Small-Signal Stability Analysis of Power Systems Integrated with Variable Speed Wind Generators

362 Pages·2018·19.035 MB·English

by  Wenjuan Du, Haifeng Wang, Siqi Bu

Wenjuan Du · Haifeng Wang · Siqi Bu
Small-Signal Stability
Analysis of Power
Systems Integrated
with Variable Speed
Wind Generators
Small-Signal Stability Analysis of Power Systems
Integrated with Variable Speed Wind Generators
(cid:129) (cid:129)
Wenjuan Du Haifeng Wang Siqi Bu
Small-Signal Stability
Analysis of Power Systems
Integrated with Variable
Speed Wind Generators
WenjuanDu HaifengWang
SchoolofElectricalandElectronic SchoolofElectricalandElectronic
Engineering Engineering
NorthChinaElectricPowerUniversity NorthChinaElectricPowerUniversity
Beijing,China Beijing,China
SiqiBu
DepartmentofElectricalEngineering
TheHongKongPolytechnicUniversity
Kowloon,HongKong
ISBN978-3-319-94167-7 ISBN978-3-319-94168-4 (eBook)
https://doi.org/10.1007/978-3-319-94168-4
LibraryofCongressControlNumber:2018947164
©SpringerInternationalPublishingAG,partofSpringerNature2018
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor
informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt
fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsorthe
editorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforanyerrors
oromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictionalclaims
inpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG.
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Preface
Doublyfedinductiongeneratorsandpermanentmagnetsynchronousgeneratorsare
thetwomaintypesofvariablespeedwindgenerators.Changesbroughtaboutbythe
grid connection of variable speed wind generators in an AC power system are
twofold. Firstly, unlike conventional synchronous generators, which are linked
directly to the power system, a variable speed wind generator is connected to the
gridviacontrolledvoltagesourceconverters.Thedynamicbehaviorofthevariable
speedwindgeneratorissignificantlydifferentfromthatofasynchronousgenerator.
Theimpactofdynamicinteractionsintroducedbythegrid-connectedvariablespeed
wind generator on power system stability needs to be examined carefully. In
addition, wind generation is variable due to the stochastic fluctuation of wind
speed. It is important to investigate how the random variation of wind speed may
affectpowersystemstability.Secondly,VSC-basedHVDClinesandmulti-terminal
DC (MTDC) networks for large scale wind power generation, especially for the
offshore wind power, have many technical advantages. Stability of a VSC-based
DC/AC power system with wind power generation is an important aspect of the
impactbroughtaboutbygrid-connectedvariablespeedwindgeneratorandneedsto
bestudied.
We started the investigation on the small-signal stability of the power system
affectedby thegrid-connectedvariablespeed wind generatorsabout a decade ago.
Ourinvestigationhascovered thetwoimportantaspectsmentioned above,i.e.,the
small-signal stability of the power system considering the impact of dynamic
interactions introduced by the VSWGs, the stochastic variations of wind speed,
andtheintegrationofVSC-basedHVDClinesandMTDCnetwork.Inthisbook,we
introducethesmall-signalstabilityanalysisofthepowersystemintegratedwiththe
variablespeedwindgeneratorsbymainlypresentingtheresultsofourinvestigation
made in the last decade. Two main methods for the investigation are the damping
torqueanalysisandmodalanalysis.Theirapplicationstoexaminetheimpactofgrid-
connectedvariablespeedwindgeneratorsonpowersystemsmall-signalstabilityare
comprehensively introduced in the book. It is worth mentioning particularly one
important phenomenon we have found recently. That is the possibility of strong
v
vi Preface
dynamic interactions introduced by the grid-connected variable speed wind gener-
atorstodegradethesmall-signalstabilityofthepowersystemundertheconditionof
open-loop modal resonance. Although we are still studying the phenomenon from
theaspectsoftheoreticalanalysisandpracticalapplications,weintroducetheinitial
resultsofourinvestigationinthebook.Wehopethepotentialinstabilityriskbrought
aboutbytheopen-loopmodalresonanceshouldbeawareofandunderstoodfullyby
morepowersystemresearchersandengineers.
Wewouldliketothankthecontributionsfromourresearchstudentstothebook.
They areMr. XiaoCHEN,Mr. Jintian BI,Mr. QiangFU, Mr. Xubin WANG, and
Mr.WenkaiDONG.
