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ModelPredictiveControlfor Doubly-FedInductionGeneratorsand Three-PhasePowerConverters This page intentionally left blank
ModelPredictive ControlforDoubly-Fed InductionGenerators andThree-PhasePower Converters AlfeuJ.SguareziFilho
Engineering,ModelingandAppliedSocialSciencesCenter FederalUniversityofABC SantoAndré,SP,Brazil
Elsevier
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1.Introduction
AlfeuJ.SguareziFilho
1.1Overview 1 1.2Structureofthebook 3
2.Inductionmachineandthree-phasepowerconverter dynamicmodels
AlfeuJ.SguareziFilho
2.1Spacevectornotation 5
2.1.1Thestationaryreferenceframe (αβ) 5
2.1.2Thesynchronousreferenceframe (dq) 6
2.2Inductionmachinedynamicmodel 7
2.2.1IMrepresentationinthree-phasesystems8
2.2.2IMrepresentationinstationaryreferenceframe (αβ) 9
2.2.3IMrepresentationinsynchronousreferenceframe (dq) 12
2.2.4Speeddynamicsrepresentation14
2.3Three-phasepowerconverterconnectedtothegriddynamic model 14
2.3.1Three-phasepowerCCGrepresentationinthree-phase systems15
2.3.2CCGrepresentationinstationaryframe (αβ) 16
2.3.3CCGrepresentationinsynchronousframe dq 17
2.4Pulse-width-modulationtechniques 18
2.4.1SinusoidalPWM18
2.4.2Spacevectormodulation21 2.5Summary 25 2.6Furtherreading 25
3.FundamentalsofvectorcontrolforDFIGandforthe three-phaseCCG
AlfeuJ.SguareziFilho
3.1Doubly-fedinductiongenerator
3.1.1Vectorcontrol28
3.1.2ClosedlooprotorcurrentcontrolusingPIcontrollers31
3.1.3DeadbeatrotorcurrentcontrolforDFIG33
3.1.4DeadbeatdirectpowercontrolforDFIG35
3.2Three-phasepowerCCGvectorcontrol 37
3.2.1Filterelements38
3.2.2VectorcontrolfundamentalsfortheCCG38
4.Fundamentalsofmodelpredictivecontrol
AlfeuJ.SguareziFilho
4.1Overview 43
4.1.1MPCappliedinpowerelectronicssystems45
4.2Finitecontrolsetmodelpredictivecontrol 45
4.2.1Principlesoffinitecontrolsetmodelpredictivecontrol45
4.2.2ConstrainsinFCS-MPC47
4.2.3Modulatedfinitecontrolsetmodelpredictivecontrol47
4.3MPCwithmodulator(MPC-WM)
4.3.1ConstrainsinMPC52
5.ModulatedFCS-MPCforDFIG-DPC
AlfeuJ.SguareziFilhoandRogérioV.Jacomini
5.1RepresentationofDFIGusingDPC
5.1.1Rotorvoltagerepresentation55
5.2DPCforDFIGusingthemodulatedFCS-MPC 57
5.2.1ComputationofthedutycycleusingmodulatedFCS-MPC58
6.AwirelesscodedmodulatedFCS-MPCDPCfor renewableenergysourcesinsmartgridenvironment
AlfeuJ.SguareziFilho,AngeloS.Lunardi,CarlosE.Capovilla,and IvanR.S.Casella
6.1Overview
6.2Three-phasepowerCCGusingdirectpowerpredictivecontrol
6.3Representationofthewirelesscommunicationsystem
6.4Analysisoftheexperimentalresults 75
6.4.1OFDM-CCresults76
6.4.2OFDM-LDPCresults77
6.4.3FastFouriertransformanalysis80
6.5Summary 83
7.MPC-WMfordoubly-fedinductiongeneratorand three-phaseCCG
AlfeuJ.SguareziFilho
7.1DFIGrotorcurrentcontrolusingMPC-WM 85
7.1.1Spacestateequations85
7.1.2RotorcurrentcontrolusingMPC-WM87
7.2DFIGDPCusingMPC-WM 91
7.2.1DPCusingMPC-WM94
7.3Three-phaseCCGcurrentcontrolusingMPC-WM 97
7.3.1Spacestateequations98
7.3.2GridcurrentcontrolusingMPC-WM100
7.3.3Simulationresults101
7.3.4Experimentalresults101
7.4Informationaboutthechoiceofweightingmatricesand horizonsvalues 103
7.5Summary 105
8.Fundamentalsofthemodelpredictiverepetitive control
AlfeuJ.SguareziFilho
8.1Fundamentalsofrepetitivecontrol 107
8.1.1IMPforanyperiodicsignal107
8.1.2BasicRCstructureanddesign108
8.2Fundamentalsofmodelpredictiverepetitivecontrol 109
8.2.1Periodicsignalsrepresentation109
8.2.2MPRCtechnique111
8.3Summary 115
9.MPRC-WMforDFIGandthree-phaseCCGoperation undervoltagedistortions
AlfeuJ.SguareziFilho,AngeloS.Lunardi,andEliomarR.CondeD.
