Citation
Modeling and control of a grid-connected small-scale windmill system using a pulse width modulated modular multilevel converter /

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Title:
Modeling and control of a grid-connected small-scale windmill system using a pulse width modulated modular multilevel converter /
Creator:
Canak, Ersin ( author )
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
1 electronic file (65 pages). : ;

Subjects

Subjects / Keywords:
Pulse-duration modulation ( lcsh )
Electric current converters ( lcsh )
Modulators (Electronics) ( lcsh )
Power electronics ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
Abstract-Topologies based on the modular multilevel converter (MMC) represent an attractive alternative against traditional two-level voltage source converter as the interphase between renewables and the ac grid. MMCs feature lower losses, improved voltage quality, scalability and redundancy. In this paper, a pulse width modulated MMC-based topology is proposed for the grid-interconnection of a small-scale wind energy conversion system (WECS). The WECS is realized through the cascaded connection of a wind turbine, a permanent magnet synchronous generator (PMSG), two back-to-back MMCs interphased through a dc-link capacitor, an LC-filter, and a coupling transformer. Mathematical modeling of the various components is developed throughout the paper, along with a control strategy able to perform both maximum power point tracking and arbitrary reactive power injection. The approach is validated via detailed PSCAD/EMTDC computer simulations using real wind speed.
Thesis:
Thesis (M.S.)--University of Colorado Denver. Electrical engineering
Bibliography:
Includes bibliographic references.
General Note:
Department of Electrical Engineering
Statement of Responsibility:
by Ersin Canak.

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University of Colorado Denver
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|Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
904408274 ( OCLC )
ocn904408274

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MODELINGANDCONTROLOFAGRID{CONNECTEDSMALL{SCALE WINDMILLSYSTEMUSINGAPULSEWIDTHMODULATEDMODULAR MULTILEVELCONVERTER by ERSINCANAK BachelorofScience,IstanbulTechnicalUniversity,2011 Athesissubmittedtothe FacultyoftheGraduateSchoolofthe UniversityofColoradoinpartialfulllment oftherequirementsforthedegreeof MasterofScience ElectricalEngineering 2014

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c r 2014 ERSINCANAK ALLRIGHTSRESERVED

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ThisthesisfortheMasterofSciencedegreeby ErsinCanak hasbeenapprovedforthe DepartmentofElectricalEngineering by FernandoMancilla{David,Chair TitsaPapantoni DanConnors November21,2014 iii

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Canak,Ersin(M.S.,ElectricalEngineering)ModelingandControlofaGrid{ConnectedSmall{ScaleWindmillSystem usinga PulseWidthModulatedModularMultilevelConverterThesisdirectedbyAssociateProfessorFernandoMancilla{David ABSTRACT Topologiesbasedonthemodularmultilevelconverter(MMC)repres entanattractivealternativeagainsttraditionaltwo{levelvoltagesource converter(VSC),as theinterphasebetweenrenewableenergysourcesandtheacgrid .InMMCtopologies,totalsystemlossesarerelativelylow;thustheeciencyiscon sequentlyhigher ascomparedtoexistingtwo{levelVSCs.Inthisthesis,apulsewidth modulated MMC{basedback{to{backtopologywithareducednumberoflevels isproposedfor thegrid{interconnectionofasmall{scalewindenergyconversionsy stem(SS{WECS). TheSS{WECSisrealizedthroughthecascadedconnectionofawindt urbine,apermanentmagnetsynchronousgenerator(PMSG),twoback{to{b ackconnectedMMCs interphasedthroughadc{linkcapacitor,aLC{lterandacouplingt ransformer. Mathematicalmodelingofthevariouscomponentsisdevelopedthro ughoutthethesis,alongwithacontrolstrategyabletoperformbothmaximumpow erpointtracking andarbitraryreactivepowerinjection.Apulsewidthmodulation(PW M)technique isimplementedinreducedlevelMMCs,toinjectpowerintothegridwith alowharmoniccontent.ThisallowssizereductionoftheLC{lter.Theappro achisvalidated viadetailedPSCAD/EMTDCcomputersimulationsusingrealwindspeed data. Theformandcontentofthisabstractareapproved.Irecommen ditspublication. Approved:FernandoMancilla{David iv

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ACKNOWLEDGMENT Foremost,Iwouldliketoexpressmydeepestgratitudetomyadviso r,Dr.FernandoMancilla{David,forhisguidance,valuableadviceandsupportd uringthewhole periodofthestudy. Igreatlythankandacknowledgetheinvaluablesupportsandguidan ceofTurkish PetroleumCorporation. IexpressmygratitudetomyfriendsMiguelCarrascoandCarlosSo rianofortheir adviceandhelponmyresearch. IgreatlyappreciateDr.TitsaPapantoniandDr.DanConnorsfor formingmy dissertationdefensecommittee,theirvaluablediscussions. Finally,andmostimportantly,Iwouldliketothankmyfamily;theywere always therecheeringmeupandstoodbymethroughthegoodandbadtime s. v

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DEDICATION Thisthesisisdedicatedtomyfamilywhohavesupportedmealltheway since thebeginningofmystudies.Theyprovidemewithagreatsourceofm otivationand inspiration.Finally,thisthesisisdedicatedtoallthosewhobelieveinth atknowledge ispower. vi

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TABLEOFCONTENTS Chapter 1.Introduction...................................12.SystemModelling................................5 2.1WindTurbine..............................52.2PermanentMagnetSynchronousGenerator.............. 6 2.3ModularMultilevelConverter.....................102.4LC{Filter.................................14 3.ControlScheme.................................15 3.1VSRTwo{Layercontroller.......................15 3.1.1SynchronizationBlock......................163.1.2SpeedControl..........................163.1.3Torque{to{CurrentTransformation...............173.1.4CurrentControl.........................17 3.2VSITwo{LayerController.......................19 3.2.1Phase{Locked{Loop.......................203.2.2Dc{linkVoltageControl.....................203.2.3Power{to{CurrentTransformation...............203.2.4CurrentControl.........................21 3.3LegEnergyController..........................23 3.3.1TotalLegEnergyControl....................233.3.2ArmEnergyDierenceControl.................23 3.4Modulator................................24 3.4.1PhaseDisposed{PulseWidthModulation...........253.4.2VoltageBalancingAlgorithm..................26 4.DesignGuidelines................................29 4.1PowerStage...............................29 vii

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4.2Controllers................................30 4.2.1CurrentControl.........................314.2.2SpeedControl..........................314.2.3Dc{linkVoltageControl.....................32 5.Simulation....................................35 5.1SimulationData.............................355.2SimulationResults............................36 6.Conclusions...................................467.Contributions..................................478.FutureWork...................................48References ......................................49 Appendix A.ParkTransformation..............................53 viii

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LISTOFTABLES Table 4.1SS{WECSparameters............................304.2Controllerparameters............................31 ix

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LISTOFFIGURES Figure 2.1CircuitschematicoftheconsideredSS{WECS.................7 2.2Powercoecientforatypicalsmall{scalewindmill...............8 2.3Cross{sectionalviewofafourpolePMSG...................8 2.4Schematicofasub{module...........................10 2.5SwitchingstatesofaSM............................11 2.6IllustrationofvoltagesynthesisthroughMMCs.................12 3.1Overviewofthecontrolsystem.........................15 3.2SchematicoftheVSRtwo{layercontrollershowingasynchro nizationblock, speedcontrol,torque{to{currenttransformation,andcur rentcontrol......16 3.3Closed{loopd{andq{axiscurrentcontrollersforVSRtwo{l ayercontroller..19 3.4SchematicoftheVSItwo{layercontrollershowingaPLL,dc{ linkvoltagecontrol,power{to{currenttransformation,andcurrentcontr ol...........19 3.5Closed{loopd{andq{axiscurrentcontrollersforVSItwo{l ayercontroller...22 3.6Schematicofthetotallegenergycontrol....................23 3.7Schematicofthearmenergydierencecontrol.................24 3.8Schematicofthelegenergycontrollerandmodulator..............25 3.9PD{PWMmodulationschemefora7levelMMC................26 3.10Flowchartofthevoltagebalancingalgorithm..................27 4.1Frequencyresponseofthespeedcontrol....................32 4.2Blockdiagramofthedc-linkvoltagecontrolloop................33 4.3Frequencyresponseofthedc{linkvoltagecontrol................34 5.1Realwindspeeddatausedinthesimulations..................35 5.2Simulationresultshowingthetheoreticalactivepower( Ptheo),shaftpower ( Pm),generatedelectricalpower( PPMSG)andactivepowerinjectedtotheac grid( Pgrid)...................................36 x

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5.3Simulationresultshowingthereactivepowerinjectedtoth eacgrid( QGrid), andreactivepowerabsorbedbythePMSG( QPMSG)..............37 5.4Simulationresultshowingthetipspeedratio( )................37 5.5Simulationresultshowingthepowercoecient( Cp)..............38 5.6Simulationresultshowingtheshaftspeed( wm)andtheoptimumshaftspeed ( wm ref)......................................38 5.7Simulationresultshowingthedc{linkvoltage( Vdc)...............39 5.8SimulationresultshowingthemodulationindexoftheVSRtw o{layercontroller.39 5.9SimulationresultshowingthemodulationindexoftheVSItw o{layercontroller.40 5.10SimulationresultshowingthevoltageatPLLon dq frame...........40 5.11SimulationresultshowingthePMSG'sstatorcurrenton dq frame......41 5.12SimulationresultshowingtheVSIcurrenton dq frame............41 5.13Simulationresultshowingthetotallegenergyofthephase{ alegoftheVSI ( Winv total a).....................................42 5.14Simulationresultshowingthearmenergydierenceofthepha se{alegofthe VSI( Winv di a)...................................42 5.15SimulationresultshowingtheSMvoltagesofthephase{aoft heVSI( Vinv c uak)..43 5.16Simulationresultshowingphase{cvoltageatprimaryofthe couplingtransformer( vinv c)andattheterminalofMMCVSI( vc)...............44 5.17Simulationresultshowingharmonicspectrumofthevoltage atPLL......44 5.18Simulationresultshowingharmonicspectrumoftheinjecte dcurrent.....45 A.1Thestationaryabcreferenceframeandtherotatingdqrefer enceframe...53 xi