Beijing,China WenjuanDu
Beijing,China HaifengWang
Kowloon,HongKong SiqiBu
April2018
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ImpactofGrid-ConnectedVSWGsontheSmall-Signal
AngularStabilityofPowerSystem. . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 ImpactoftheVSWGs:ABriefReview. . . . . . . . . . . . . . . 2
1.1.2 ImpactoftheVSWGs:Discussions. . . . . . . . . . . . . . . . . . 5
1.2 Small-SignalStabilityoftheVSC-BasedDC/AC
PowerSystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.1 Small-SignalStabilityofaSingleGrid-Connected
VSCSystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.2 Small-SignalStabilityofIntegratedVSC-Based
DC/ACPowerSystems. . . . . . . . . . . . . . . . . . . . . . . . . . 16
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 LinearizedModelofaPowerSystemwithaGrid-Connected
VariableSpeedWindGenerator. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1 LinearizedModelofaPMSG. . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.1 LinearizedModelofthePermanentMagnetSG. . . . . . . . . 27
2.1.2 LinearizedModelofMachineSideConverter
andAssociatedControlSystem. . . . . . . . . . . . . . . . . .. . . 30
2.1.3 LinearizedModelofGridSideConverter
andAssociatedControlSystem. . . . . . . . . . . . . . . . . .. . . 33
2.1.4 LinearizedModeloftheEntirePMSGSystem. . . . . . . . . . 39
2.2 LinearizedModelofaDFIG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.1 LinearizedModeloftheInductionGenerator
andTwo-MassShaftRotationalSystem. . . . . . . . . . . . . . 41
2.2.2 LinearizedModeloftheRSCandAssociated
ControlSystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2.3 LinearizedModeloftheGSCandAssociated
ControlSystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.4 LinearizedModeloftheEntireDFIG. . . . . . . . . . . . . . . . 53
vii
viii Contents
2.3 LinearizedModelofthePowerSystem. . . . . . . . . . . . . . . . . . . . 55
2.4 Closed-LoopInterconnectedModelofthePowerSystem
withaGrid-ConnectedVSWG. . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.1 Closed-LoopInterconnectedModelofthePower
SystemwithaPMSG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.2 Closed-LoopInterconnectedModelofthePower
SystemwithaDFIG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3 DampingTorqueAnalysisofSmall-SignalAngularStability
ofaPowerSystemAffectedbyGrid-ConnectedWindPower
InductionGenerators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1 ImpactofGrid-ConnectedWindPowerInduction
GeneratorsonSmall-SignalAngularStability. . . . . . . . . . . . . . . . 63
3.2 SystemModelingforDampingTorqueAnalysis
ofaPowerSystemAffectedbyGrid-ConnectedWindPower
InductionGenerators. . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . .. . 65
3.2.1 Phillips-HeffronModelofaPowerSystem
withWindPowerInductionGeneratorsasaGeneric
Open-LoopController. . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.2 AggregateModelandTransferFunctionofWind
PowerInductionGenerators. . . . . . . . . . . . . . . . . . . . . . . 69
3.3 ImplementationFrameworkforDampingTorqueAnalysis
ofaPowerSystemAffectedbyGrid-ConnectedWind
PowerInductionGenerators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4 AnalyticalComparisononDampingEffectiveness
AndRobustnessofType1and3WindPower
InductionGenerators. . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . .. . 72
3.4.1 Step1:DetailedDFIGModel. . . . . . . . . . . . . . . . . . . . . . 73
3.4.2 Step2:DFIGModelWithoutRSCDynamics. . . . . . . . . . 75
3.4.3 Step3:DFIGModelwithOffsetRotorVoltageOnly. . . . . 77
3.4.4 Step4:DFIGModelwithConstantRotorVoltage. . . . . . . 77
3.4.5 Step5:FSIGModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.4.6 MainFindingsinAnalyticalComparisononDamping
MechanismofType1and3WindPowerInduction
Generators.. . . . . .. . . . .. . . . . .. . . . .. . . . . .. . . . .. . 79
3.5 NumericalComparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.5.1 Example3.1(BaseCaseComparisonStudy). . . . . . . . . . . 80
3.5.2 Example3.2(ComparisonStudyUnderDifferent
WindPenetrationConditions). . . . . . . . . . . . . . . . . . . . . . 84
3.6 SummaryofAnalyticalandNumericalComparisonAnalysis. . . . 86
Contents ix
Appendix3.1:ATypicalExampleofaSMIBSystem
withInterfaceEquationsofaWPIG. . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Appendix3.2:DataofExamples3.1and3.2. . . . . . . . . . . . . . . . . . . . 88
Example16-Machine68-BusNewYorkandNewEngland
PowerSystem[36](Tables3.4,3.5and3.6). . . . . . . . . . . . . .. . . 88
DataofDFIGandFSIG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4 ModalAnalysisofSmall-SignalAngularStabilityofaPowerSystem