9.1Representationofvoltagedistortions 117
9.2ModelofDFIGunderstatordistortedvoltage 118
9.2.1Influenceofdistortedvoltageinthestatoractiveand reactivepowerrepresentation119
9.2.2InfluenceofdistortedvoltageinDClinkvoltage121
9.3DFIGrotorcurrentcontrolusingMPRC-WM 123
9.3.1Criterionforchoosingpolynomial D(z) 126 9.3.2Experimentalresults128
9.4Three-phasepowerCCGmodelundergriddistortedvoltage 131
9.4.1Influenceofdistortedvoltageintheactiveandreactive powerrepresentation133
9.5Three-phasepowerCCGcurrentcontrolusingMPRC-WM 134
9.5.1Criterionforchoosingthepolynomial Dg (z) 139 9.5.2Experimentalresults139
10.Finitepositionsetphase-lockedloopoperatingunder nonidealgridvoltages
AlfeuJ.SguareziFilho,FernandoLino,andRogérioV.Jacomini
10.1PLLfundamentals 145 10.1.1PLLforthree-phasesystems146
10.2Representationofgridvoltagedisturbances 147
10.3FinitepositionsetPLLoperationundergriddisturbances 149
10.3.1RepresentationoftheDSOGI149 10.3.2RepresentationoftheMAF151 10.3.3FinitepositionsetPLL152 10.4Experimentalresults
11.ImplementationofDFIGMPC-WMandthree-phase powerCCGMPRC-WMusingSimulink/MATLAB®
AlfeuJ.SguareziFilho,AngeloS.Lunardi,andEliomarR.CondeD.
11.1Introduction 157
11.2BuildingembeddedfunctionsforPark–Clarketransformation 157 11.2.1Park–Clarketransformation157
11.2.2InversePark–Clarketransformation159 11.2.3Pulsewidthmodulation160
11.3BuildingsimulationmodelforDFIG 168
11.3.1BuildingsimulationmodelforDFIGusingMPC-WM173 11.3.2BuildingsimulationmodelforDFIGusingMPRC-WM178
11.4Buildingsimulationmodelforthree-phasepowerCCG 184
11.4.1BuildingsimulationMPCforpowerconverter185
11.5Summary 190
12.DFIGandthree-phasepowerCCGexperimental setup
AlfeuJ.SguareziFilho
12.1Experimentalsetups 191 12.1.1DFIGsetup191
12.1.2Three-phaseCCGsetup191
12.1.3ThePLLsetup192
12.1.4Dataacquisition,powersupply,andDCmotor192
12.1.5Systeminitialization194
12.2Informationaboutthemicrocontroller 195
12.2.1Functionalityofthemicrocontroller195
12.3Predictivecontrolimplementation 196
12.3.1BuildingembeddedcontrollerinDSP196
12.4Summary 198
A.DFIGparameters
B.Three-phasepowerCCGparameters
C.DClinkvoltagerepresentation
Bibliography205 Index213
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Listoffigures Fig.1.1 BasicstructurediagramofaDFIGconnectedtotheelectricalgrid. 2
Fig.1.2 Structureblockdiagramofthebook. 3
Fig.2.1 Thestationaryandsynchronousreferenceframesforthespacevector. 7
Fig.2.2 Inductionmachinerepresentationinathree-phasesystem. 8
Fig.2.3 DetailedcircuitofCCG. 15
Fig.2.4 SimplifiedcircuitofCCG.
