PSCAD-Based Modeling and Analysis of a Gearless Variable Spe

PSCAD/EMTDC-BasedModelingandAnalysisofaGearlessVariableSpeedWindTurbine

Seul-KiKimandEung-SangKim

Abstract—Thispaperpresentsdynamicmodelingandsimula-tionofagridconnectedvariablespeedwindturbine(VSWT)usingPSCAD/EMTDC,http://ponentmodelsandequationsareaddressedandtheirim-plementationsintoPSCAD/EMTDCaredescribed.Controllablepowerinverterstrategyisintendedforcapturingthemaximumenergyfromvaryingwindspeedandmaintainingreactivepowergenerationatapre-determinedlevelforconstantpowerfactororvoltageregulation.Thecomponentmodelsandentirecontrolschemeareconstructedbyuser-de nedfunctionprovidedintheprogram.Simulationstudiesprovidecontrolperformanceanddy-namicbehaviorofagearlessVSWTundervaryingwindspeeds.Inaddition,thesystemresponsestonetworkfaultconditionshavebeensimulated.Thismodelingstudycanbeemployedtoevaluatethecontrolscheme,outputperformanceandimpactsofaVSWTonpowergridatplanningordesigningstage.

IndexTerms—Gearlesswindgenerator,gridconnection,maxi-mumpowercapture,powerelectronicsinterface,reactivepowercontrol,variablespeedwindturbine(VSWT).

Fig.1.SchematicrepresentationofagearlessVSWT.

Id,IqMAXCPλOPTη

Pref,QrefVrefVrmsPFQlimitsSinvd-andq-axiscurrentatVSWTterminal[A]Maximumpowercoef cient

MAX

λwhereCP=CP(λOPT)

Electricalef ciencyofgeneratorandinverterRealandreactivepowertargets[kW],[kVar]Phasevoltagemagnitudetarget

PhasevoltagemagnitudeofVSWT(rms)Desiredpowerfactor

Reactivepowercapabilitylimits[kVar]Ratingofinverter[kVA]

LISTOFSYMBOLS

λωMR

VWINDPMρCPTMfBNP

RPMTURHiKTEθiωMωEEfIfVdcα

Pinv,QinvVinv,IinvVd,Vq

Tipspeedratio

Mechanicalspeedofwindturbine[rad/s]Bladeradius[m]windspeed[m/s]

Mechanicalpowerfromwindturbine[kW]Airdensity[kg/m3]Powercoef cient

Mechanicaltorquefromwindturbine[N·m]Electricalbasefrequencyofgenerator[Hz]Numberofpoles

Ratedspeedofwindturbine[rpm]Inertiaconstantofithmass[s]Shaftspringconstant[Nm/rad]

Electricaltorqueofgenerator[N·m]

Massangleofithmass(referenceongenerator)Mechanicalspeedofgenerator[rad/s]Electricalspeedofgenerator[rad/s]Fieldvoltageofexciter[V]Fieldcurrentofexciter[A]DClinkvoltage[V]IGBTswitchingsignal

Measuredrealandreactivepower[kW],[kVar]Measuredvoltageandcurrentofinverter[V],[A]

d-andq-axisvoltageatVSWTterminal[V]

V

ManuscriptreceivedAugust10,2004;revisedFebruary17,2005.Paperno.TEC-00235-2004.

DigitalObjectIdenti er

10.1109/TEC.2005.858063

I.INTRODUCTION

ARIABLEspeedoperationyields20to30percentmoreenergythanthe xedspeedoperation,reducespower uctuationsandimprovesreactivepowersupply[1].Fallingpricesofthepowerelectronicshavemadethevariablespeedtechnologymoreeconomicalandcommon.Suchwindturbinesystem,aswithothertypesofdistributedgeneration,ismostlyconnectedtodistributionfeeders.Thedistributedgenerationcannotconnecteasilytotheelectricpowernetworkwithoutconductingcomprehensiveevaluationsoncontrolperformanceandgridimpact.Stablegridinterfacerequiresareliabletoolforsimulatingandassessingthedynamicsofagridconnectedvariablespeedwindturbine.