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1.Introduction Inrecentyears,small{scalegenerators|alsocalleddistributedge nerators(DGs)| areoneofhighinterestinthepowerindustry.Accordingto[1],DGs( i )increasethe eciencyofthesystembyavoidingpowertransmissionoverlongdist ances;( ii )reduceemissions,sincearemostlybasedonrenewablesourceslikewind andsolar;( iii ) improvesecurityofthepowersupplyduetocollectionofenergyfro mmanysources; and( iv )areconnectedtothedistributiongridwhichallowsactivepowerpar ticipation bycustomerstothegrid. AccordingtotheAmericanWindEnergyAssociation(AWEA),wind{ba sedDGs withapowerratinglessthan100kWareusuallyreferredasSS{WECS .In[2],itis statedthattheSS{WECS( i )iseasiertoconstructandnanceincomparisonwith mid{scaleandlarge{scalewindenergyconversionsystems;and( ii )requireslittleto nopermitting.However,theirpresenceinthegridisstillreduced|2 16MWinthe USpowergridattheendof2012|butitisincreasingatafastpace:3 5%ofallUS windinstallationsinthesameyearcorrespondtoSS{WECS. ManySS{WECSapplicationsarepresentedeitherintheliteratureor inthe industry.In[3,4],aSS{WECSisutilizedtochargeabatterybank.An otherimportantSS{WECSapplication,availableinthemarket,iswaterpumping,a ndgrinding grain[5].In[6,7],dynamicsofastandaloneSS{WECSmodelthatprov ideselectricitytoawaterpumpisexamined.Finally,in[8],aSS{WECSisusedtopr ovide electricitytoautilitygrid. Accordingto[9],aSS{WECSconsistofthefollowingcomponents:( i )awind turbinetoconvertpowerfromwindtomechanicalpower,( ii )anelectricalgenerator toconvertthemechanicalpowercreatedbywindturbinetoelectr icalpower,( iii ) apowerelectronicinterphasetotransmitelectricityintoanapplicat ion,and( iv )a controlunittoregulatethepowertransfer. 1

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Awindturbineisadevicethatconvertskineticenergyfromthewindin tomechanicalpower[9].Accordingto[5],windturbinesareavailableintwoma jorcongurations:Verticalaxiswindturbinesandhorizontalaxiswindtur bines(HAWT). Inthisthesis,themorecommonHAWTmodelisused,anditisoperate datvariable speed.In[9],thedynamicsofaHAWTareexaminedandreported. Theelectricalgenerator'sdutyistoconvertthemechanicalpowe rintoelectrical power.InaSS{WECS,twocommontypesofelectricalgenerators areusedwhichare theself{excitedinductiongenerator(SEIG)andthepermanentm agnetsynchronous generator(PMSG).Authorsof[10,11]statethat,forbothSEI GandPMSG,agearbox mightbeusedtoconvertthelow{speedofthewindturbineintohighs peedofthe generators.Accordingto[12,13],comparingwiththeSEIG,thePM SG( i )ismore ecient,( i )ismoresimpletoconstructandcontrol.Therefore,inthisthesisa PMSG isemployedasthegenerator. SS{WECSsareconnectedtoanapplicationviaapowerelectronicsint erphasethat istypicallybasedonVSCtopology.Themainroleofthisinterphaseisto convert thevariable{frequencypowerproducedbytheSS{WECSintoapplic ation{frequency power.However,itmayalsobeusedto( i )injectthepoweratanarbitrarypower factorintothegrid[14];and( ii )performthemaximumpowerpointtracking(MPPT) functiontoextractthemaximumavailablepowerfromtheSS{WECS[1 5].Themost commonpowerelectronicsinterphaseusedinSS{WECSistheback{t o{backtopology, inwhichtwoconvertersareconnectedthroughadc{linkcapacitor [11,16].According to[11],theback{to{backtopology( i )ecientlydecouplesthegeneratorfromgrid, ( ii )improvesfaultresponse,( iii )allowsthewindturbinetooperateawidespeed range,leadingimprovedpowerextractionfromthewind,and( iv )ismorecostlyand lossy,butalsooersindependentrealandreactivepowercontro l. TheMMCisamultilevelVSCtopologywhichwasoriginallyintroducedinto theliteratureby[17]forveryhighvoltageapplications,specicallyn etworkinterties 2

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inpowergeneration.In2011,thecompanySiemensrstintroduce danMMCbased HighVoltageDirectCurrent(HVDC)applicationtothemarketunder thecommercial nameofHVDCPlus[18].IntheMMCtopology,theconverteractsasc ontrollable voltagesourceswithahighnumberofpossiblediscretevoltagestep s.TheMMC concept( i )provideslowerlossescomparedtoatwo{levelequivalentVSC[19];( ii ) featuresanincreasedoutputvoltagequality,requiringsmallerorn oharmoniclters [20];( iii )providesscalabilitytovariousvoltageandpowerlevels[21];and( iv )reduces thevoltagestressonthesemiconductordevices[18]. TheMMCtopologyisbeingwidelyadoptedforHVDCandrexiblealternat ing currenttransmissionsystems(FACTS)[10,22,23].In[24],aMMC{b asedSTATCOMapplicationisinvestigatedinadistortedandunbalancedmedium{v oltagelarge{ currentsystem.Whilethistopologyhasbeenalreadyproposedfor theinterconnection ofwindpowerplantsinthemegawatt{scale[25,26],itsapplicationtot heinterconnectionofSS{WECSisstillbeingexplored.In[8],aninverterbasedon theMMC topologywasusedtoinjectthepowergeneratedbyasmall{scalewin dturbineatan arbitrarypowerfactorintoasingle{phaseacgrid.However,thee lectricalgenerator wasinterphasedthrougharectierwithoutperformingtheMPPTf unction. InSS{WECS,aMPPTcontrolshouldbeemployedinordertogetmaxim um powerfromthewindturbine.TheMPPTcontrolmethodscanbeclas siedintowith sensorsorwithoutsensors.Themethodswithoutsensorsarediv idedintoperturbationandobservation(P&O)andincrementalconductance(IC)me thods.In[27,28], anexperimentalset{upofaSS{WECSisusedtostudyeectivenes softheP&O method.ICmethodsareexaminedin[2,29]byusingcomputersimulat ions.The methodsusingsensorsachieveMPPTcontrolbyregulatingspeedo rtorqueofthe generator.In[14,16],asensorcontrolmethodisexaminedforbo thSEIGandPMSG. Asinthecaseofthetwo{levelVSCs,theMMCsprovideindependent control ofactiveandreactivepower.In[10,21],powercontrolapproach forMMC{based 3

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back{to{backtopologyispresented.InMMCtopology,theenerg yoftheMMChas tobecontrolledinordertoensureastableoperationoftheconver ter.Severalcontrol methodsareexplainedinliteraturetoovercomethisproblem.Oneap proachisso calledlegenergycontrolthatispresentedin[30].Anotherapproac hiscalledthe circulatingcurrentmanipulationwhichpresentedin[31,32]. InMMCtopology,thenearest{levelmodulation(NLM)techniquean dPWM techniquesarethemainmodulationmethods.Accordingto[19,23],t hemorecommonNLMtechniqueisusedforMMCswithhighnumberoflevelsandhighp ower applications.However,PWMtechniquesareusedforMMCswithredu cednumber oflevelsandlowpowerapplications.Inthisthesis,thephasedispose d{pulsewidth modulation(PD{PWM)techniqueisemployedinMMCs.In[33,34],thePD {PWM techniqueispresented,andchallengingtechnicalaspectsoftheP D{PWMtechnique isdiscussed. In[10],itisstatedthatavoltagebalancingalgorithmmustbeusedwith inmodulationprocessforstableoperationoftheMMC.Toachieveit,in[25, 35]avoltage balancingalgorithmmethodispresented. Thethesisisorganizedasfollows;Chapter2describesthemodellingo fthepower stage,followedbythedescriptionofthecontrolapproachinchap ter3.InChapter 4,designguidelinesoftheSS{WECSisexplained.InChapter5,thepo werstage andthecontrolschemesarearevalidatedviadetailedPSCAD/EMTD Ccomputer simulationsusingrealwindspeeddata.Theconcludingremarksofth ethesisare statedinChapter6.InChapter7,thecontributionsofthethesis arestated.Finally, thefutureworkopinionsoftheChapter8closethethesis. 4

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2.SystemModelling Thecircuitschematicofgure2.1illustratesthepowerstageofthe SS{WECS, andthepowerelectronicsinterphaseconsideredinthisthesis.Itin cludesawind turbineandthecascadedconnectionof:aPMSG;aMMCvoltage{so urcerectier (VSR);adc{linkrealizedthroughacapacitor;aMMCvoltage{sourc einverter(VSI); andaLC{lterinserieswithacouplingtransformerthatconnectst othethree{phase acgrid. IntheSS{WECS,aphase{locked{loop(PLL)isusedtosynchronize VSItothe acgridattheLC{lter'soutput.Ath e veninequivalentisusedtomodelthebehavior ofthethree{phaseacgridatthepointofcommoncoupling(PCC).2.1WindTurbine Inwindenergyconversionsystems,thedutyofthewindturbineist oconvert kineticenergyofthewindtomechanicalenergy.Themechanicalpo werprovidedby thewindturbineisgivenby[9]: P m =0 : 5 AC p ( ) V 3 w ; (2.1) where istheairdensity( kg=m 3 )(at15 Cand1atm, =1.225 kg=m 3 ),Aisthe areasweptbytheblades( m 2 ),and V w isthewindspeed( m=s ). Function C p ( )iscalledtheperformancecoecientorpowereciencyfunction ofthewindturbine. C p ( )isastatic,nonlinear,functionof anditissmallerthan 0.59(Betzlimit)[9].Thetip{speedratio, ,isdenedas = rw m V w ; (2.2) whereristhebladesradiusand w m istheshaftsrotationalspeed. Itcanbeobservedfrom(2.1)that P m iscomprisedoftwoterms.Therstterm is0 : 5 AV 3 w ,andthesecondtermis C p ( )whichisanonlinearfunctiondependson thegeometryofthewindturbine.Theprevioustermisproportiona lto V w .As V w 5