Fig.2.5 BlockdiagramforimplementationoftheSPWM.
15
19
Fig.2.6 SPWMcurves:(a)comparisonofthecarrierandthemodulatingsignals, (b) va 0 ,(c) vb 0 ,and(d) vab 19
Fig.2.7 Voltagebyusingthirdharmoniccomponent.
Fig.2.8 THSPWMdiagram.
20
20
Fig.2.9 Spacevectorrepresentationbyusingtheswitchesstatesinthe αβ frame. 21
Fig.2.10 SVMdigitalimplementation.
Fig.3.1 DFIGconnectedtothemainsblockdiagram.
Fig.3.2 Orientationdiagrams:(a)voltageorientationand(b)statorfluxorientation.
Fig.3.3 DFIGrotorcurrentcontroldiagram.
Fig.3.4 DFIGdeadbeatrotorcurrentcontroldiagram.
Fig.3.5 Detailofdeadbeatdiagram.
Fig.3.6 DFIGdeadbeatdirectpowercontrolgeneralscheme.
Fig.3.7 Three-phasepowerCCGclosed-loopgridcurrentcontrolbyusingPI controllers.
Fig.4.1 MPCbasicdiagram.
Fig.5.1 Graphicalrepresentationofconverterswitchingconditionsandtherotor voltagevectorintherotorreference.
Fig.5.2 DPCforDFIGusingmodulatedFCS-MPCblockschemeofthe implementedcontrolalgorithm.
Fig.5.3 DPCforDFIGusingmodulatedFCS-MPCblockschemeoftherotorvoltage prediction.
Fig.5.4 ModulatedFCS-MPCDPC.Steptestsforapparentpower:(a)activepower and(b)reactivepower.
Fig.5.5 ModulatedFCS-MPCDPC.Detailofthesteptestforapparentpower: (a)activepowerand(b)reactivepower.
Fig.5.6 ModulatedFCS-MPCDPC.Detailofthesteptestforapparentpower: (a)reactivepowerandactivepower,(b)statorcurrentandvoltage.
Fig.5.7 ModulatedFCS-MPCDPC.Detailofthesteptestforapparentpower: (a)reactivepowerandactivepower,(b)statorcurrentandvoltage.
Fig.5.8 ModulatedFCS-MPCDPC.THDoftherotorvoltageduringthetest.
Fig.5.9 ModulatedFCS-MPCDPC.Rotorspeed.
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Fig.5.10
ModulatedFCS-MPCDPC.Steptestforapparentpower:(a)statoractive powerand(b)statorreactivepower.
66
Fig.5.11 ModulatedFCS-MPCDPC.Rotorcurrentduringseveral-speedoperation. 66
Fig.6.1 Smartgridinfrastructure.
Fig.6.2 VSIsextant.
Fig.6.3 BlockdiagramforthemodulatedFCS-MPCDPCforCCG.
Fig.6.4 Blockdiagramforthewirelesscommunicationsystem.
Fig.6.5 Experimentalsetupfortests.
Fig.6.6 Responseofreceivedpowersteptest, Pgref and Qgref ,usingOFDM-CC.
Fig.6.7 GridvoltageandcurrentsignalsusingOFDM-CCandresponseofreceived Pgref steptestusingOFDM-CC.
Fig.6.8
GridcurrentsignalsusingOFDM-CC(Q =−300var).Theblue(grayin printversion)lineisthereferencesignalandthedashedred(darkgrayin printversion)lineisthecurrentsignal.
Fig.6.9 Responseofreceivedpowersteptest, Qgref and Pgref ,usingOFDM-LDPC.
Fig.6.10
Fig.6.11
GridvoltageandcurrentsignalsusingOFDM-LDPCandresponseof received Pgref steptestusingOFDM-LDPC.
GridcurrentsignalsusingOFDM-CC(Qgref =−300var).
Fig.6.12 FFTanalysisforswitching.