PSCAD/EMTDCisanindustrystandardsimulationtoolforstudyingthetransientbehaviorofelectricalnetworks.Itsgraphic-baseduserinterfaceallowstheusertographicallyassemblethecircuit,runthesimulation,analyzetheresults,andmanagethedatainacompletelyintegratedgraphicalenvironment.Itscomprehensivelibraryofmodelssupportsmostofpowerplantacanddccomponentsandcontrols.Itprovidesthe exibilityofbuildinguser-de nedmodelseitherbyassemblingthemvisuallyusingexistingmodelsorbyutilizinganintuitivelygraphicaldesigneditorandwritingcodesinFortran,PSCADscript,CandMATLAB.Itprovidesapowerfulresourceforassessingtheimpactofnewpowertechnologiesinthepowernetwork[2],[3].

ThepurposeofthispaperistoprovidesimulationanddynamicperformanceandgridimpactanalysiscapabilityofagearlessVSWTbasedonPSCAD/EMTDC.TheschematicdiagramofthewindgenerationmodelisshowninFig.1.The

0885-8969/$25.00©2005IEEE

http://ponentsofaproposedsimulationmodel.

TABLEI

PARAMETERSFORWINDTURBINEM

ODEL

modelsystemiscomposedofa xed-pitchstallregulatedwindturbine,agearlessdirectdrivegeneratorandacontrollablepowerelectronicssystem,whichconsistsofasimpledioderecti erandasix-IGBTvoltagesourceinverter(VSI)[4].Agraphic-basedmodelsuitableforelectromagnetictransientstudieshasbeenproposedbasedonmathematicalequationsandpowerelectronicscontrolscheme.Thelargebaseofprogram’sbuilt-incomponentsanduser-de nedmodels,ifaparticularmodeldoesnotexist,havebeenusedformodelingtheVSWTcomponentsandcontrolscheme.SimulationresultsdemonstratethemodelingstudyprovidesareliableandusefulsimulationtoolforassessingthedynamicbehaviorofagearlessVSWTintegratedintopowersystem.

II.PSCAD/EMTDCBASEDMODELING

Fig.2presentsaschematicdiagramoftheproposedsimula-tionmodel,whichconsistsofthefollowingcomponents:

Windmodel;Windturbine;

Directdrivegenerator;Shaftdynamics;

Recti erandvoltagesourceinverter;andPowerelectronicscontrol.

semblingbuilt-infunctionsandlogiccircuitsprovidedintheprogram.B.WindTurbine

Windbladetorquefromwindspeedisdescribedbythefol-lowing(2)–(4)

λ=PM=TM

ωMRVWIND

13ρπR2CPVWIND2

(2)(3)(4)

2ωMPM15

==ρπRCP3.ωM2λ

Themechanicaltorqueobtainedfrom(4)entersintotheinput

torquetothewindgenerator,andisdrivingthegenerator.CPmaybeexpressedasafunctionofthetipspeedratio(TSR)λgivenby(5),[7]

π(λ 2)

0.00184(λ 2)β

13 0.3β

(5)

whereβisthebladepitchangle.Fora xedpitchtype,thevalueofβissettoaconstantvalue.TheTableIshowsparametersenteredfortheuser-de nedwindturbinemodel.CP=(0.44 0.0167β)sinC.Direct-DriveGenerator