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cannotbecontrollable,thersttermcannotbecontrollable.Howe ver,itcanbe seenfromgure2.2, C p ( )isavariablequantitywhichcanbemanipulatedby Itcanbeobservedfromgure2.2thatwhen increases, C p ( )alsoincreases untilitreachesapeakvalueat = .Thereafter,afurtherincreasein resultsin adropin C p ( ).Thus,thewindturbinemustbeoperatedat inordertoextract themaximumpossiblepower.Thevalueof istypicallyknown.Assumingthat V w ismeasuredorestimated,theMPPTfunctionboilsdowntocontrolt heshaft'sspeed w m around w m ref ,computedas w m ref = V w r : (2.3) 2.2PermanentMagnetSynchronousGenerator ThePMSGisatypeofsynchronousgenerator(SG)wheretheexcit ationeld isprovidedbyapermanentmagnetinsteadofacoil.Asshowningure 2.3,the rotatingassemblyinthecenterofthePMSG(rotor)containsthep ermanentmagnets insteadofanexcitationsystemusedinregularSGs,andthearmatu rewindingsare woundedonthestatorthatiselectricallyconnectedtoaloadoragr id.Instator, thethree{phasewindingsaredistributedat120electricaldegree saparttogenerate threebalancedvoltagesattheterminalofthePMSG,andtocreat eanuniformforce ortorqueontherotor[36].InPMSG,eachrevolutionoftheshaft, therotorsweeps byeachofthethreestatorwindings,therebyinducingavoltageine achstatorthat is120 outofphasewiththeadjacentwindings. APMSG( i )provideslowerelectricallossesandhasbetterthermalcharact eristicsbecauseofhavingnoexcitationlosses;( ii )providessmallergeneratingunitsize duetohavingnorotorwindings;( iii )lackingrotorslipringsreducesmaintenance requirements[11,16].Onthecontrary,thePMSGhassomedisadva ntages:athigh temperaturethepermanentmagnetsontherotoraredemagnet ized,dicultiesto handleinmanufacture,andhighcostofpermanentmagnetmateria l[37]. 6

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L arm N Lf RfCf LsRs MMCVSRMMCVSI Irec ` aIrec uaIinv uaIinv ` aVdc ref VwwmVSRtwo{layercontroller Modulator s recijk V inv ua V rec ua V rec ` a V inv ` a Irec aIrec bIrec cCoupling transformer PCC PLL SM n SM 1 SM 1 SM n SM n SM 1 SM 1 SM 1 SM 1 SM 1 SM 1 SM 1 SM 1 SM 1 SM 1 SM n SM n SM n SM n SM n SM n SM n SM n SM n Irec d refIrec jLegenergycontroller Vrec cijkVdcIinv jvinv jModulator s invijk Qinvref Iinv aIinv bIinv cVSItwo{layercontroller Tm;wm V w Vinv cijk Legenergycontroller VdcN WindTurbine PMSG eabc LC{lter vinv avinv bvinv c Figure2.1:CircuitschematicoftheconsideredSS{WECS.7

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C p ( ) ¤ C ¤ p Figure2.2:Powercoecientforatypicalsmall{scalewindmill. a a b b c c Non{magneticmaterial Ironcore PermanentMagnet Stator Rotor Shaft Figure2.3:Cross{sectionalviewofafourpolePMSG.TheelectricalequationsthatdescribethebehaviorofthePMSGint herotor dq referenceframearegivenby[14]as: 264 d d 375 = 264 L d 0 0 L q 375 264 I d I q 375 + 264 m 0 375 ; (2.4) d dt 264 d q 375 = 264 0 w w 0 375 264 d q 375 + 264 R s 0 0 R s 375 264 I d I q 375 + 264 v d v q 375 ; (2.5) where d and q arethestator dq axisruxcomponents, I d I q v d ,and v q represent thestatorcurrentsandthestatorterminalvoltages, w istheelectricalfrequency,and 8

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theparameter m representstheruxgeneratedbytherotormagnetswhichlinked withstatorwindings, L d and L q arethed{axisandq{axisstatorinductancesthat dependonthemachinegeometryandrotorsaliency;inasurfacemo unted{PMSG L d = L q Thestandardstatespaceformofthe I d and I q canbederivedbyeliminating d and q between(2.4),(2.5).Theresultis L d I d = R s I d + wL q I q v d ; (2.6) L q I q = R s I q wL d I d w m + v q ; (2.7) Theelectricalfrequencyisrelatedtothemechanicalshaftspeed viathenumber ofpolepairs,p, w = p 2 w m : ThemechanicaldynamicsofthePMSGaredescribedby J w m = T m T e ; (2.8) where J istherotorinertia,and T m isthemechanicaltorqueappliedtowindmill shaftthatfollowsfrom(2.1)and(2.2)as T m = P m w m = 1 2 Ar C p ( ) V 2 w ; and T e istheelectricaltorque,givenby T e = 3 2 p 2 m I q : (2.9) 2.3ModularMultilevelConverter 9

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ThecircuitdiagramoftheMMCsactingasrectierandinverterares hownin gure2.1.AMMCisbasedonamulti{levelvoltage{sourcetopology.S ub{module (SM)isthebasiccomponentoftheMMC.Dependingonthelevelofth eMMC,more than300SMsmaybeusedinaconverter[18].ThecircuitschemeofaS Misshown ingure2.4. C SM S1 S2 D1D2 Figure2.4:Schematicofasub{module.ASMiscomposedofhalfbridgeconnectedtwoIGBTswitchesandaloc aldc{ storagecapacitor( C SM ).Asshowningure2.5,theswitchingoperationofaSMcan beexpressedbytwostates: SMSwitched{On| S 1 isswitchedon, S 2 isswitchedo Inthisoperation,thevoltageofthe C SM isappliedtotheterminalsofthe SM,disregardingonthecurrentrowdirection.Dependingonthedir ection ofcurrent,thecurrenteitherrowsthroughtheD1andcharges the C SM ,or throughtheS1andtherebydischargesthe C SM SMSwitched{O| S 1 isswitchedo, S 2 isswitchedon Inthiscase,the C SM voltageremainsunchanged.Also,thecurrenteitherrows throughtheS2ortheD2dependingonitsdirectionwhichensuresth atzero voltageisappliedtotheterminalsoftheSM. Inathree{phaseMMC,therearethreelegs,oneforeachphase. Aconverterleg ismadeupofanupperandalowerarm.Theseriesconnectionofanum berofSMs 10

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SMSWITCHEDON SMSWITCHEDOFF D1D2D1D2 D1D2D1D2 S1S2S1S2 S1S2 S1S2 Figure2.5:SwitchingstatesofaSM.makesupanarm.Thenumberofthevoltagelevelsdependsonthenu mberofSMs availableineacharm.Thereisalsoaninductorineacharm, L arm ,inordertosmooth thevoltagedierencethatisproducedwhenaSMisconnectedordis connected[23]. Thegeneralconceptofmultilevelconvertersisthesynthesisofa sinusoidalvoltage byseverallevelsofvoltages.InthecaseoftheMMC,thesevoltag elevelsareobtained fromthe C SM ofeachSM.Atanyinstant,anumberofSMsareswitchedon,sotha t thevoltageattheconverterterminalsequalstheinstantaneousv alueofthevoltageto besynthesized[20].Figure2.6showsanexampleofNLMmodulatedMMC realized through8SMsperarm,witheachSMfeaturingavoltage V c .Thegureshows voltagewaveformsforthreedierentlevelsofoutputvoltage.It maybeobserved thatasthepeakvalueoftherequiredacvoltageincreases,sodoe sthenumberof voltagelevels,henceimprovingthewaveformquality.Inpractice,t henumberofSMs willbemuchlargerthan8(200-300SMs)andthereforeeventhewo rst-casescenario willstillfeatureaveryhighqualitywaveform. 11

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Vct t t 2VcVcVc4Vc Figure2.6:IllustrationofvoltagesynthesisthroughMMCs.ThearmvoltagecanbecomputedconsideringthestatusoftheSM's switches, s ijk ,asfollows[10]: V ij = n X k =1 s ijk V c ijk ; where i = u;` representstheupperandlowerarm,respectively; j = a;b;c isthe phase;and k =1 ; 2 ;:::;n denotestheSM.Thearmcurrentscanbedeterminedas I uj = I j 2 + I dc 3 + I circ j ; I ` j = I j 2 + I dc 3 + I circ j ; where I circ j isthecirculatingcurrentforphase j ,and I circ a + I circ b + I circ c =0.These circulatingcurrentshavenoeectontheacsideordcsidevoltages .Ontheother hand,theyhavesignicantimpactonSM'scapacitorvoltagesandth eratingvalues oftheMMCcomponents[10].Finally,theacsideanddcsidevoltagesof theMMC arecomputedas 12

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V j = V dc 2 V uj L arm dI uj dt R arm I uj = V dc 2 + V ` j L arm dI ` j dt R arm I ` j ; V dc = V uj + V ` j + L arm dI uj dt + dI ` j dt + R arm ( I uj + I ` j ) ; where R arm istheequivalentresistanceoftheSMsinanarm.Itisrelatedtonumb er oftheSMsinanarmviatheresistanceofoneofSM'sIGBTswitch, R sm R arm = nR sm : Assumingthatthevoltageinanarmisequallysharedamongthearm'sS Ms,the energystoredinthearm i ofthephase j canbecomputedas W ij = C arm 2 ( V arm ij ) 2 ; (2.10) where C arm istheequivalentarmcapacitordeterminedas C arm = C SM =n ,and V arm ij isthearmvoltagewhenallSMsareswitchedonthatderivedas: V arm ij = n X k =1 V c ijk : Therefore,theenergydierencebetweenarms,andthetotale nergystoredinthe legofphase j arecalculatedas: W total j = W uj + W ` j ; W di j = W uj W ` j : 2.4LC{Filter 13