Fig.6.13 CurrentFFTanalysisforOFDM-LDPC.
Fig.6.14 CurrentFFTanalysisforOFDM-CC.
Fig.7.1 DFIGrotorcurrentcontrolbyusingMPC-WMdiagram.
Fig.7.2
Fig.7.3
Fig.7.4
Fig.7.5
Fig.7.6
Fig.7.7
Fig.7.8
Fig.7.9
Fig.7.10
Fig.7.11
Fig.7.12
Fig.7.13
Fig.7.14
Fig.7.15
Fig.7.16
Fig.7.17
Fig.7.18
MPC-WM.Steptestsforrotorcurrent:(a) q –quadratureaxis,(b) d –direct axis,(c)inthe αβ frame,and(d)inthethree-phaserotorframe.
MPC-WM.Steptestsforrotorcurrentinthe dq frame.
MPC-WM.Detailofsteptestforrotorcurrentinthe dq frame.
MPC-WM.Statorvoltageandcurrentduringstepofrotorcurrent ir,d : (a)statorvoltageandcurrent,(b)rotorcurrentvectorcomponents.
MPC-WM:Statorvoltageandcurrentduringstepofrotorcurrent ir,q (a)Statorvoltageandcurrent.(b)Rotorcurrentvectorcomponents.
MPC-WM:Severalspeedoperationtest.(a)Speedoftherotor.(b)Rotor currentinrotorframe.(c)Rotorcurrentvectorcomponentsin dq frame.
MPC-WM:DFIGDPC.
DPCMPC-WM.Steptestsforactiveandreactivepower:(a)activepower, (b)reactivepower.
DPCMPC-WM.Detailofsteptestforactivepower:(a)activepower, (b)reactivepower.
DPCMPC-WM.Statorvoltageandcurrentduringstepofactivepower: (a)reactiveandactivepower,(b)statorvoltageandcurrent.
DPCMPC-WM.Statorvoltageandcurrentduringstepofreactivepower: (a)reactiveandactivepower,(b)statorvoltageandcurrent.
DPCMPC-WM.Several-speedoperationtest:(a)rotorspeed,(b)rotor current,(c)reactiveandactivepower.
MPC-WM.CCGcurrentcontroldiagram.
MPC-WM.Simulationresultofthegridcurrentbehaviorduringthepower steptests.
MPC-WM:THDofthegridcurrent.
MPC-WM.Steptestsforgridpowercontrol:(a)activepower,(b)reactive power.
MPC-WM.Detailofgridactivepowerstep:(a)activepower,(b)reactive power.
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Fig.7.19
Fig.7.20
Fig.7.21
MPC-WM.Gridcurrentduringpowersteptests:(a)realcomponentofthe gridcurrentvector,(b)imaginarycomponentofthegridcurrentvector. 105
MPC-WM.Gridcurrentduringthereactivepowerstep:(a)activeand reactivepower,(b)gridvoltageandcurrent.
MPC-WM.Gridcurrentduringtheactivepowerstep:(a)activeandreactive power,(b)gridvoltageandcurrent.
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106
Fig.8.1 ControlsystemloopbyusingtheIMP. 108
Fig.8.2 RCinaplug-inscheme.
Fig.8.3 MPRCdiagram.
Fig.9.1 DiagramofrotorcurrentcontrolofDFIGusingMPRC-WM. 127
Fig.9.2
Fig.9.3
Fig.9.4
Fig.9.5
Fig.9.6
Fig.9.7
Fig.9.8
Fig.9.9
Fig.9.10
Fig.9.11
Fig.9.12
Fig.9.13
Fig.9.14
Fig.9.15
Fig.9.16
Fig.9.17
Fig.9.18
Fig.9.19
Fig.9.20
MPRC-WM.Steptestsforrotorcurrentvectorcomponents.
MPRC-WM.Detailsofthesteptestfor ir,q .
MPRC-WM.Detailofthesteptestfor ir,q :(a)statorvoltageandcurrent, (b)rotorcurrentvectorcomponents.
MPRC-WM.Detailsofthesteptestfor ir,d :(a)statorvoltageandcurrent, (b)rotorcurrentvectorcomponents.