Thecost,weightandmaintenanceneedsofmechanicalgear-ingplaceaseriouslimitationonfurtherincreaseofpowerratings.Direct-coupled,low-speedgeneratorsareunderdevel-opmentinresponsetotheseneedsandsomearealreadyinservice[8].Unlikecommonsynchronousgenerators,thedirectdrivegeneratorscoveramuchlowerspeedrangeatabout20to60rpmandhaveamuchhighernumberofpoles,e.g.,50upto300.Theyarenotreadilyavailableandhavetobecustommade.Adirect-coupledgenerator,excitedusingarotorwinding,maybedescribedbyasynchronousmachinetheorysinceitisidenticaltoasynchronousgeneratorinbasicstructureand

A.WindModel

Awindmodelselectedforthisstudyisafour-componentmodel[5],andcanbedescribedby

VWIND=VBASE+VGUST+VRAMP+VNOISE

whereVBASE=VGUST=VRAMP=VNOISE=

basecomponent[m/s];

gustwindcomponent[m/s];rampwindcomponent[m/s];noisewindcomponent[m/s].

(1)

Thebasecomponentisaconstantspeed.Thewindgustcom-ponentmaybeexpressedasasineorcosinewavefunction[6]andacombinationofdifferentcosinefunctionshasbeenused.Therampwindcomponentcanberepresentedbythebuilt-inrampfunctionoftheprogram.Thenoisecomponentofwindspeedhasbeende nedbyatrianglewavefunction,ofwhichfrequencyandmagnitudeareadjustable.Basedontheabovefourcomponents,awindspeedmodelisconstructedbyas-

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TABLEII

BASICDATAFORTHEDIRECT-DRIVEGENERA

TORTABLEIII

DATAFORSHAFTSYSTEMM

ODEL

Fig.3.GraphicalmodelofshaftdynamicsinPSCAD/EMTDC.

Fig.4.

Recti erandVSIcircuitforVSWTmodeling.

operationexceptforitshighernumberofpolesandlowspeed.PSCAD/EMTDCprovidesafullydevelopedsynchronousma-chinemodel,basedonthegeneralizedmachinetheory[2].Withthismodel,bothsub-transientandtransientbehaviorcanbeex-amined.ItisconsideredthatthegeneratorisequippedwithanexciteridenticaltoIEEEtype1model[9].Theexciterplaysaroleofhelpingthedclinktomeettheadequatelevelofinverteroutputvoltageasgivenin(6)below

√

2·VACRMS

(6)Vdc≥

DMAX

whereVACRMSisRMSlinetoneutralvoltageoftheinverterandDMAXismaximumdutycycle.

Ingearlesstypevariable-speedoperation,electricalspeedofthewindgeneratorisnotconsistentwiththesynchronousspeedoftheelectricnetworkandgenerallymuchslowerthanthesyn-chronousspeed.Theelectricalbasefrequencyofthemachinemustbesetequaltotheratedspeedofthewindturbine.ThebaseangularfrequencyωBmaybeobtainedfrom(7)and(8).Basicparametersusedforthedirect-drivegeneratormodelaregiveninTableII[10].Manyotherinputparametersregardinginherentcharacteristicsofamachine,e.g.,damping,leakage,saturation,havebeenlefttodefaultvaluesprovidedinPSCAD/EMTDC[2]

fB=

NPRPMTUR

·260

RPMTUR

.60

(7)(8)

TableIIIshowsdatausedfortheshaftdynamicsmodeloftheVSWT.

E.PowerElectronicsControl

Severaltypesofpowerelectronicsinterfaceshavebeeninves-tigatedforvariablespeedwindturbines[4],[12].Thissectionaddressesapowerconversionsystemcomposedofasix-dioderecti erandasix-IGBTvoltagesourceinverter,whichissim-ple,cost-effectiveandwidelyusedforindustrialapplications.TheVSIincludesaLCharmonic lteratitsterminaltoreduceharmonicsitgenerates.Fig.4presentsarecti erandVSImodelofthestudiedVSWT.Therecti erconvertsacpowergeneratedbythewindgeneratorintodcpowerinanuncontrollableway;therefore,powercontrolhastobeimplementedbytheVSI.Acurrent-controlledVSIcantransferthedesiredrealandreac-tivepowerbygeneratinganaccurrentwithadesiredreferencewaveform[12].

