Vector control motor.docx

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