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AccordingtoIEEE{1547standards,toconnectaDGtoanacgrid, THDofthe injectedcurrentsatPCCmustbelowerthan5%.Toachievethis,LC {ltersareused toeliminatehighorderharmoniccontents. TheLC{lterachieveshighereciencyalongwithcostsavings,given theoverall weightandsizereductionofthecomponents.LC{ltersminimizethe amountof currentdistortioninjectedintothegrid[38].Goodperformanceca nbeobtained intherangeofpowerlevelsuptohundredsofkW,withtheuseofsma llvaluesof inductanceandcapacitor. ThecircuitschematicsLC{ltermodelisshowninFigure2.1,where L f C f and R f aretheLC{lterinductance,capacitorandthedampingresistorr espectively. 14

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3.ControlScheme Eachconverteroftheback{to{backcongurationshowninFigur e2.1canindependentlysynthesizeathree{phasesinusoidalvoltageatitste rminals,denedby theiramplitudeandphaseangle.Thesetwodegreesoffreedomallow theVSRtocontroltheshaftspeed,andthereactivepowerabsorbedbythePM SG.Inturn,theVSI controlsthedc{linkvoltage,andthereactivepowerinjectedintot hegrid.Assuggestedingure3.1,thecontrolofeachconverterinvolves:( i )atwo{layercontroller whichisspecicforeachconverter;( ii )alegenergycontroller;and( iii )amodulator whichincludesamodulationtechnique,andavoltagebalancingalgorith m.w mrefV w E rec j s recijk VSRtwo{layercontroller MPPT P inv ref Q invref VSItwo{layercontroller V dcrefT rec ref I rec qrefI rec dref torque{to{ currenttransformation Modulation I inv qrefI inv dref Legenergycontrol power{to{ currenttransformation E inv j s invijk Modulation speed control dc{linkvoltage control current control current control Legenergycontrol Figure3.1:Overviewofthecontrolsystem.3.1VSRTwo{Layercontroller VSRtwo{layercontrollerregulates w m andthereactivepowerabsorbedbythe PMSG.Itisshowningure3.2,thecontrollerisbrokendownintofour blocks:( i ) asynchronizationblocktocomputetheshaftangle;( ii )speedcontrol;( iii )torque{ to{currenttransformation;and( iv )conventionalcurrentcontrolinthe dq frame. 15

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current wrecm + + + + Irec dref + + Irec qIrec dIrec qref Erec j + speedcontrol wm MPPT w m {limiter p 2!m 1 s !rec rec ^ w m w m wmref Vw rec controlI{limiter ^ i q i q PIwm + Lrec !rec synchronizationblock PIirec Irec j rec Tabcdq Tabcdq p 2m Trec ref torque{to{ ( ) 1 current 2 3 PIirec Figure3.2:SchematicoftheVSRtwo{layercontrollershowingasynchro nizationblock, speedcontrol,torque{to{currenttransformation,andcur rentcontrol.3.1.1SynchronizationBlock ThesynchronizationblocksynchronizesthePMSGwiththeVSR.Itc omputes theshaftangle, rec ,accordingto: rec = Z p 2 w m dt 3.1.2SpeedControl Inthespeedcontrolblock,thereferenceshaftspeed, w m ref ,comparedwiththe measuredshaftspeed,andcorrespondingerrorsaredriventoz erobyusingPI{type compensator. w m ref iscalculatedusing(2.3)inordertoextractthemaximumpower fromthewindturbine. w m canbeeithermeasuredfromsystemdirectly,orcanbe observedbyusingobservercontrollers.Thespeedcontroltrac ks w m ref bygenerating atorquereference, T rec ref ThetransferfunctionofthePI m isgivenas PI m (s)=Kp m + Ki m s ; 16

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whereKp m andKi m aretheproportionalandintegralgainofthespeedcontrol respectively. InVSRtwo{layercontroller,theVSRmustbepreventedfromgett ingintononlinearoperationmode.Toachieveit,aspeedlimiterusedafterMPPTa lgorithm thatkeeps w m ref between^ w m ,and w m 3.1.3Torque{to{CurrentTransformation Thetorquereferencecanbereadilyconvertedintoacurrentref erence, I rec q ref ,by using(2.9).Accordingto(2.9), I rec d doesnotcontributetotheelectricaltorque.Thus, inVSRtwo{layercontroller,togetmaximumtorqueper{ampere,th ed{axiscurrent reference, I rec d ref ,issettozero. I rec q isnowequaltothetotalcurrent,andperpendicular totheeldrux[16].3.1.4CurrentControl Inthecurrentcontrolblock, I rec d ref and I rec q ref areusedasreferencesignals.Both currentreferencesarecomparedwiththeactualstatorcurre ntsandthecorresponding errorsaredriventozerothroughproperlytunedtwode-coupled compensators.Zero steady{stateerrorcanbeachievedbyusingPI-typecompensat ors.Thecurrent controlleroutputsamodulatingsignaltofeedthemodulator. Thecurrentcontrolloopiscreatedbymodifyingthe dq framestatespaceequationsofthePMSGthataregivenat(2.6)and(2.7).Assumingastead y-stateoperatingconditionandsubstitutingfor w = w rec ;v d ; q = v rec d ; q ;I d ; q = I rec d ; q in(2.6)and(2.7), thestatespaceequationsthatrepresentsthecurrentcontro lloopcanbededucedas, L rec I rec d = R rec I rec d + w rec L rec I rec q v rec d ; (3.1) L rec I rec q = R rec I rec q w rec L rec I rec d w rec m + v rec q ; (3.2) where L rec and R rec istheequivalentinductance,andresistanceoftheVSRrespectively.Theyaredenedas 17

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R rec = R s + R arm 2 ; L rec = L s + L arm 2 : In(3.1)and(3.2), I rec d and I rec q arestatevariables, v rec d and v rec q arecontrolinputs, and w rec m isthedisturbanceinput.Duetothepresenceof w rec L rec termsin(3.1) and(3.2),dynamicsof I rec d and I rec q arecoupled.Todecouplethedynamics,twonew variables u recd and u recq areintroduced. u recd = L rec w rec I rec q + v rec d ; (3.3) u recq = L rec w rec I rec d m w rec + v rec q ; (3.4) Byusing u recd and u recq in(3.1)and(3.2),twodecoupled,rstorder,single{input{ single{output(SISO)subsystemcanbegenerated; L rec dI rec d dt + R rec I rec d = u recd ; L rec dI rec q dt + R rec I rec q = u recq : Ingure3.3,closedloopd{axisandq{axiscurrentcontrollerdiagra misshown. Inthegure,bothd{axis,andq{axisPIregulatorsprocessthee rrors e recd and e recq andcommands u recd and u recq .ThetransferfunctionofthePI i rec is; PI i rec ( s )=Kp i rec + Ki i rec s ; whereKp i rec istheproportionalconstantandKi i rec istheintegralconstantofthe PI i rec Inthecurrentcontrolloop,itisnecessarytopreventcirculation oflargecurrents throughtheSM'ssemiconductordevices.Therefore,currentlimit ersareusedtokeep I rec d and I rec q betweenthelimits ^ I d ; q and I d ; q 18

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I rec qref+ e recq u recq I rec dref+ e recd u recd I rec d PI i rec q{axisclosed{loopcurrentcontrol 1 L rec s + R rec d{axisclosed{loopcurrentcontrol 1 L rec s + R rec I rec q PI i rec Figure3.3:Closed{loopd{andq{axiscurrentcontrollersforVSRtwo{l ayercontroller.3.2VSITwo{LayerController TheVSItwo{layercontrollerutilizedhereincorrespondstoaconve ntionalcurrent controlandadc{linkcontrol.Theoverallcontrolscheme,shown ingure3.4,can bebrokendownintofourblocks:( i )aPLLutilizedforsynchronizationwiththe acgrid;( ii )dc{linkvoltagecontrol;( iii )power{to{currenttransformation;and( iv ) conventionalcurrentcontrolinthe dq frametotransferthegeneratedpowerintothe acgridatanarbitrarypowerfactor. power{to{ currentdc{linkvoltagecontrol v inv d + V qref=0 inv inv PLL v dcrefv dc current + + + I inv qref ++I inv d I inv q I inv dref E inv j inv controlI{limiter ^ i d i d + PI inv L inv T abcdq inv T abcdq v inv d v inv q + I{limiter ^ i q i q ( ) 1 2 3 ( ) 1 2 3 PI dc + ( ) 2 ( ) 2 v inv d v inv d Q invref P inv ref T abcdq PI vq 1 s v inv q I inv j inv PI invFigure3.4:SchematicoftheVSItwo{layercontrollershowingaPLL,dc{ linkvoltage control,power{to{currenttransformation,andcurrentco ntrol.19