TheentireVSIcontrolschemeispresentedinFig.5.Maincontroltargetsarethedesiredrealandreactivepower,PrefandQreftobefollowedbyactualrealandreactivepower,PinvandQinv.Thedesiredvaluesarespeci edaccordingtopowercontrolstrategyoftheVSWT.Thestrategyistocapturethemaximumenergyfromvaryingwindspeedwhilemaintainingreactivepowergenerationforconstantpowerfactororvoltageregulation.Detailsontherealandreactivepowertargetsspeci -cationaccordingtothestrategywillbeaddressedinthefollow-ingSectionII-FandG.Oncethetargetvaluesaredetermined,d–qtransformationcontrolisappliedtoenablerealandreac-tivecomponentofacoutputpowertobeseparatelycontrolled.Thebasicconceptofd–qcontrolareasfollows:variablesinthea–b–ccoordinatemaybetransformedintothoseinthed–qcoordinaterotatingatsynchronousspeedbytherotationald–qtransformationmatrixT(θ)[13].1/2

T(θ)=2/3 cosθ

sinθ

1/2

cos(θ 2π/3)sin(θ 2π/3)

1/2

cos(θ+2π/3) (9)sin(θ+2π/3)

ωB=2πfB=π·NP·

D.ShaftDynamics

Whilethewindturbineandthegeneratorarerotatingviathesameshaft,torsionaloscillationmayresultbetweentwopredominantmassesmutuallycoupledwiththeshaftof nitestiffness.Inordertoseetorsionalcharacteristicsoftheturbine-generator,theshaftsystemdynamicsmustbeconsidered.Theshaftdynamicscanberepresentedbythemultimasstorsionalshaftmodel,whichisbasedonthewell-knownshaftsystemmodelandequations[11].GraphicalmodelofmultimassshaftdynamicsisshowninFig.3.ThemultimassmodelcanbeeasilyinterfacedwiththesynchronousmachinemodelinPSCAD.

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Fig.5.CurrentcontrolschemeofVSI.

where

[υ0υdυq]T=T(θ)[υaυbυc]T;

variablesontheo-d-qframe;υ0,υd,υq=

variablesonthea-b-cframe;υa,υb,υc=

θ=phaseangleofυainradian.

Inabalancedthreephasesystem,theinstantaneousactiveandreactivepower,PandQ,aredescribedby(10)

P=

3

(VdId+VqIq),2

Q=

3

(VdIq VqId).2

(10)

Here,VqisidenticaltothemagnitudeoftheinstantaneousvoltageattheVSWTterminalandVdiszerointherotatingd–qcoordinate,sothe(10)maybecontractedintoasimpler(11)

P=

3

|VO|Iq,2

3

Q= |VO|Id

2

(11)

Fig.6.

CurrentcontrolschemeimplementedinPSCAD/EMTDC.

where|VO|istheinstantaneousVSWTvoltagemagnitude.Sincethevoltagemagnituderemainsalmostasconstantasgridacvoltage,therealandreactivepowercanbecon-trolledbyregulatingtheq-andd-axiscurrent,IqandId,respectively.

Throughappropriateproportional-integral(PI)controlgains,errorsbetweenPrefandPinvandbetweenQrefandQinv(orbetweenVrefandVrmsdependingonreactivepowercontrolmode)inFig.5areprocessedintotheq-andd-axisreferencecurrentIqrefandId,respectively,whicharetransformedintothea-,b-andc-axisreferencecurrentIaref,IbrefandIcrefbythedqtoabctransformationblock.Thephase-lock-loop(PLL)blockgeneratesasignalsynchronizedinphasetotheinverteroutputvoltageVatoprovidethereferencephaseangleθreffortherotationalinversed–qtransformationT(θ) 1.Whenthedesiredcurrentsonthea-b-cframeareset,apulsewidthmodulation(PWM)techniqueisappliedbecauseofitssimplicityandexcellentperformance.InthePWMgeneratorblock,thedesiredcurrentvectorIabcrefandtheactualcurrentvectorIabcoftheVSWTarecompared.Theerrorsignal