AffectedbyGrid-ConnectedDFIG. . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.1 DecomposedModalAnalysisoftheImpactofaGrid-Connected
DFIGonPowerSystemSmall-SignalAngularStability. . . . . . . . 97
4.1.1 MethodofDecomposedModalAnalysis. . . . . . . . . . . . . . 97
4.1.2 Example4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2 ImpactofDynamicInteractionsIntroducedbyaGrid-Connected
DFIGonPowerSystemSmall-SignalAngularStability. . . . . . . . 110
4.2.1 TheIndexofDynamicInteractions(IDI). . . . . . . . . . . . . . 111
4.2.2 TheImpactofDynamicInteractionsIntroduced
bytheDFIG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.2.3 Example4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Appendix4.1:DataofExample4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Example16-Machine68-BusNewYorkandNewEngland
PowerSystem[3](Tables4.10,4.11,4.12). . . . . . . . . . . . . . . . . 138
DataofDFIG[4](Tables4.13,4.14,4.15). . . . . . . . . . . . . . . . . . 143
Appendix4.2:DataofExample4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . 143
DataofNewEnglandPowerSystem[13](Tables4.16,4.17
and4.18). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
DataofDFIG[16](Tables4.19,4.20and4.21). . . . . . . . . . . . . . 146
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5 Small-SignalAngularStabilityofaPowerSystemAffected
byStrongDynamicInteractionsIntroducedfrom
aGrid-ConnectedVSWG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.1 ImpactofStrongDynamicInteractionsIntroduced
byaGrid-ConnectedPMSG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.1.1 StrongDynamicInteractionsIntroduced
bytheGrid-ConnectedPMSGandtheImpact. . . . . . . . . . 149
5.1.2 Example5.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.2 ImpactofStrongDynamicInteractionsIntroduced
byaGrid-ConnectedDFIG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5.2.1 StrongDynamicInteractionsIntroduced
bytheGrid-ConnectedDFIGandtheImpact. . . . . . . . . . . 173
5.2.2 Example5.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
x Contents
Appendix5.1:DataofExamples5.1and5.2. . . . . . . . . . . . . . . . . . . . 199
DataofNewEnglandPowerSystem. . . . . . . . . . . . . . . . . . . . . . 199
DataofDFIG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
DataofPMSG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
6 Small-SignalStabilityofaPowerSystemwithaVSWG
AffectedbythePLL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
6.1 ImpactofOpen-LoopModalResonanceCaused
bythePLLforaGrid-ConnectedPMSG. . . . . . . . . . . . . . . . . . . 203
6.1.1 Closed-LoopInterconnectedModelofaPower
SystemwithaPMSG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
6.1.2 Open-LoopModalResonanceCausedbythePLL. . . . . . . 206
6.2 Small-SignalStabilityofaGrid-ConnectedPMSGWind
FarmAffectedbythePLL. . . . .. . . . . . . . . . . .. . . . . . . . . . .. . 209
6.2.1 Example6.1:APMSGConnectedtoanExternal
PowerSystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
6.2.2 Example6.2:APMSGWindFarmConnected
toanExternalPowerSystem. . . . . . . . . . . . . . . . . . . . . . 219
6.3 Example6.3:ElectromechanicalOscillationModes
ofaPowerSystemAffectedbythePLL. . . . . . . . . . . . . . . . . . . . 222
6.3.1 Test1:ChangesofPowerSystem
OperatingConditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
6.3.2 Test2:VariationofPLLGains(SRFPLLforPMSG1). . . 227
6.3.3 Test3:VariationofSCRandWindPower
Penetration(SRFPLLforPMSG1). . . . . . . . . . . . . . . . . . 232
6.3.4 Test4:DSOGIPLLforPMSG. . . . . . . . . . . . . . . . . . . . . 235
6.3.5 Test5:TheCaseofDFIG. . . . . . . . . . . . . . . . . . . . . . . . 236
Appendix6.1:DataofExample6.1(Tables6.5,6.6and6.7). . . . . . . . . 240
Appendix6.2:DataofExample6.2. . . . . . . . . . . . . . . . . . . . . . . . . . . 240
DataofPMSG1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
LineData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
Appendix6.3:DataofExample6.3. . . . . . . . . . . . . . . . . . . . . . . . . . . 240
DataofNewEnglandPowerSystem. . . . . . . . . . . . . . . . . . . . . . 240
DataofPMSG(Tables6.8,6.9and6.10). . . . . . . . . . . . . . . . . . . 240
DataofSRFPLL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
7 Small-SignalStabilityofaPowerSystemIntegratedwithan
MTDCNetworkfortheWindPowerTransmission. . . . . . . . . . . . . 243
7.1 Small-SignalAngularStabilityofanACPowerSystem
AffectedbytheIntegrationofanMTDCNetwork
fortheWindPowerTransmission. . . . . . . . . . . . . . . . . . . . . . . . 244
7.1.1 TheOpen-LoopModalResonance(OLMR)
intheMTDC/ACPowerSystem. . . . . . . . . . . . . . . . . . . . 244
7.1.2 ExampleMTDC/ACPowerSystems. . . . . . . . . . . . . . . . . 256