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3.2.1Phase{Locked{Loop Inordertoperformthegridsynchronization,aPLLisimplemented. ThePLL computesthegridphaseanglebysensingthegridvoltageandproje ctingthecorrespondingspacevectoronthed-andq-axisofa dq rotatingframe.This dq frameis thenrotatedinsuchawaythatensuresthatthed{axisofthe dq frameisaligned withthegridvoltagevector,thatis, v inv q =0.Insteadystate,the dq framerotational speedequalsthegridangularfrequencyandtheextractedanglee qualstothegrid voltageangle, inv .Thisangleisusedtosynchronizethe dq referenceframeforthe currentcontrol.Asshowningure3.4,thePLLisimplementedherein througha simplePIcontrollerwhichforces v inv q =0. 3.2.2Dc{linkVoltageControl Thedc{linkvoltagecontrolloopregulatesthedc{linkvoltageatitsr atedvalue bygeneratinganactivepowerreference, P ref .Thedc{linkvoltagecontrolloopis aclosed{loopcontrolmechanismasshowningure3.4thatcompare s V 2 dc withits referencecommandandadjusts P inv ref suchthatnetpowerchangewiththedc{link capacitor, C dc iskeptatzero. Indc{linkvoltagecontrolloop,thePIcompensatordrivethedc{lin kvoltage errortozerotoregulatedc{linkvoltage.Thetransferfunctiono fthePI dc isgiven as; PI dc = Kp dc + Ki dc s : 3.2.3Power{to{CurrentTransformation Fromtheactiveandreactivepowerreferences,the dq currentscanbecomputed accordingto: P inv ref = 3 2 v inv d I inv d ref ;Q invref = 3 2 v inv d I inv q ref ; 20

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assumingthatPLLforces v inv q =0.MMCtopologiesoerindependentcontrolof reactivepower.Dependingonthegridconditions,bycontrollingrea ctivepower, MMCVSIcaneithergenerateaspeciedreactivepowertotheacgr id,orcanregulate thepowerfactor.3.2.4CurrentControl Asshowningure3.5,inthecurrentcontrolloop,thecurrentref erencesare comparedwiththeactual dq currentsandthecorrespondingerrorsaredriventozero throughproperlytunedtwodecoupledPI{typecompensators.F inally,theoutput signalistransformedintotheabcframeandoutputsamodulatings ignaltofeed themodulator.TheacsidedynamicsoftheVSIcanbedescribedbyt hefollowing space{phasorequationin abc referenceframe, L inv I inv j dt = R inv I inv j + V inv j v inv j ; where, V inv j and I j arethe3{phaseacvoltagesandcurrentsatVSI'sacterminals respectively,and L inv and R inv aretheequivalentinductanceandresistanceatVSI side.Theyaredenedas; L inv = L f + L arm 2 ; R inv = R arm 2 : TheacsidedynamicsoftheVSIcanberepresentsin dq referenceframebyusing theParktransformation. L inv dI inv d dt = R inv I inv d + w inv L inv I inv q + V inv d v inv d ; (3.5) L inv dI inv q dt = R inv I inv q w inv L inv I inv d + V inv q v inv q : (3.6) 21

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TodesignacurrentcontrolloopforVSItwo{layercontroller,likein section3.1.4, twonewcontrolvariablesshouldbeintroduced; u invd = w inv L inv I inv q + V inv d v inv d ; (3.7) u invq = w inv L inv I inv d + V inv q v inv q : (3.8) Byusing(3.5)and(3.6),in(3.7)and(3.8);twodecoupled,rstorde r,single{ input{single{output(SISO)subsystemscanbegenerated; L inv dI inv q dt = R inv I inv q + u invq ; L inv dI inv d dt = R inv I inv d + u invd : Iinv d ref + einvdPIi inv uinvdIinv d Iinv q ref + einvqPIi inv uinvqIinv q d{axisclosed{loopcurrentcontrol 1 L inv s + R inv 1 L inv s + R inv q{axisclosed{loopcurrentcontrol Figure3.5:Closed{loopd{andq{axiscurrentcontrollersforVSItwo{l ayercontroller.ThetransferfunctionofthePI i inv isgivenas PI inv (s)=Kp inv + Ki inv s Akeyadvantageofutilizingacurrentcontrollimitersinthecurrent controlis thattheVSIisprotectedagainstovercurrents.Assuggestedin gure3.4,current 22

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limiterspreventthecirculationoflargecurrentsthroughtheSMs, protectingtheVSI shouldashortcircuitontheacsideoccur.3.3LegEnergyController InMMCtopology,theenergyofeachofthethreelegshastobecon trolledin ordertoensureastableoperationoftheconverter.Toachieveit ,the V arm ij needto bemeasured,andthe W ij shouldbecalculatedusing(2.10).Figure3.8showsthe schematicofthelegenergycontrolleralongwiththemodulator,des cribedinthe following.Thelegenergycontrollercomprisedofthetotallegenerg ycontrolandthe armenergydierencecontrol.3.3.1TotalLegEnergyControl Thetotallegenergycontrolregulates W total j toadesiredreferenceenergylevel. Thereferenceforthetotallegenergycontroller( W ref total j )istypicallythe W ij ofthe legwhenthe V arm ij equalsthedc{linkvoltage.The W total j saredrivento W ref total j by PI{basedregulatoras U total j =( W ref total j W total j ) Kp total j + Ki total j s : Wref totalj Varm ` jVarm uj ( )2 + + Carm 2 ( )2 + Utotalj PItotal Figure3.6:Schematicofthetotallegenergycontrol.3.3.2ArmEnergyDierenceControl Thearmenergydierencecontrolaimstothecancel W di j bymanipulating I circ j Accordingto[30],therearetwoproblemsrelatedwiththecontrol.F irst, I circ j can 23

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notbedirectlycontrolled,butitcanbemanipulatedthroughthe U circ j .Second, thephaseofthecontroloutputmustlead I circ j byargumentof Z arm ,denedas Z arm = L arm + R arm ,andargumentof V j .Itisnoteworthytosaythatinsteadystate, W di j containsconsiderablefundamentalcomponents.Therefore,at theoutputofthe dierencecontrolleralow{passlterisusedtoeliminatehigh{freque ncycomponents. Tocancelthe W di j ,thereferenceforthelegenergybalancecontrolshouldbe chosen0. W di j saredriventotheircorrespondingreferencesbyaPIregulatora s U di j =( W ref di j W di j ) Kp di j + Ki di j s cos (arg(V j )+arg(Z arm )) : Wref dij Varm ` jVarm uj ( )2 + Carm 2 ( )2 + arg( ) VjZarm arg( ) + + cos( ) PIdi Udij Lp{ Filter Figure3.7:Schematicofthearmenergydierencecontrol.3.4Modulator InMMCtopology,tosynthesizeacwaveformvoltageattheac{side oftheMMC, SMsmustbeconsistentlyswitchedinorswitchedoutofthesystem. Therefore, inanypointoftime,thenumberofSMsswitchedonineacharm( N ij )mustbe calculated.Besides,regardlessoftheswitchingstate,theSMs'v oltagemustbe balancedinordertonottodistortthevoltageattheac{sideandto keeptheMMC stable.Basically,inMMCtopology,themodulatoriscomprisedofamod ulation techniquethatisemployedtocalculatethe N ij ,andavoltagebalancingalgorithm isusedtodeterminetheSMsswitchedoninthearm.Inthefollowingsu bsections, 24

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N ua N ub N uc I ua V cuak S ua1 S uan PD{ PWM Voltage balancingalgorithm U totalj U dijI ` a V c` ak S ` a1 S ` an + n N ua Voltage balancingalgorithm N ` a Armenergydierencecontrol Totallegenergycontrol W ref dijW ref totaljV cijk V cijk + Vdc 2 V armij V j E j + M uj Figure3.8:Schematicofthelegenergycontrollerandmodulator.themodulationtechniqueandthevoltagebalancingalgorithmusedint hisworkare described.3.4.1PhaseDisposed{PulseWidthModulation IntheSS{WECS,theback{to{backtopologyisbasedonreducedle velMMCs. Therefore,toinjectthepowerintotheacgridwithalowharmonicco ntent,thePD{ PWMtechniqueispreferredinsteadofcommonNLMtechnique[34].Th ePD{PWM techniquesarebasedoncomparisonofhigh{frequencytriangular multiwaveforms (thecarriers)withamodulatingsignal.ThenumberofSMsswitchedo ndetermined byintersectionsofthemodulatingsignalandthecarriers.Forthe upperandlower armsofeachleg,themodulatingsignalsarecomputedas; M uj = 1 V arm uj V dc 2 E j U total j U diff j ; M ` j = 1 V arm ` j V dc 2 + E j U total j U diff j ; 25

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where M uj and M ` j representthemodulatingsignalfortheupperandlowerarm respectively. Ingure3.9,a7levelPD{PWMschemeisshown.Itcanbeseenthatf ora n +1 levelMMC, n carriersareusedfeaturingthesamefrequency,andamplitude.A lso, thecarriersaredisplacedsymmetricallywithrespecttozero{axis. Thenumberof SMstobeswitchedonorinsertedinthephase j upperarm, N uj ,iscomputedby comparingthemodulatingsignalwitheachcarrier[34]. 0 0.5 1 Modulatingsignalandthecarrierwaveforms 0 1 2 3 4 5 6 OverallnumberofswithcedonSMs Figure3.9:PD{PWMmodulationschemefora7levelMMC.3.4.2VoltageBalancingAlgorithm InMMCtopologies,the V c ijk mustbemonitoredandkeptequalinordertoachieve stableoperationconditions.Therefore,avoltagebalancingalgorit hmmustbeused inmodulationprocess.Inthiswork,thevoltagebalancingalgorithmis armspecic, 26

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Yes I ij 0 No Start Insert N ij SMswith thelowestvaluesof V c ijk Insert N ij SMswith thehighesvaluesof V c ijk Input V cij1;:::;V cijkI ij N ij Initialization ofthe StorageMatrix L(Labelvector) SortingAlgorithm Figure3.10:Flowchartofthevoltagebalancingalgorithm.andaimstosortthe V c ijk inthearmanddecideswhichSMsshouldbeswitchedon basedon V c ijk valuesandthedirectionofthe I ij Inthiswork,thevoltagebalancingalgorithmisbasedonthealgorithm stated in[25].Ingure3.10,therowchartofthevoltagebalancingalgorithm isshown. Therowchartiscomprisedofthreesteps.Intherststep,ther owchartacceptsthe SMsvoltagemeasurementdata,thearmcurrentmeasurementda taandnumberof SMsswitchedon.Inthesecondstep,theSMvoltagesaresortedin toanascending sequencematrix.Finally,inthethirdsteptheSMsinsertedonarede cidedaccording todirectionofarmcurrent.Ifthethearmcurrentdirectionispos itive,thecapacitor ofainsertedSMwillbechargedanditsvoltageincreases.Therefor e,thevoltage 27