vec-

torIerriscomparedwithatrianglewaveformvectortocre-ateswitchingsignalsforthesixIGBTsoftheVSI.Theupperandlowerlimitsoftheq-axisreferencecurrentIqupperandIqareusuallysetat1.1to1.5timestheVSI’sratedcur-renttoprotectthesystemfromexcessiveheating.Thed-axisreferencecurrentlimitsIdupperandIdlowermaybespeci- edbasedon(11)andreactivepowercapabilitylimitsoftheinverter,(15).

Fig.6showstheVSIcontrolschemeimplementedinPSCAD/EMTDC.ThePref&Qrefgeneratorblock,auser-de nedcomponent,speci estargetvaluesfortherealandreac-tivepoweroftheVSWTaccordingtoitscontrolstrategy.

Thebuilt-ininterpolated ringpulsescomponentreturnsthe ringpulseandtheinterpolationtimerequiredforaninterpo-latedturn-onandturn-offofsixIGBTs(S1–S6)intheformof

KIMANDKIM:PSCAD/EMTDCBASEDMODELINGANDANALYSISOFAGEARLESSVARIABLESPEEDWINDTURBINE425

TABLEIV

PARAMETERSUSEDINPICONTROLB

LOCKS

reactivepowerQrefmaybespeci edby(14).

Qref=Pref·

1 PF.

PF

(14)

Fig.7.Powerversusturbinespeedcurve.

Involtageregulationmode,reactivepowercompensationiscontrolledinsuchamannerthatthevoltagemagnitudeoftheVSWTterminaliskeptconstantataspeci edlevel.Therefore,thetargetforreactivecontrolisthedesiredvoltagemagnitudeVref.Itmustbesetasthenominalvoltageoftheacgrid,wherepossibleadditionoftheVSWTisconsidered.

Whetherthemodecontrolspowerfactororvoltage,thereac-tivepowergenerationislimitedbyreactivepowercapabilityoftheVSWT.Thelimitsofreactivecapabilityaredeterminedbyratingoftheinverterandmayberepresentedby(15).

Qlimits

2 P2.=±Sinvinv

(15)

atwo-elementarray.Theoutputofthecomponent,on-offstatus

andtimeoftheIGBTs,isbasedonacomparisonofcurrenter-rorsandtrianglecarriersignalswhichenterintothecomponentintheformoffoursix-elementarrays(HLHOFFandLTableIVpresentsparametersusedinthePIcontrolblocksinFig.6.Theq-axisreferencecurrentlimitshavebeensetat1.2timesthemaximumloadcurrent.F.VariableSpeedControl

Belowratedwindspeeds,therealpoweroftheVSWTisregulatedtocapturethemaximumwindenergyfromvaryingwindspeed.Themaximumpoweravailablecanbedescribedby(12)anditmaybedepictedbyFig.7.Thissimplymeansthatthemaximumpowerisobtainedbyvaryingtheturbinespeedwithwindspeedsuchthatitisonthetrackofthemaximumpower

MAX

[1],[14]atalltimes.OnereliablewayofcapturingcurvePM

themaximumpoweristospecifythedesiredrealpowerPrefoftheinverterastheavailablemaximumpowermultipliedbythesystemef ciencyηasgivenin(13)

MAXPM

MAX

15CP3=πρRωM

2λOPT

MAXηPM.

