Introduction to AC machine design

524 Pages·2017·16.03 MB·English

by  T. A

INTRODUCTION TO
AC MACHINE DESIGN
IEEEPress
445HoesLane
Piscataway,NJ08854
IEEEPressEditorialBoard
TariqSamad,EditorinChief
GiancarloFortino XiaoouLi RayPerez
DmitryGoldgof AndreasMolisch LindaShafer
DonHeirman SaeidNahavandi MohammadShahidehpour
EkramHossain JeffreyNanzer ZidongWang
INTRODUCTION TO
AC MACHINE DESIGN
THOMAS A. LIPO
EmeritusProfessor
UniversityofWisconsin
Madison,WI
ResearchProfessor
FloridaStateUniversity
Tallahassee,FL
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CONTENTS
PREFACEANDACKNOWLEDGMENTS xiii
LISTOFPRINCIPALSYMBOLS xv
ABOUTTHEAUTHOR xxiii
CHAPTER1 MAGNETICCIRCUITS 1
1.1 Biot–SavartLaw 1
1.2 TheMagneticFieldB 2
1.3 Example—ComputationofFluxDensityB 3
1.4 TheMagneticVectorPotentialA 5
1.5 Example—CalculationofMagneticFieldfromtheMagneticVectorPotential 6
1.6 ConceptofMagneticFlux 7
1.7 TheElectricFieldE 9
1.8 Ampere’sLaw 10
1.9 MagneticFieldIntensityH 12
1.10 BoundaryConditionsforBandH 15
1.11 Faraday’sLaw 17
1.12 InducedElectricFieldDuetoMotion 18
1.13 Permeance,Reluctance,andtheMagneticCircuit 19
1.14 Example—SquareToroid 23
1.15 MultipleCircuitPaths 23
1.16 GeneralExpressionforReluctance 24
1.17 Inductance 27
1.18 Example—InternalInductanceofaWireSegment 28
1.19 MagneticFieldEnergy 29
1.20 TheProblemofUnits 31
1.21 MagneticPathsWhollyinIron 33
1.22 MagneticMaterials 35
1.23 Example—TransformerStructure 37
1.24 MagneticCircuitswithAirGaps 40
1.25 Example—MagneticStructurewithSaturation 42
1.26 Example—CalculationforSeries–ParallelIronPaths 43
1.27 MultipleWindingMagneticCircuits 44
1.28 MagneticCircuitsAppliedtoElectricalMachines 46
1.29 EffectofExcitationCoilPlacement 48
1.30 Conclusion 50
Reference 50
vii
viii CONTENTS
CHAPTER2 THEMMFANDFIELDDISTRIBUTIONOFANACWINDING 51
2.1 MMFandFieldDistributionofaFull-PitchWindingforaTwoPoleMachine 51
2.2 FractionalPitchWindingforaTwo-PoleMachine 54
2.3 DistributedWindings 56
2.4 ConcentricWindings 62
2.5 EffectofSlotOpenings 64
2.6 FractionalSlotWindings 67
2.7 WindingSkew 70
2.8 PolePairsandCircuitsGreaterthanOne 73
2.9 MMFDistributionforThree-PhaseWindings 73
2.10 ConceptofanEquivalentTwo-PhaseMachine 76
2.11 Conclusion 77
References 77
CHAPTER3 MAINFLUXPATHCALCULATIONSUSINGMAGNETICCIRCUITS 79
3.1 TheMainMagneticCircuitofanInductionMachine 79
3.2 TheEffectiveGapandCarter’sCoefficient 80
3.3 TheEffectiveLength 84
3.4 CalculationofToothReluctance 86
3.5 Example1—ToothMMFDrop 89
3.6 CalculationofCoreReluctance 94
3.7 Example2—MMFDropOverMainMagneticCircuit 102
3.8 MagneticEquivalentCircuit 111
3.9 FluxDistributioninHighlySaturatedMachines 112
3.10 CalculationofMagnetizingReactance 116
3.11 Example3—CalculationofMagnetizingInductance 120
3.12 Conclusion 123
References 124
CHAPTER4 USEOFMAGNETICCIRCUITSINLEAKAGEREACTANCE
CALCULATIONS 125
4.1 ComponentsofLeakageFluxinInductionMachines 125
4.2 SpecificPermeance 127
4.3 SlotLeakagePermeanceCalculations 129
4.4 SlotLeakageInductanceofaSingle-LayerWinding 134
4.5 SlotLeakagePermeanceofTwo-LayerWindings 135
4.6 SlotLeakageInductancesofaDouble-CageWinding 137
4.7 SlotLeakageInductanceofaDouble-LayerWinding 139
4.8 End-WindingLeakageInductance 144
4.8.1 MethodofImages 144
4.8.2 End-WindingLeakageInductanceofRandom-WoundCoils 147
4.8.3 End-WindingLeakageInductanceofaCoilwithStatorIronTreated
asaPerfectConductor 148
4.8.4 End-WindingLeakageInductanceofaCoilwithStatorIronTreated
asAir 150
4.8.5 End-WindingLeakageInductanceperPhase 153
4.8.6 End-WindingLeakageofForm-WoundCoils 153
4.8.7 Squirrel-CageEnd-WindingInductance 155
CONTENTS ix
4.9 StatorHarmonicorBeltLeakage 156
4.10 ZigzagLeakageInductance 159
4.11 Example4—CalculationofLeakageInductances 164
