,therotorinductancetorotorresistanceratio.
4.Currentvectorisconvertedto(d,q)coordinatesystem.
5.d-axiscomponentofthestatorcurrentvectorisusedtocontroltherotorfluxlinkageandtheimaginaryq-axiscomponentisusedtocontrolthemotortorque.WhilePIcontrollerscanbeusedtocontrolthesecurrents, bang-bang typecurrentcontrolprovidesbetterdynamicperformance.
6.PIcontrollersprovide(d,q)coordinatevoltagecomponents.Adecouplingtermissometimesaddedtothecontrolleroutputtoimprovecontrolperformancetomitigatecrosscouplingorbigandrapidchangesinspeed,currentandfluxlinkage.PI-controlleralsosometimesneed low-passfiltering attheinp
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