III.SIMULATIONSTUDY

Usingtheproposedmodel,comprehensivesimulationstudy

wascarriedouttoobservethedynamicbehaviorsofaVSWTwithvaryingwindconditionsanditsresponsetonetworkfaultconditions.Fig.8presentstheVSWTsystemimplementedinPSCAD/EMTDC.Thewindturbineof1MWratinghasbeenconnectedtodistributionfeedersthrougha0.69/22.9kVtrans-former.Theratingoftheinverteris1.2MVAanditsPWMswitchingfrequencyis3.6kHz.Theshortcircuitcapacityofthe22.9kVbusis68.4MVA.TheX/Rratioofthebusimpedanceis52.Bothtypesofreactivepowercompensation,constantpowerfactorandvoltageregulation,aresimulatedtocomparetheirimpactsontheVSWTloadvoltage.Thesetvalueisunityinpowerfactormode,andthedesiredvoltageissetto1.005puinvoltageregulation.

A.PerformanceTestsUnderVaryingWindSpeed

TheVSWTisinunitypowerfactoroperationunderthewindspeedconditionpresentsinFig.9.Fig.10presentstheturbineangularspeedvariationinresponsetothevaryingwindspeed.Therotorspeedhasvariedsmoothlyinresponsetochangesinwindspeed,owingtotheinertiaoftheturbineandgenerator.Thepowercoef cientinFig.11wasmaintainedatthemax-imumvalueof0.44,whichindicatesthattheturbinespeediswellcontrolledtocapturethemaximumenergy.Fig.12(a)and(b)presentstheaerodynamictorquecreatedbythewindtur-bine,theelectricaltorqueproducedbythegeneratorandthemechanicaltorqueexertedonthedirectdriveshaft.Thetor-sionaloscillationsoftheshafttorqueinFig.12(b)resultfromtheinteractionbetweentheaerodynamicinputtorqueandelec-tricaloutputtorque.Fig.13presentstheaerodynamicpowerofthewindbladeandtherealandreactivepoweroftheVSWTatunitypowerfactor.Theaerodynamicpowerhas uctuateddirectlywithwindspeedchange,whereastherealpowerhasvariedsmoothly.Thisispossibleduetotheinertiasmoothing

(12)(13)

Pref=

Aboveratedwindspeeds,themaximumpowercontrolisoverriddenbystallregulationforconstantpower.Inthisstudy,thewindbladeisassumedtobeideallystallregulatedatratedpowersothatrotorspeedkeepsconstantatratedspeedunderhighwindspeeds.Thedynamicbehaviorofstallregulation,however,hasnotbeenconsideredinthework.Moredetailedstudyonactualstallcontroldynamicswillproceedinafuturework.

G.ReactivePowerControl

Variouscontrolmodescanbeusedfordeterminingtheamountofnecessaryreactivepowergeneration.Possiblecon-trolmodesincludepowerfactor,kvar,currentandvoltage.Inthestudy,constantpowerfactorandvoltageregulationhavebeenimplemented.Inconstantpowerfactormode,thedesired

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Fig.8.VSWTimplementedin

PSACD/EMTDC.

Fig.9.Wind

speed.Fig.11.Powercoef cientCP

.

Fig.10.Windturbinespeed.

effectandVSIinterfacecontrol.TheVSWTloadvoltagevaria-tionisgiveninFig.14andthevoltagemagnitude uctuatedwithwindspeed.Fig.15showsthedclinkvoltageanditwasmain-tainedatalevelsuf cienttomeettheacconversionrequirement.Fig.16showsthereferencecurrentandtheactualcurrent.Thevoltagewaveformsattheprimarybusbar(0.69kVside)oftheVSWTtransformerarepresentedinFig.17.Thevoltagewave-formsandharmonicspectraattheinverterandVSWTterminalareshowninFig.18(a)and(b).TheharmonicdistortionswerereducedtoasatisfactorylevelforgridconnectionthroughtheLCharmonic lter.