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balancingalgorithmwillchoosetheSMswithlowestvoltagestoreduce thevoltage dierencebetweenSMs.Oppositely,whenthearmcurrentisnegat ive,thecapacitor ofainsertedSMwillbedischargedanditsvoltagedecreases.Inthis case,thevoltage balancingalgorithmwillchoosetheSMswithhighestvoltages. 28

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4.DesignGuidelines4.1PowerStage Intheproposedback{to{backconguration,bothMMCsareiden tical,andthe throughputpoweroftheMMCsareselectedat24kVA.Thedc{linkv oltageisselected inordertoensurethatthemodulationindexoftheVSRtwo{layerco ntrollerisbelow 0.95.TheratedphasevoltageofthePMSGis185V.Therefore, V dc = 2 p 2 185 0 : 95 = 600V : Theharmoniccontentoftheinjectedcurrentstotheacgridisrela tedwith numberofSMsperarm(n).Therefore,ineachMMC,nischosen6so thatTHDof theinjectedcurrentsarebelow5%usingareducedsizeLC{lter.T hetotalvoltage ofonearmequalsthedc{linkvoltage,andthereare6SMsinonearm. Therefore, theratedvoltageofeachSMis100V.SinceonlyoneofthetwoIGBTs inaSM isconductinginstantaneously,thevoltageblockingcapabilityofeac hIGBTmustbe higherthan100V.TheIGBTmodelFGH50N3manufacturedbyFairc hildisselected withavoltageblockingcapabilityof300Vandamaximalforwardcurre ntof50 A.TheresistanceoftheselectedIGBTis63mn.Therefore,theto talresistanceof eachconverterarmconsideringtheseriesconnectionof6SMsis37 8mn.TheSM capacitorissizedinordertoensurethatthecapacitorvoltageripp leisbelow5%. Theselected C SM is27 : 6mF.Finally,thearminductance L arm isselectedas15%of thesystembaseimpedance[23]: Z s = ( v inv j ) 2 S ; L arm =0 : 15 Z s ; where Z s isthesystembaseimpedance.Fortheproposeddesign, L arm =1 : 9mH. Thecouplingtransformerisratedat24kVAwithatransformationr atioof 240/480andaleakageimpedanceof8%. 29

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Accordingto[18],fortheMMCwithmorethan200level,noLC{lterisr equired atacterminals.However,fortheMMCwithareducednumberofleve ls,LC{lters maybeusedinordertoreduceharmoniccontentsattheactermina ls.Inthiswork, thePD{PWMmodulationtechniqueisemployedtoreducetheharmonic contentsat theacterminals.Therefore,itwillreducethesizeoftheLC{lter. TheLC{lteris designedtoensuretheharmonicconditionsgiveninIEEE1576stand ards.TheLC{ lterinductance,capacitoranddampingresistancewereselected as L f =0 : 23mH, C f =6 : 9 F, R f =0 : 69nrespectively.Intable4.1,theparametersoftheSS{WECS aregiven. Table4.1:SS{WECSparameters Item Value Item Value Windturbine Couplingtransformer Bladeradius r =3 : 24m Ratedpower24kVA PMSG Turnratio240 = 480 RatedPower24kW Leakageinductance8% RatedVoltage185V Filter Polepairsp=24 Filterinductance L f =0 : 23mH Statorresistance R s =0 : 18n Filtercapacitor C f =6 : 6 F Statorinductance L s =0 : 018mH Dampingresistance R f =0 : 69n Flux m =0 : 6977Wb Grid Inertia J =4 : 8kgm 2 Gridvoltage480V MMCs Gridfrequency60Hz NumberofSMin Shortcircuitpower3MVA onearm n =6 X/Rratio1.5 SMcapacitor C =27 : 6mF Arminductance L arm =1 : 9mH Rateddc{link voltage600V Dc{linkcapacitance5mF Switchingfrequency5kHz 4.2Controllers 30

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Table4.2:Controllerparameters Parameter Value Parameter Value VSItwo{layer VSRtwo{layer controller controller Currentcontrolloop Currentcontrolloop Timeconstant i =0 : 5 ms Timeconstant i =0 : 5 ms ProportionalconstantKp inv =4 : 4 ProportionalconstantKp rec =4 IntegralconstantKi inv =37 : 8 IntegralconstantKi rec =360 Dc{linkcontrolloop Speedcontrolloop ProportionalconstantKp dc = 0 : 00439 ProportionalconstantKp w m =3 : 43 IntegralconstantKi dc = 48 : 578 IntegralconstantKi w m =61.49 Inthissection,thevariousPIcompensatorgainsoftheVSIandVS Rtwo{layer controllersaregivenintable4.2,andtuningmethodsusedinthiswork areexplained. 4.2.1CurrentControl InboththeVSRandVSIcurrentcontrolloops,Kp i rec ; inv andKi i rec ; inv derivedas follows[14]: Kp i rec ; inv = L rec ; inv = i ; Ki i rec ; inv = R rec ; inv = i ; where i isthetimeconstantofthecurrentcontrols. i isadesignchoice,anditis generallyselectedintherangeof0.5-5ms[14].4.2.2SpeedControl ParametersofthePI w m computedasfollows[39]: Kp m = J! sc K ; Ki m =Kp m sc 5 ; 31

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where sc denotesthecut{ofrequencyofthespeedcontrolloop.InVSR two{layer controller,thecurrentcontrolloopneedstobeatleast5timefas terthanthespeed controlloop[37].Therefore, sc canbecomputedas; sc cc 5 : where cc isthecut{ofrequencyoftheVSRcurrentcontrolloop. -100 -50 0 50 100 Magnitude(dB) 101 102 103 104 -180 -135 -90 Phase(deg)Frequency(rad/sec) Figure4.1:Frequencyresponseofthespeedcontrol.Ingure4.2,frequencyresponseofthespeedcontrolisshown. Itcanbeobserved fromthegure4.2that,the w sc is100rad/secwhichis20timessmallerthan w cc 4.2.3Dc{linkVoltageControl Thedc{linkvoltagecontrolblockdiagramshowningureblablacanbe brokendownintofourblocks:( i )thePIcompensator,( i )currentcontrolloopwhichis representedwitharst{orderlow{passlter,anditdenotesthe transferfunctionof 32

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P inv =P inv ref ,( iii )dc{linkvoltagedynamicsthatisformulatedbasedontheprincipleof powerbalance. vdcref + + ( )2 Pext v2 dc + PIvdc Pinv ref Currentregulator 1 is +1 Dc{linkvoltagedynamics2 Cdcs +1 s Pinv Figure4.2:Blockdiagramofthedc-linkvoltagecontrolloop.Thedc{linkvoltagedynamicsaredescribedasfollows[14]: G dc ( s )= V 2 dc P inv = 2 C dc s +1 s ; (4.1) thetimeconstant isdeducedas, = 2 L inv P inv ss 3( v inv d ) 2 ; where P inv ss isthesteady{statevalueofthetransferredactivepowertothe acgrid. Thedc{linkcontroldesignisbasedonfrequencyresponsemethod .Thereasonis thatopenlooptransferfunctionofthedc{linkcontrol, G ol dc ,isahigh{ordertransfer functionanditischaracterizedbyitsbandwidthratherthanitsroo tloci. G ol dc is describedasfollows[14]: G ol dc ( s )=PI dc 1 i s +1 2 C dc s +1 s ; Infrequencyresponsemethod,theobjectiveistoselectparame tersofKp dc and Ki dc suchthat G ol dc ( jw )crossesthe0dBaxis-20dB/decatthecross{overfrequency ( w dc ),andthephaseof G ol ( jw dc )islargerthan 180 byareasonablephasemargin. w dc isthegaincross{overfrequencyofthedc{linkvoltagecontrol.In VSItwo{ layercontroller,itisnotdesiredtohaveveryfastdc{linkcontrol.B ecause,the dc{linkcapacitoristypicallylargeandthedc{linkvoltagewillnotchang esorapidly. Typically,thedc{linkvoltagecontrolisatleast5timesslowerthanth ecurrentcontrol 33

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-100 -50 0 50 100 Magnitude(dB) 101 102 103 104 -180 -135 -90 Phase(deg)Frequency(rad/sec) Figure4.3:Frequencyresponseofthedc{linkvoltagecontrol.loop.Therefore, w dc shouldbeatleast5timesmallerthanthecut{ofrequencyof theVSIcurrentcontrol[14]. 34

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5.Simulation InordertovalidatethecontrolschemeintroducedinSection3,an devaluatethe performanceoftheSS{WECSpowerstageexplainedinSection2,ad etailedcomputer simulationinPSCAD/EMDTCofaSS{WECSisimplemented.Theperforma nceof SS{WECSistestedconsideringadetailedmodelforthesystemofg ure2.1,with parametersspeciedinchapter4.5.1SimulationData Thewindspeedproleshowningure5.1isusedforthesimulationstud ies.It wasconstructedusingrealmeasurementscollectedbytheNation alWindTechnology CenterinBoulder,Colorado,USA.Thewindspeedwasmeasuredat1 00Hzat36.6 mabovethegroundusingacupanemometer.Itcanbeseenfromth egure5.1,the proleisrichinturbulenceandexhibitsgustybehaviorattimes. 7 8 9 10 11 12 13 14 10(sec/div)Windspeed(m/sec) V w Figure5.1:Realwindspeeddatausedinthesimulations.IntheSS{WECS,asiscustomary,thewindturbinepowercoecient isassumed tobegivenbythefunction 35