MPRC-WM.Testusingseveral-speedoperation:(a)speedoftherotor, (b)rotorcurrentinrotorframe,and(c)rotorcurrentvectorcomponentsin the dq frame.
MPRC-WM.Testundervoltagedistortedby7%ofthe5thharmonic component:(a)statorvoltageandcurrent,(b)rotorcurrentvectorcomponents.
MPRC-WM.THDandharmonicscomponentsofstatorcurrent.
MPC-WM.Testundervoltagedistortedby7%ofthe5thharmonic component:(a)statorvoltageandcurrent,(b)rotorcurrentvectorcomponents.
MPC-WM.THDandharmonicscomponentsofthestatorcurrent.
DiagramofgridcurrentcontrolusingMPRC-WM.
MPRC-WM.Steptestsforactiveandreactivepower:(a)activepower, (b)reactivepower.
MPRC-WM.Detailsofthesteptestforactivepower:(a)activepower, (b)reactivepower.
MPRC-WM.Steptestsforgridcurrentvectorcomponents:(a)real componentofgridcurrentvector,(b)imaginarycomponentofgridcurrent vector.
MPRC-WM.Gridvoltageandcurrentactionduringsteptestofactivepower: (a)reactiveandactivepower,(b)gridvoltageandcurrent.
MPRC-WM.Gridvoltageandcurrentactionduringasteptestofreactive power:(a)reactiveandactivepower,(b)gridvoltageandcurrent.
MPRC-WM.Gridvoltageandcurrentactionduringasteptestofactive powerduringthedistortedgridvoltage:(a)reactiveandactivepower, (b)gridvoltageandcurrent.
MPRC-WM.THDofstatorcurrentduringthedistortedgridvoltage.
MPC-WM.Gridvoltageandcurrentactionduringasteptestofactivepower duringthedistortedgridvoltage:(a)reactiveandactivepower,(b)grid voltageandcurrent.
MPC-WM.THDofstatorcurrentduringthedistortedgridvoltage.
Fig.10.1 BasicstructureofthePLLblockdiagram.
Fig.10.2 PLLforthree-phasesystems’blockdiagram.
Fig.10.3 ExperimentalresultofSRF-PLLtestforunbalancedvoltagesag: (a)three-phasevoltage,(b)gridvoltageselementsinthe dq frame,(c)grid frequency,and(d)gridangle.
Fig.10.4 BlockdiagramofstructureoftheDSOGI.
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Fig.10.5 DiagramoftheDSOGI-MAF-FPS-PLL.
Fig.10.6
ExperimentalresultofDSOGI-MAF-FPS-PLLtestforunbalancedsag: (a)three-phasevoltage,(b)positivesequenceofthegridvoltageselementsin the dq frame,(c)gridfrequency,and(d)gridangle.
Fig.10.7 ExperimentalresultofDSOGI-MAF-FPS-PLLtestforvoltagesagwiththe 5thharmonic:(a)three-phasevoltage,(b)positivesequenceofthegrid voltageselementsinthe dq frame,(c)gridfrequency,and(d)gridangle.
Fig.10.8
ExperimentalresultofDSOGI-MAF-FPS-PLLtestunderdistortedvoltage: (a)three-phasevoltage,(b)positivesequenceofthegridvoltageselementsin the dq frame,(c)gridfrequency,and(d)gridangle.
Fig.11.1 Clarketransformation(CT).
Fig.11.2 Parktransformation(PT).
Fig.11.3 Parktransformation(PT)inSimulink.
Fig.11.4 InverseClarketransformation.
Fig.11.5 InverseParktransformation.
Fig.11.6 PWMinSimulink.
Fig.11.7 SVMinSimulink.
Fig.11.8 Modelforthree-phasepowerconverterinSimulink.
Fig.11.9 Three-phasegridvoltagesmodel.
Fig.11.10 Currents’blockofDFIGsimulationmodel.
Fig.11.11 Fluxes’blockofDFIGsimulationmodel.
Fig.11.12 TorqueblockofDFIGsimulationmodel.
Fig.11.13 DFIGsystemsimulationblock.