Inordertoseethesystemperformanceindifferentreactivecontrolmodes,about600kVarofreactiveloadwasaddedatthesecondbusbar(22.9kVside)ofthetransformer.Fig.19and20presenttheresultsofconstantpowerfactorandvoltageregula-tionoperation,respectively.Asadditionalloadwasadded,theterminalbusvoltagemadeasuddendropinFig.19(a).Itis

be-

Fig.12.TorquesofVSWT.(a)Aerodynamictorqueandelectricaltorque,(b)Mechanicaltorqueondirectdriveshaft.

causetheVSWTinunitypowerfactoroperationdidnotproducereactivegenerationandtheaddedloadwasservedbythepowernetwork,asshowninFig.19(b).However,theVSWTinconstantvoltageoperationsharedtheaddedreactivedemandbysupply-ingabout300kVartothepowergridandmaintainedtheloadvoltageataspeci edlevel,asshowninFig.20(a)and(b).

KIMANDKIM:PSCAD/EMTDCBASEDMODELINGANDANALYSISOFAGEARLESSVARIABLESPEEDWINDTURBINE

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Fig.13.Aerodynamicpowerofwindandrealandreactivepowerof

VSWT.

Fig.18.Voltageharmonics.(a)VoltagewaveformsatinverterandWTtermi-nal,(b)Harmonic

spectra.

Fig.14.Terminalbus

voltage.

Fig.15.DClink

voltage.

Fig.19.Caseofpowerfactorcontroloperation.(a)Terminalvoltagemagni-tude,(b)ReactivegenerationofVSWTandreactiveinjectionintogrid.

B.DynamicResponsetoSystemFaultConditions

Fig.16.

Referencecurrentandactual

current.

Fig.17.VoltagewaveformsatprimarybusbarofVSWT

transformer.

Generally,themostcommontypeofnetworkfaultisasinglelinetogroundfaultandthemostseveretypeisathree-phaseshortcircuitfault.FaulttestswerecarriedouttoexaminetheVSWT’sresponseinpower,torqueandrotorspeedunderbothtypesofnetworkfaultconditions.Faultswereappliedonthe22.9kVfeeder(Fig.21)during0.16[sec].Incaseofnetworkfaults,thedistributedgenerationshouldceasetoenergizetheareaelectricpowersystemwithinatleast0.16[sec]afterthestartoftheabnormalconditioninaccordancewithIEEEP1547[15].ItwasassumedthattheVSWToperatesatfullloadingundertheratedwindspeed.

1)SingleLinetoGroundFault:Fig.22(a),(b),and(c)presentthevoltageandcurrentofthefaultedlineandrealand

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Fig.20.Caseofvoltageregulationoperation.(a)Terminalvoltagemagnitude.(b)ReactivegenerationofVSWTandreactiveinjectioninto

grid.

Fig.21.Faultonthe22.9kVfeederwith

VSWT.

Fig.23.Systemresponsetoasinglephasefaultinturbinespeedandtorques.(a)Windturbinespeed.(b)Aerodynamictorqueandelectricaltorque.(c)Me-chanicaltorque.

Fig.22.Systemresponsetoasinglephasefaultinvoltage,currentandpower.(a)Voltagewaveformofthefaultedphase.(b)Referenceandactualcurrentwaveformsofthefaultedphase.(c)Realandreactivepower uctuationsofthe

VSWT.

reactivepoweroftheVSWT.ThefaultcurrentinjectioninFig.22(b)didnotexceedthe1.2timesthemaximumloadcurrentvalue,i.e.,0.82[kA],sincetheactualcurrentoftheinverterisforcedtofollowthereferencecurrentwaveformwithitsmag-nitudelimitedbytheq-axisreferencecurrentlimits(refertoTableI).Fig.23presentsthesystemresponseinturbinespeedandtorques.Attheinstantoffault,therewereminor uctua-tionsintheturbinespeedandtorquesoftheVSWTbuttheydiedawayaftertheclearanceoffault.