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C p ( )= e c p1 c p2 c p3 + c p4 ; wherethecoecients c pm m =1 ;:::; 4arewindturbinespecics.Thesecoecients weretakenfrom[3],andhavethefollowingvalues: c p1 =21, c p2 =125 : 229, c p3 = 9 : 7803, c p4 =0 : 0068.Thisyields =8 : 1and C p =0 : 4801. Theacgridisratedas480V/60Hzwithashort{circuitpowerof3MVA ,and X/Rratiois10.5.2SimulationResults Figure5.2depictstheactivepowergenerationoftheSS{WECS.Itis observed thatMMC-basedback-to-backtopologysuccessfullytransfers thegeneratedelectrical powerofthePMSGtotheacgrid. 0 5 10 15 20 25 ActivePower(kW)10(sec/div) P theo P m P PMSG P grid Figure5.2:Simulationresultshowingthetheoreticalactivepower( Ptheo),shaftpower ( Pm),generatedelectricalpower( PPMSG)andactivepowerinjectedtotheacgrid( Pgrid).Figure5.3showsthereactivepowerresultsoftheSS{WECS.Inthe simulation, aunitypowerfactorinjectionisconsidered.The Q invref atthepointofsynchronization canbecomputedas Q invref =0 Q c ,where Q c isthereactivepowerinjectedbythe 36

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-10 -5 0 5 10 Reactivepower(kVAr)10(sec/div) Q Grid Q PMSG Figure5.3:Simulationresultshowingthereactivepowerinjectedtoth eacgrid( QGrid), andreactivepowerabsorbedbythePMSG( QPMSG). 7 8 9 Tipspeedratio10(sec/div) Figure5.4:Simulationresultshowingthetipspeedratio( ).LC{ltercapacitorsandcanbecalculatedas Q c =1 : 5( v inv d ) 2 w inv C f ,assumingthat thePLLforces v inv q =0. TheperformanceoftheMPPTisshowningure5.4and5.5.Itisobser vedthat ingure5.4thewindturbineoperatesat .Also,thegure5.5showsthatthewind turbineisoperatedat C p .Therefore,theMPPTcontroloperatessuccessfully. 37

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0.47 0.48 0.49 Powercoecient10(sec/div) Cp Figure5.5:Simulationresultshowingthepowercoecient( Cp). 10 20 30 40 Speed(rad = sec)10(sec/div) w m w m ref Figure5.6:Simulationresultshowingtheshaftspeed( wm)andtheoptimumshaftspeed ( wm ref).Figure5.6showstheperformanceofthespeedcontrol.Itcanbes eenthat,the speedcontrolsuccessfullytracksthereferenceshaftspeed( w m ref ).Recalling(2.3), w m ref iscomputedusingtheactualwindspeeddata. Itcanbeobservedfromgure5.7thatthedc{linkvoltagecontrol loopregulates thedc{linkvoltageatratedvoltagevalue. 38

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550 575 600 625 650 10(sec/div)Voltage(V) Vdc Figure5.7:Simulationresultshowingthedc{linkvoltage( Vdc).Figure5.8depictsthemodulationindexoftheVSRtwo{layercontrolle r.Itcan beobservedthatthemaximumvalueofthemodulationindexiscloseto 0.9whichis lowerthandesiredpeakmodulationindex. 0 0.5 1 1.5 2 Modulationindex10(sec/div) M rec Figure5.8:SimulationresultshowingthemodulationindexoftheVSRtw o{layercontroller.39

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Figure5.9showsthemodulationindexoftheVSItwo{layercontroller .Itcanbe seenthattheVSItwo{layercontrollerlinearoperationzone. 0 0.5 1 1.5 2 Modulationindex10(sec/div) M inv Figure5.9:SimulationresultshowingthemodulationindexoftheVSItw o{layercontroller.Figure5.10showsthemeasured3{phasevoltageatPLLon dq frame.Itis observedthat, v inv q =0,andthePLLsuccessfullysynchronizedtheVSIwiththeac grid. 0 100 200 300 400 Voltage(V)10(sec/div) vinv d vinv q Figure5.10:SimulationresultshowingthevoltageatPLLon dq frame.40

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Figure5.11showsthemeasured3{phasestatorcurrenton dq frame.Itcanbe seenthat, I rec d =0.Thus,themaximumtorqueperamperecontrolisachievedin VSRtwo{layercontroller. 0 25 50 75 Current(A)10(sec/div) I rec d I rec q Figure5.11:SimulationresultshowingthePMSG'sstatorcurrenton dq frameFigure5.12showsthemeasured3{phaseVSIcurrenton dq frame.Itisobserved that, I inv q =0.Therefore,thereactivepowerinjectiontothegridis0,whichis the desiredobjectinthesimulation. 0 25 50 75 Current(A)10(sec/div) I inv d I inv q Figure5.12:SimulationresultshowingtheVSIcurrenton dq frame41

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Figure5.13showsthetotallegenergyofthephase{alegoftheVSI .Itcanbe seenthat,the W inv total a isregulatedatitstypicalvaluewhichisthetotallegenergy whenthe V arm ia equalsthedc{linkvoltage. 0 5 10 15 20 Legenergy(J)10(sec/div) W total c Figure5.13:Simulationresultshowingthetotallegenergyofthephase{ alegoftheVSI ( Winv total a). 0 2 4 6 8 10 Armenergydierence(J)10(sec/div) W di c Figure5.14:Simulationresultshowingthearmenergydierenceofthepha se{alegofthe VSI( Winv di a).42

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Figure5.14depictsthearmenergydierenceofthephase{alegoft heVSI.It canbeseenthat,thearmenergydierencecontrolcancelsthe W inv di a 80 90 100 Vinv cua1 80 90 100 Vinv cua2 80 90 100 Voltage(V) Vinv cua3 80 90 100 Vinv cua4 80 90 100 Vinv cua5 80 90 100 10(sec/div) Vinv cua6 Figure5.15:SimulationresultshowingtheSMvoltagesofthephase{aoft heVSI( Vinv c uak).Figure5.15depictsthe V inv c uak .ItcanbeseenfromthegurethattheSMvoltage rippleiswithin5%range.Also,thevoltagebalancingalgorithmisabletoe qualize theSMvoltages,alwayskeepingthedierencebetweenthemunder 2mV. 43

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-300 0 300 1 = 60(sec/div)Voltage(V) vc vinv c Figure5.16:Simulationresultshowingphase{cvoltageatprimaryofthe couplingtransformer( vinv c)andattheterminalofMMCVSI( vc).Ingure5.16,phase{cvoltageatprimaryofthecouplingtransfor merandthe phase{cterminalvoltageoftheVSIareshown. 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 Voltagemagnitude(V)Frequency(kHz) Figure5.17:Simulationresultshowingharmonicspectrumofthevoltage atPLL.HarmonicspectrumoftheVSIvoltageatPLLisshowningure5.18.I nthe gure,themaincomponentofthevoltage,whichis240Vat60Hz,isn otshownto zoominhighordervoltagecomponents.TheTHDofthevoltageis2 : 5%,thusthe 44

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voltageharmonicsoftheSS{WECSarecloseto0. 1 2 3 4 5 6 7 8 9 10 0 0.1 0.2 0.3 0.4 0.5 0.6 Currentmagnitude(A)Frequency(kHz) Figure5.18:Simulationresultshowingharmonicspectrumoftheinjecte dcurrent.Harmonicspectrumoftheinjectedcurrentisshowningure5.18.I nthegure, themaincomponentofthecurrent,whichis14Aat60Hz,isnotshow ntozoom inhighordercurrentcomponents.Itcanbeobservedthat,lower frequencyorder harmonicsarecloseto0,andhighfrequencycurrentharmonicsar eeliminated.The THDoftheinjectedcurrentis3 : 8%,thustheSS{WECSaccomplishtheharmonic conditionsstatedinIEEE1576standards. 45

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6.Conclusions Inthisthesis,aMMC{basedback{to{backtopologywithreducedn umberof levelsisproposed,astheinterphaseofaSS{WECSwithathree{pha seacgrid.The variouscomponentsinvolvedintherealizationofaSS{WECSaredesc ribedandthe controlapproachisexplained.Inaddition,thedesignguidelineofth eSS{WECSand tuningmethodsusedintheVSIandVSRtwo{layercontrollerareexp ressed.The proposedsystemisvalidatedviadetailedPSCAD/EMTDCcomputersim ulations usingrealwindspeeddata. Comprehensivecontrolleranalysisshowsthattheresponseofthe VSIandthe VSRtwo{layercontrollersarefastandaccurate,whilebothcontr ollersprovidea fasterinnerloopandslowerouterloopcontrol,asdesired.Thesimu lationresults showthattheSS{WECSarchitectureisabletoperformtheMPPTfu nctionfor theSS{WECS,whilesimultaneouslytransfersthegeneratedpower intothegridat anarbitrarypowerfactor.Thesimulationresultsalsoshowthatan eectivespeed controlisachievedwithinthephysicalconstraintsofthesystemu nderbothsteady andvariablewindconditions.Inaddition,thedc{linkcontrolsucces sfullyregulates V dc underbothsteadyandvariablepowerconditions.Thenumericalre sultshave shownthatthelegenergycontrolandthevoltagebalancingalgorit hmassurebalanced SMcapacitorvoltages.TheSS{WECSoperatescorrectlyunderst eady{stateand transientoperatingconditions. ItisshownthatbyusingPD{PWM,theMMC{basedback{to{backco nverter consistsofareducednumberoflevelsandasmallLC{lterisabletoin jectcurrents intothegridwithTHDlowerthan5%. 46

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7.Contributions Thecontributionsofthethesisarethefollowings: AMMC{basedback{to{backtopologywithareducednumberofleve lsisproposedastheinterphaseofaSS{WECSwithathree{phaseacgrid. Thecontrolstrategydiscussedinthethesisisabletoperformthe MPPTfunctionfortheSS{WECS,andsimultaneouslytransferthegenerated powerinto thegridatanarbitrarypowerfactor. ThePD{PWMtechniqueisimplementedtoinjectpowerintothegridwith a lowharmoniccontent.Thisallowsforasizereductionoftheaclter. ThecontrolschemesandmodelsarevalidatedviadetailedPSCAD/EM TDC computersimulationsusingrealwindspeeddata. 47