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Fig.11.14 Modelpredictivecontrolblock,MATLAB/Simulinkimplementation. 174
Fig.11.15 PredictiveRepetitivecontrolblock,MATLAB/Simulinkimplementation. 179
Fig.11.16 Completethree-phasepowerCCGmodelinSimulink.
Fig.11.17 CurrentreferenceinSimulink.
Fig.11.18 Modelpredictivecontrolblock,MATLAB/Simulinkimplementation. 187
Fig.12.1 TheexperimentalsetupofDFIGusedinMPCtests. 191
Fig.12.2 Theexperimentalsetupofthree-phaseCCGusedinMPCtests. 192
Fig.12.3 TheexperimentalsetupforPLLtests.
193
Listoftables Table2.1 Switchingstatesandvoltagevectors.
Table2.2 PWMtimescaledefinition.
Table2.3 Timesforregistersinfunctionofthesector.
Table3.1 Doubly-fedinductionmachineoperationconditions.
Table5.1 Switchingstatesandvoltagevectors.
Table5.2 Sectorofreferencerotorvoltagevector.
Table5.3 Calculationofthedutycycleoftheadjacentvectorstoeachsector k
inthe αβr frame.
Table6.1 Switchingstatesandvoltagevectors.
Table9.1 Distortedvoltageharmonicscomponents.
TableA.1 IMparameters.
TableB.1 Three-phasepowerCCGparameters.
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Listofcontributors CarlosE.Capovilla,FederalUniversityofABC,SantoAndré,SP,Brazil
IvanR.S.Casella,FederalUniversityofABC,SantoAndré,SP,Brazil
EliomarR.CondeD.,FederalUniversityofABC,SantoAndré,SP,Brazil
RogérioV.Jacomini,FederalInstituteofSãoPaulo,Hortolândia,SP,Brazil
FernandoLino,FederalUniversityofABC,SantoAndré,SP,Brazil
AngeloS.Lunardi,FederalUniversityofABC,SantoAndré,SP,Brazil
AlfeuJ.SguareziFilho,FederalUniversityofABC,SantoAndré,SP,Brazil
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Biography ProfessorDr.AlfeuJ.SguareziFilho
HewasborninCuiabá–MT–Brazilin1981,receivedhisElectricalEng.degreefromÁREA1–FacultyofEngineeringinBa–Brazilin2005,hisMaster’s andPhDdegreesfromCampinasUniversityinSP–Brazilin2007and2010, respectively.HeisIEEESeniormember.Since2012,heisafulltimeprofessor atFederalUniversityofABC–UFABC,inSantoAndré–SP–Brazil,teaching intheareasofElectricalMachines,PowerElectronics,andElectricalDrives.
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Abbreviationlist Abbreviations
ACAlternatingCurrent
CCGConverterConnectedtotheGrid
DCDirectCurrent
DFIGDoubly-FedInductionGenerator
DFTDiscreteFourierTransform
DPCDirectPowerControl
DTCDirectTorqueControl
DSPDigitalSignalProcessor
FCSFiniteControlSet
FOCFieldOrientedControl
IMInductionMachine
IMPInternalModelPrinciple
IGBTInsulated-GateBipolarTransistor
MPCModelPredictiveControl
MPRCModelPredictiveRepetitiveControl
PWMPulseWidthModulation
PIProportional-Integral
PLLPhaseLockedLoop
SPWMSinusoidalPWM
SVOCStatorVoltageOrientedControl
SVMSpaceVectorModulation
THSPWMThirdHarmonicSinusoidalPWM
RCRepetitiveControl
VSIVoltageSourceInverter
WMWithModulator
ZOHZeroOrderHold
Variablesandsymbols I m Imaginarycomponentofthecomplexnumber
Re Realcomponentofthecomplexnumber
i Instantaneousvalueofcurrentasafunctionoftime
l Relatedtotheharmoniccomponents
s Laplaceoperator
v Instantaneousvalueofvoltageasafunctionoftime #» v Voltagevector
Currentvector
Fluxvector J Costfunction
xxiv Abbreviationlist
TL Loadormechanicaltorque
ω Speedorangularfrequency
NP Polepairs
ny Predictionhorizon
nu Controlhorizon
R Resistance
L Inductance
Lm Mutualinductance