2)ThreePhaseShort-CircuitFault:Thevoltageandcurrentwaveformsandtherealandreactivepower uctuationsoftheVSWTaregiveninFig.24.Thefaultcurrentwaslimitedtothe1.2timestheratedcurrentvaluebythereferencelimitsoftheinverter.Fig.25showsthesystemresponseintheturbinespeedandtorques.Duetogreatinertiaofthemulti-polegener-ator,theturbinespeedreturnedtothenormalspeed(thelevelbeforefault)severalseconds,i.e.,6secondsinthiscase,aftertheclearanceofthefault(Fig.25(a)).Asthefaultoccurred,theturbinespeedslowlyroseandwentofftheoptimalspeedforthemaximumpowercapture,andtheaerodynamictorquedecreased(Fig.25(b)).Afterthefaultwasremoved,theaerody-namictorquestartedincreasingwiththedecreasingrotorspeedinFig.25(a).Unliketheturbinetorque,adrasticchangecanbeseenintheelectricaltorque.Responsetimedifferencebetweentherapidelectricalresponseofthegeneratorandslowaerody-namicresponseoftheturbineresultedinthemechanicaltorquevariationasshowninFig.25(c).

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IV.CONCLUSION

AdynamicmodelofagearlessVSWTwithpowerelectronicinterfacewasproposedforcomputersimulationstudyandwasimplementedinareliablepowersystemtransientanalysispro-gram,PSCAD/EMTDC.TheVSWTcomponentmodelsandcontrolschemewerebuiltbyusinguser-de nedandbuilt-incomponentsprovidedinthesoftware.Dynamicresponsesofthewindturbinetovaryingwindspeedanddifferentreactivecontrolschemesweresimulatedandanalyzedbasedonthemod-eledsystem.Faulttestswerecarriedouttostudythedynamicbehaviorsofpower,torqueandrotorspeedofaVSWTunderabnormalconditions.

Inelectricutilities’perspective,gridinterfaceofintermittentgenerationsourcessuchaswindturbineshasbeenachallengebecausesuchinterfacemaylowerpowerqualityofpowersys-tems.Therefore,comprehensiveimpactstudiesarenecessarybeforeaddingwindturbinestorealnetworks.Inaddition,usersorsystemdesignerswhointendtoinstallordesignwindturbinesinnetworksmustensurethattheirsystemshavewellperformedwhilemeetingtherequirementsforgridinterface.Theworkil-lustratedinthisstudymayprovideareliabletoolforevaluatingtheperformanceofagearlessVSWTanditsimpactsonpowernetworksintermsofdynamicbehaviors;therefore,serveasapreliminaryanalysisforactualapplications.

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Fig.25.Systemresponsetoathree-phasefaultinturbinespeedandtorques.(a)Windturbinespeed.(b)Aerodynamictorqueandelectricaltorque.(c)Mechanicaltorqueonshaft.

430IEEETRANSACTIONSONENERGYCONVERSION,VOL.22,NO.2,JUNE

2007

Seul-KiKimreceivedtheB.S.andM.S.degreesinelectricalengineeringfromKoreaUniversity,Korea,in1998and2000,respectively.

HehasbeenaSeniorResearcherinthepowersystemresearchgroupofKoreaElectrotechnologyResearchInstitute(KERI),Kyongnam,Korea.Hisareaofinterestismodelingandanalysisofdistributedgenerationsforgridinterface

analysis.

Eung-SangKimreceivedtheB.S.degreeinelec-tricalengineeringfromSeoulNationalUniversityofTechnology,Seoul,Korea,andtheM.S.andPh.D.degreesinelectricalengineeringfromSoongsilUniversity,Seoul,Korea.Currently,heisaPrinci-palResearcherinthepowersystemresearchgroupoftheKoreaElectrotechnologyResearchInstitute,Kyongnam,Korea.Hisareaofinterestispowerqual-ity,integrationandgrid-connectionofdistributedgeneration.