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8.FutureWork Thepossiblefutureworkscanbelistedasfollows: Developsystematicdesignmethodforthetotallegenergycontro landlegenergy balancecontrol. Implementationofthewindspeedestimationtechniquestocompute w m ref StudyofthebehaviouroftheMMC{basedSS{WECSunderfaultcon ditions. 48

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REFERENCES [1]W.El{KhattamandM.M.A.Salama.DistributedGenerationTechn ologies DenitionsandBenets. ElectricPowerSystemsResearch ,71(2):119{128,2004. [2]M.Abarzadeh,H.M.Kojabadi,andL.Chang.PowerElectronics inSmallScale WindTurbineSystems. AdvancesinWindPower ,2012. [3]F.Mancilla{DavidandR.Ortega.AdaptivePassivity{BasedContr olforMaximumPowerExtractionofStand{AloneWindmillSystems. ControlEngineering Practice ,20(2):173{181,2012. [4]ABroe,S.Drouilhet,andV.Gevorgian.APeakPowerTrackerfo rSmallWind TurbinesinBatteryChargingApplications. IEEETransactionsonEnergyConversion ,14(4),Dec.1999. [5]E.HauandH.Renouard. WindTurbines:Fundamentals,Technologies,Application,Economics .Springer,2013. [6]E.Muljadi,G.Nix,andJ.T.Bialasiewicz.AnalysisoftheDynamicsof aWind{ TurbineWater{PumpingSystem.In IEEEPowerEngineeringSocietySummer Meeting ,pages2506{2519,Jul.2000. [7]S.M.MirandaandD.Ineld.AWind{PoweredSeawaterReverse{ Osmosis SystemWithoutBatteries. Desalination ,153(1{3):9{16,2003. [8]P.SotoodehandR.D.Miller.ANewMulti{levelInverterwithFACTS CapabilitiesforWindApplications.In IEEEGreenTechnologiesConference ,pages 271{276,Apr.2013. [9]G.M.Masters. RenewableandEcientElectricPowerSystems .JohnWiley& Sons,2013. [10]M.SaeedifardandR.Iravani.DynamicPerformanceofaModula rmultilevel back{to{backHVDCSystem. IEEETransactionsonPowerDelivery ,25:2903{ 2912,Oct.2010. [11]M.SinghandS.Santoso. DynamicModelsforWindTurbinesandWindPower Plants .NationalRenewableEnergyLaboratory,2011. [12]K.Seul{KiandK.Eung{Sang.PSCAD/EMTDC{BasedModelingan dAnalysis ofaGearlessVariableSpeedWindTurbine. IEEETransactionsonEnergy Conversion ,22(2):421{430,Jun.2007. 49

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[13]W.Haining,C.Nayar,S.Jianhui,andD.Ming.ControlandInter facingofa Grid{ConnectedSmallScaleWindTurbineGenerator.In AustralasianUniversitiesPowerEngineeringConference ,pages1{5,Sep.2009. [14]A.YazdaniandR.Iravani. Voltage{SourcedConvertersinPowerSystems .John Wiley&Sons,2010. [15]M.Ors.MaximumPowerPointTrackingforSmallScaleWindTurbine with Self{ExcitedInductionGenerator. JournalofControlEngineeringandApplied Informatics ,11(2):30{34,2009. [16]ShuhuiL.,T.A.Haskew,R.P.Swatloski,andW.Gathings.Optim aland Direct{CurrentVectorControlofDirect{DrivenPMSGWindTurbin es. IEEE TransactionsonPowerElectronics ,27(5):2325{2337,May2012. [17]A.LesnicarandR.Marquardt.AnInnovativeModularMultilevel Converter TopologySuitableforaWidePowerRange.In IEEEBolognaPowerTech ConferenceProceedings ,Jun.2003. [18]M.Davies,M.Dommaschk,J.Dorn,J.Lang,D.Retzmann,and D.Soerangr. HVDCPlus{BasicsandPrincipleofOperation. SiemensEnergySector ,3,2008. [19]T.Westerweller,K.Friedrich,U.Armonies,A.Orini,D.Parquet ,andS.Wehn. TransBayCable{World'sFirstHVDCSystemUsingMultilevelVoltage{SourcedConverter. CIGR EB4Session ,2010. [20]H.Knaak.ModularMultilevelConvertersandHVDC/FACTS:ASu ccessStory. In ProceedingsoftheEuropeanConferenceonPowerElectronic sandApplications ,pages1{6,Aug.2011. [21]L.Wei,G.Luc-Andre,andJ.Belanger.ControlandPerfor manceofaModular MultilevelConverterSystem.In CIGR EConferenceonPowerSystems ,2011. [22]S.P.Teeuwsen.ModelingtheTransBayCableProjectasVoltag e{SourcedConverterwithModularMultilevelConverterDesign.In IEEEPowerandEnergy SocietyGeneralMeeting ,pages1{8,2011. [23]J.Peralta,H.Saad,S.Dennetiere,J.Mahseredjian,andS.N guefeu.Detailed andAveragedModelsfora401{levelMMCHVDCSystem. IEEETransactions onPowerDelivery ,27(3):1501{1508,Jul.2012. [24]H.P.MohammadiandM.T.Bina.ATransformerlessMedium{Volt ageSTATCOMTopologyBasedonExtendedModularMultilevelConverters. IEEETransactionsonPowerElectronics ,26(5),May2011. [25]T.H.Nguyen,D.{C.Lee,andC.{K.Kim.ACost{EectiveConver terSystemfor HVDCLinksIntegratedwithOshoreWindFarms.In 39thAnnualConference oftheIEEEIndustrialElectronicsSociety ,pages7978{7983,Nov.2013. 50

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[26]J.Yang,Y.Yang,Z.He,andH.Wang.SystemDesignofMMCVSC {HVDC DemonstrationProjectforWindfarmConnection.In InternationalConference onACandDCPowerTransmission ,pages1{6,Dec.2012. [27]M.G.MolinaandP.E.Mercado.ANewControlStrategyofVaria bleSpeed WindTurbineGeneratorforThree{PhaseGrid{ConnectedApplicat ions.In LatinAmericaIEEE/PESTransmissionandDistributionConf erenceandExposition ,pages1{8,Aug.2008. [28]C.Patsios,A.Chaniotis,andA.Kladas.AHybridMaximumPowerP oint TrackingSystemforGrid{ConnectedVariableSpeedWind{Generat ors.In IEEE PowerElectronicsSpecialistsConference ,pages1749{1754,Jun.2008. [29]J.Yaoqin,Y.Zhongqing,andCaoB.ANewMaximumPowerPointTr acking ControlSchemeforWindGeneration.In PowerConInternationalConference onPowerSystemTechnology ,pages144{148,Oct.2002. [30]A.Antonopoulos,L.Angquist,andH.Nee.OnDynamicsandVolt ageControl oftheModularMultilevelConverter.In EP13thEuropeanConferenceonPower ElectronicsandApplications ,pages1{10,Sep.2009. [31]S.Du,J.Liu,andJ.Lin.Leg{BalancingControloftheDC{linkVo ltagefor ModularMultilevelConverters. JournalofPowerElectronics ,12(5):739{747, 2012. [32]G.Chun,J.Jianguo,Y.Xingwu,X.Liang,andC.Kai.ANovelTop ologyand ControlStrategyofModularMultilevelConverter.In InternationalConference onElectricalandControlEngineering ,pages967{971,Sep.2011. [33]A.Hassanpoor,S.Norrga,H.Nee,andL.Angquist.Evaluatio nofDierent Carrier{BasedPWMMethodsforModularMultilevelConvertersfor HVDCApplication.In 38thAnnualConferenceonIEEEIndustrialElectronicsSoci ety Oct.2012. [34]M.RajanandR.Seyezhai.ComparativeStudyofMulticarrierPW MTechniques foraModularMultilevelInverter. InternationalJournalofEngineeringand Technology ,2013. [35]S.Xu,HRao,Q.Song,W.Liu,andX.Zhao.ExperimentalResea rchofMMC BasedVSC{HVDCSystemforWindFarmIntegration.In 2013IEEEInternationalSymposiumonIndustrialElectronics ,pages1{5,May2013. [36]S.Chapman. ElectricMachineryFundamentals .McGraw{HillEducation,2005. [37]A.Cimpoeru.EncoderlessVectorControlofPMSGforWindTur bineApplications. AalborgUniversitet,InstituteofEnergyTechnology ,2010. 51

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AppendixA.ParkTransformation Parktransformationtheoryisusedtotransformthree-phasea bcreferenceframe quantitiestothedqreferenceframequantities.Inthistransfor mtheory,itisassumed thatthedqreferenceframeisrotatingatsynchronousspeedwit hrespecttotheabc referenceframewithaphaseangle .ThereferenceframesareshowninFigureA.1. Parktransformationtheorysimpliesanalysisandcontrolof3pha sesynchronous machinesandthree-phaseinverters.Also,Parktransformation canbereversed,which meansdqquantitiescanbetransformbacktoabcquantities.a{axis b{axis c{axis d{axis q{axis wt FigureA.1:Thestationaryabcreferenceframeandtherotatingdqrefer enceframeThedqquantitiesrelatetotheabccounterpartsaccordingto X dq = T dq abc X abc ; X abc = T abc dq X dq ; where T dq abc representstheParktransformationmatrix, T dq abc = 2 3 264 cos( )cos( 2 3 )cos( 4 3 ) sin( )sin( 2 3 )sin( 4 3 ) 375 ; 53

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and T abc dq standsfortheinverseParktransformationmatrix, T abc dq = 3 2 266664 cos( )sin( ) cos( 2 3 )sin( 2 3 ) cos( 4 3 )sin( 4 3 ) 377775 : Theexpressionoftheactiveandreactivepowerindqreferencefr amearegiven by P = 3 2 ( v d i d + v q i q ) ; Q = 3 2 ( v q i d v d i q ) : 54