σ Globalleakage
Te Electromagnettorque
JJ Totalmomentofinertia
x State
u Incrementofinput
λs , |λs | Magnitudeofstatorflux
rmsRootmeansquarevalue
q 1 Backwardshiftoperator
k Instantsampling
(k + 1) Nextsampling
I Identitymatrix
O Zeromatrix
θ Angularposition
P Activepower
Q Reactivepower
Wy Weightingmatrixforpredictioneffort
Wu Weightingmatrixforcontroleffort
u Input out
Numberofoutputs
Superscript
“
∗ ”Conjugateofthecomplexnumber
Subscripts s Relatedtothestator
r Relatedtotherotor
g Relatedtotheelectricalgrid
αβ Relatedtothestationaryreferenceframe
α Relatedtotherealcomponentofthestationaryreferenceframe
β Relatedtotheimaginarycomponentofthestationaryreferenceframe
αβr Relatedtotherotorreferenceframe
αr Relatedtotherealcomponentoftherotorreferenceframe
βr Relatedtotheimaginatycomponentoftherotorreferenceframe
ρ Relatedtothefilterorder
dq Relatedtothesynchronousreferenceframe
d Relatedtotherealcomponentofthesynchronousreferenceframe
q Relatedtotheimaginatycomponentofthesynchronousreferenceframe
ee Relatedtotheexpandedmodel
ir Relatedtotherotorcurrent
mec Relatedtothemechanicalcomponentsofthemachine
pq Relatedtothestatoractiveandreactivepower
ref Relatedtothereferences
sl Relatedtotheslip
Chapter1 Introduction AlfeuJ.SguareziFilho
FederalUniversityofABC,SantoAndré,SP,Brazil
1.1Overview
Theevolutionofpowersemiconductorcomponentspermittedprocessingpower atlevelsofthousandsofvoltsandampers.Inthiscontext,severalpowerelectronicsdevicesbuiltwitharrangementsofthesesemiconductorelementsenabledtheconversionofenergyfromAC–AC,withdifferentfrequenciesand amplitudes,DC–AC,AC–DC,andDC–AC[1].Thus,itwaspossibletomake thedifferentwaysofusingelectricenergymoreflexibleand,consequently,to diversifythewaysofitsapplication.Finally,theevolutionofpowersemiconductors,theincreaseintheprocessingandstoragecapacityofprocessorsand theirperipherals,respectively,enabledgreaterflexibilityintheimplementation ofmorecomplexcontrolalgorithms.
Oneapplicationofpowerelectronicsisinrenewableenergysuchaswind, smallhydroelectricplants,orinelectricalenergystoragesystems,amongothers [2].Thistypeofapplicationisimportantduetothegrowingdemandforenergy indevelopedanddevelopingcountries,andinthesearchforalternativeenergy sourcesratherthanusingfossilfuels.Inthiscase,powerelectronicscanbeused toprocessenergyfromelectricgeneratorsortoprocessenergypresentinthe energystoragesystems.
Amongthegeneratorsemployedintherenewableenergy,thedoubly-fedinductiongenerator(DFIG)hasbecomepopular.Thistypeofgeneratoremerged asanalternativetopermanentmagnetssynchronousgenerators,duetoitslow costandrobustness.TheordinaryconfigurationofDFIGemployedinrenewableenergysystemshasitsstatorconnecteddirectlytothegridanditsrotor connectedtothegridthroughabidirectionalconverter,whichprocessesamaximumof30%ofthetotalpowerofthegenerator[3].Inthisway,itdecreasesthe costofthesystem.Thebidirectionalconverter,calledback-to-backconverter, isanarrangementoftwoelectronicpowerconvertersthathaveACinput/output andsharethesameDClink.AdiagramoftheDFIGusingthisconfigurationis depictedinFig. 1.1.Itispossibletonoticethebasicstructureofthegridandrotorsideconverterscontrolusingthemeasurementsofcurrent,torque,poweror speedofthegenerator,orusingthemeasurementsofcurrent,voltageorpower ofthegrid.
