Introduction toModernAnalysis of Electric Machines and Drives ffirs3d 1 30/11/2022 3:24:31PM IEEEPress 445HoesLane Piscataway,NJ08854 IEEEPressEditorialBoard SarahSpurgeon,EditorinChief JónAtliBenediktsson AndreasMolisch DiomidisSpinellis AnjanBose SaeidNahavandi AhmetMuratTekalp AdamDrobot JeffreyReed Peter(Yong)Lian ThomasRobertazzi ffirs3d 2 30/11/2022 3:24:31PM Introduction to Modern Analysis of Electric Machines and Drives Paul C. Krause Thomas C. Krause IEEE Press Series on Power and Energy Systems Ganesh Kumar Venayagamoorthy, Series Editor ffirs3d 3 30/11/2022 3:24:31PM Copyright©2023byTheInstituteofElectricalandElectronicsEngineers,Inc.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. 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Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprint maynotbeavailableinelectronicformats.FormoreinformationaboutWileyproducts,visitour websiteatwww.wiley.com. LibraryofCongressCataloging-in-PublicationData Names:Krause,PaulC.,author.|Krause,ThomasC.,author. Title:Introductiontomodernanalysisofelectricmachinesanddrives/ PaulC.Krause,ThomasC.Krause. Description:Hoboken:Wiley,[2023]|Series:IEEEPressseriesonpower andenergysystems|Includesbibliographicalreferencesandindex. Identifiers:LCCN2022032455(print)|LCCN2022032456(ebook)|ISBN 9781119908159(hardback)|ISBN9781119908166(adobepdf)|ISBN 9781119908173(epub) Subjects:LCSH:Electricmachinery.|Electricdriving. Classification:LCCTK2000.K682023 (print)|LCCTK2000 (ebook)|DDC 621.31/042–dc23/eng/20220824 LCrecordavailableathttps://lccn.loc.gov/2022032455 LCebookrecordavailableathttps://lccn.loc.gov/2022032456 Setin9.5/12.5ptSTIXTwoTextbyStraive,Pondicherry,India ffirs3d 4 30/11/2022 3:24:31PM v Contents AuthorBiography ix Foreword xi Preface xv 1 CommonAnalysisTools 1 1.1 Introduction 1 1.2 Steady-StatePhasorCalculations 1 1.2.1 PowerandReactivePower 7 1.3 StationaryMagneticallyLinearSystems 9 1.3.1 Two-WindingTransformer 13 1.4 WindingConfigurations 18 1.5 Two-andThree-PhaseStators 23 1.5.1 Two-PhaseStator 23 1.5.2 Three-PhaseStator 25 1.5.3 Line-to-LineVoltage 28 1.6 Problems 30 Reference 32 2 AnalysisoftheSymmetricalStator 33 2.1 Introduction 33 2.2 Tesla’sRotatingMagneticField 33 2.2.1 Two-PoleTwo-PhaseStator 34 2.2.2 Two-PoleThree-PhaseStator 39 2.3 ReferenceFrameTheory 41 2.3.1 Two-PhaseTransformation 41 2.3.2 Three-PhaseTransformation 43 2.4 StatorVoltageandFluxLinkageEquationsintheArbitraryReference FrameandtheInstantaneousPhasor 46 ftoc3d 5 29/11/2022 4:57:30PM vi Contents 2.4.1 Two-PhaseStator 46 2.4.2 Three-PhaseStator 49 2.4.3 InstantaneousandSteady-StatePhasors 50 2.5 Problems 52 References 53 3 SymmetricalInductionMachine 55 3.1 Introduction 55 3.2 SymmetricalMachines 55 3.3 SymmetricalTwo-PoleRotorWindings 59 3.3.1 Two-PhaseRotorWindings 59 3.3.2 Three-PhaseRotorWindings 62 3.4 SubstituteVariablesForSymmetricalRotatingCircuitsandEquivalent Circuit 62 3.4.1 Two-PhaseMachine 62 3.4.2 Three-PhaseMachine 70 3.5 ElectromagneticForceandTorque 70 3.6 P-PoleMachines 78 3.7 FreeAccelerationVariablesViewedfromDifferentReference Frames 83 3.8 Steady-StateEquivalentCircuit 89 3.9 Problems 102 References 104 4 SynchronousMachines 105 4.1 Introduction 105 4.2 AnalysisofthePermanent-MagnetacMotor 106 4.2.1 Torque 109 4.2.2 UnequalDirect–andQuadrature–AxisInductances 112 4.2.3 Three-PhaseMachine 116 4.3 WindingsoftheSynchronousMachine 117 4.4 EquivalentCircuit–VoltageandTorqueEquations 120 4.4.1 Torque 122 4.4.2 RotorAngle 122 4.5 DynamicandSteady-StatePerformances 123 4.6 AnalysisofSteady-StateOperation 127 4.7 TransientStability 130 4.7.1 Three-PhaseFault 130 4.8 Problems 136 Reference 136 ftoc3d 6 29/11/2022 4:57:30PM Contents vii 5 DirectCurrentMachineandDrive 137 5.1 Introduction 137 5.2 Commutation 138 5.3 VoltageandTorqueEquations 141 5.4 Permanent-MagnetdcMachine 143 5.5 DCDrive 146 5.5.1 Average-ValueTime-DomainBlockDiagram 148 5.5.2 TorqueControl 149 5.6 Problems 151 Reference 152 6 BrushlessdcandField-OrientedDrives 153 6.1 Introduction 153 6.2 TheBrushlessdcDriveConfiguration 154 6.3 NormalModeofBrushlessdcDriveOperation 159 6.4 OtherModesofBrushlessdcDriveOperation 166 6.4.1 Maximum-TorquePerVoltOperationofaBrushlessdcDrive (ϕ =ϕ ) 166 v vMT V 6.4.2 Maximum-TorquePerAmpereOperationofaBrushlessdcDrive (ϕ =ϕ ) 170 v vMT A 6.4.3 TorqueControl 174 6.5 Field-OrientedInductionMotorDrive 177 6.6 Problems 185 References 186 7 Single-PhaseInductionMotors 187 7.1 Introduction 187 7.2 SymmetricalComponents 188 7.3 AnalysisofUnbalancedModesofOperation 192 7.3.1 UnbalancedStatorVoltages 194 7.3.2 UnbalancedStatorImpedances 197 7.3.3 Open-CircuitedStatorPhase 199 7.4 Single-PhaseandCapacitor-StartInductionMotors 200 7.4.1 Single-PhaseInductionMotor 200 7.4.2 Capacitor-StartInductionMotor 201 7.5 DynamicandSteady-StatePerformanceofaCapacitor-StartSingle-Phase InductionMotor 204 7.6 Split-PhaseInductionMotor 207 7.7 Problems 208 References 209 ftoc3d 7 29/11/2022 4:57:30PM viii Contents 8 StepperMotors 211 8.1 Introduction 211 8.2 BasicConfigurationsofMultistackVariable-ReluctanceStepper Motors 211 8.3 EquationsforMultistackVariable-ReluctanceStepperMotors 218 8.4 OperatingCharacteristicsofMultistackVariableReluctanceStepper Motors 221 8.5 Single-StackVariable-ReluctanceStepperMotors 225 8.6 BasicConfigurationofPermanent-MagnetStepperMotors 229 8.7 EquationsforPermanent-MagnetStepperMotors 233 8.8 Problems 236 References 237 AppendixA Abbreviations,Constants,Conversions,andIdentities 238 Epilogue 241 Index 245 ftoc3d 8 29/11/2022 4:57:31PM