Voltage Stability in ElectricalPower Systems IEEEPress 445HoesLane Piscataway,NJ08854 IEEEPressEditorialBoard SarahSpurgeon,EditorinChief JónAtliBenediktsson AndreasMolisch DiomidisSpinellis AnjanBose SaeidNahavandi AhmetMuratTekalp AdamDrobot JeffreyReed Peter(Yong)Lian ThomasRobertazzi Voltage Stability in Electrical Power Systems Concepts, Assessment, and Methods for Improvement Farid Karbalaei Shahid Rajaee Teacher Training University Tehran, Iran Shahriar Abbasi Technical and Vocational University of Iran Kermanshah, Iran Hamid Reza Shabani Aalborg University Esbjerg, Denmark Copyright©2023byTheInstituteofElectricalandElectronicsEngineers,Inc.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. 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Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,pleasecontact ourCustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outsidetheUnited Statesat(317)572-3993orfax(317)572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprint maynotbeavailableinelectronicformats.FormoreinformationaboutWileyproducts,visitour websiteatwww.wiley.com. LibraryofCongressCataloging-in-PublicationData: Names:Karbalaei,Farid,author.|Abbasi,Shahriar(AssistantProfessor), author.|Shabani,HamidReza,author. Title:Voltagestabilityinelectricalpowersystems:concepts, assessment,andmethodsforimprovement/FaridKarbalaei,Shahriar Abbasi,andHamidRezaShabani. Description:Hoboken,NewJersey:Wiley,[2023]|Includesindex. Identifiers:LCCN2022041340(print)|LCCN2022041341(ebook)|ISBN 9781119830597(hardback)|ISBN9781119830641(adobepdf)|ISBN 9781119830658(epub) Subjects:LCSH:Electricpowersystemstability.|Electricpower systems–Control. Classification:LCCTK1010.K3672022 (print)|LCCTK1010 (ebook)|DDC 621.319–dc23/eng/20220919 LCrecordavailableathttps://lccn.loc.gov/2022041340 LCebookrecordavailableathttps://lccn.loc.gov/2022041341 CoverDesign:Wiley CoverImage:©SergMyshkovsky/GettyImages Setin9.5/12.5ptSTIXTwoTextbyStraive,Pondicherry,India Toourfamilies vii Contents AuthorBiographies xiii Preface xiv PartI ConceptofVoltageStability,EffectiveFactorsandDevices, andSuitableSystemModeling 1 1 HowDoesVoltageInstabilityOccur? 3 1.1 Introduction 3 1.2 Long-TermVoltageInstability 5 1.2.1 ASimpleSystem 5 1.2.2 VoltageCalculation 6 1.2.3 IllustrationofVoltageCollapse 7 1.2.4 TheReasonofVoltageCollapseOccurrence 8 1.2.5 TheImportanceofTimelyEmergencyMeasures 11 1.3 Short-TermVoltageInstability 13 1.3.1 TheProcessofInductionMotorsStalling 14 1.3.2 DynamicAnalysis 15 1.3.3 StaticAnalysis 17 1.3.4 TheRelationshipBetweenShort-TermVoltageInstabilityand LoadabilityLimit 19 1.4 Summary 20 References 20 2 LoadsandLoadTapChanger(LTC)TransformerModeling 21 2.1 Introduction 21 2.2 StaticLoadModels 24 2.2.1 TheConstantPowerModel 24 2.2.2 ThePolynomialandExponentialModels 25 viii Contents 2.3 DynamicLoadModels 26 2.3.1 ExponentialRecoveryModel 27 2.3.2 InductionMotorModel 31 2.4 TheLTCTransformers 35 2.4.1 TheLTCPerformance 35 2.4.2 TheLTCModeling 36 2.4.3 TheLTCTransformerModel 38 2.5 Summary 44 References 44 3 GeneratorModeling 47 3.1 Introduction 47 3.2 SynchronousGeneratorModeling 47 3.2.1 SynchronousMachineStructure 48 3.2.2 DynamicEquations 48 3.2.3 VoltageandCurrentPhasors 52 3.2.4 Steady-StateEquations 54 3.2.5 SimplificationofSynchronousMachineEquations 56 3.2.6 SaturationModeling 57 3.2.7 SynchronousGeneratorCapabilityCurve 59 3.2.8 ExcitationSystemModeling 62 3.2.9 GovernorModeling 63 3.2.10 OverexcitationLimiter(OXL)Modeling 65 3.3 WindPowerPlants 66 3.3.1 Fixed-SpeedInductionGenerator(FSIG)-basedWindTurbine 69 3.3.1.1 PhysicalDescription 69 3.3.1.2 InductionMachineSteady-StateModel 69 3.3.1.3 InductionGeneratorDynamicModel 72 3.3.2 DoublyFedInductionGenerator(DFIG)-basedWindTurbine 75 3.3.2.1 PhysicalDescription 75 3.3.2.2 DFIGSteady-StateCharacteristic 76 3.3.2.3 OptimumWindPowerExtraction[5] 77 3.3.2.4 TorqueControl 78 3.3.2.5 VoltageControl 80 3.4 Summary 81 References 82 4 ImpactofDistributedGenerationandTransmission–Distribution InteractionsonVoltageStability 83 4.1 Introduction 83 4.2 InteractionsofTransmissionandDistributionNetworks 83