4.12 EffectiveResistanceandInductancePerPhaseofSquirrel-CageRotor 171
4.13 FundamentalComponentofRotorAirGapMMF 175
4.14 RotorHarmonicLeakageInductance 177
4.15 CalculationofMutualInductances 181
4.16 Example5—CalculationofRotorLeakageInductancePerPhase 186
4.17 SkewLeakageInductance 187
4.18 Example6—CalculationofSkewLeakageEffects 189
4.19 Conclusion 190
References 190
CHAPTER5 CALCULATIONOFINDUCTIONMACHINELOSSES 193
5.1 Introduction 193
5.2 EddyCurrentEffectsinConductors 194
5.3 CalculationofStatorResistance 203
5.4 Example7—CalculationofStatorandRotorResistance 205
5.5 RotorParametersofIrregularlyShapedBars 212
5.6 CategoriesofElectricalSteels 216
5.7 CoreLossesDuetoFundamentalFluxComponent 217
5.8 StrayLoadandNo-LoadLosses 222
5.9 CalculationofSurfaceIronLossesDuetoStatorSlotting 228
5.10 CalculationofToothPulsationIronLosses 237
5.11 FrictionandWindageLosses 244
5.12 Example8—CalculationofIronLossResistances 244
5.13 Conclusion 250
References 250
CHAPTER6 PRINCIPLESOFDESIGN 251
6.1 DesignFactors 251
6.2 StandardsforMachineConstruction 252
6.3 MainDesignFeatures 255
6.4 TheD2LOutputCoefficient 258
6.4.1 Essen’sRule 259
6.4.2 MagneticShearStress 261
6.4.3 TheAspectRatio 265
6.4.4 BaseImpedance 268
6.5 TheD3LOutputCoefficient 269
6.6 PowerLossDensity 277
6.7 TheD2.5LSizingEquation 277
6.8 ChoiceofMagneticLoading 278
6.8.1 MaximumFluxDensityinIron 279
6.8.2 MagnetizingCurrent 280
6.9 ChoiceofElectricLoading 281
6.9.1 VoltageRating 281
6.9.2 CurrentDensityConstraints 282
6.9.3 RepresentativeValuesofCurrentDensity 285
x CONTENTS
6.10 PracticalConsiderationsConcerningStatorConstruction 287
6.10.1 RandomWoundvs.FormedCoilWindings 288
6.10.2 Deltavs.WyeConnection 289
6.10.3 LaminationInsulation 290
6.10.4 SelectionofStatorSlotNumber 290
6.10.5 ChoiceofDimensionsofActiveMaterialforNEMADesigns 291
6.10.6 SelectionofWireSize 292
6.10.7 SelectionofAirGap 293
6.11 RotorConstruction 293
6.11.1 SlotCombinationstoAvoid 294
6.11.2 RotorHeatingDuringStartingorUnderStalledConditions 294
6.12 TheDesignProcess 295
6.13 EffectofMachinePerformancebyaChangeinDimension 299
6.14 Conclusion 302
References 302
CHAPTER7 THERMALDESIGN 305
7.1 TheThermalProblem 305
7.2 TemperatureLimitsandMaximumTemperatureRise 306
7.3 HeatConduction 307
7.3.1 SimpleHeatConductionThroughaRectangularPlate 308
7.3.2 HeatConductionThroughaCylinder 309
7.3.3 HeatConductionwithSimpleInternalHeatGeneration 311
7.3.4 Example9—StatorWindingHeating 313
7.3.5 One-DimensionalConductiveHeatFlowwithDistributedInternal
HeatGeneration 314
7.3.6 Two-andThree-DimensionalConductiveHeatFlowwithInternal
DistributedHeatGeneration 316
7.3.7 ApplicationofTwo-DimensionalHeatFlowtoStatorTeeth 317
7.3.8 RadialHeatFlowOverSolidCylinderwithInternalHeatGeneration 318
7.3.9 HeatFlowOverCylindricalShellwithInternalDistributed
HeatGeneration 320
7.4 HeatConvectiononPlaneSurfaces 325
7.5 HeatFlowAcrosstheAirGap 327
7.6 HeatTransferbyRadiation 328
7.7 CoolingMethodsandSystems 329
7.7.1 SurfaceCoolingbyAir 329
7.7.2 InternalCooling 329
7.7.3 CoolinginaCirculatorySystem 329
7.7.4 CoolingwithLiquids 330
7.7.5 DirectGasCooling 330
7.7.6 GasasaCoolingMedium 331
7.7.7 LiquidsasaCoolingMedium 332
7.8 ThermalEquivalentCircuit 333
7.9 Example10—HeatDistributionof250HPInductionMachine 338
7.9.1 HeatInputs 339
7.9.2 ThermalResistances 342
7.10 TransientHeatFlow 353
7.10.1 ExternallyGeneratedHeat 353
CONTENTS xi
7.10.2 InternallyGeneratedHeat—StalledOperation 354
7.10.3 ThermalInstability 356
7.11 Conclusion 357
References 357
CHAPTER8 PERMANENTMAGNETMACHINES 359
8.1 MagnetCharacteristics 359
8.2 Hysteresis 362
8.3 PermanentMagnetMaterials 364
8.4 DeterminationofMagnetOperatingPoint 366
8.5 SinusoidallyFEDSurfacePMMotor 369
8.6 FluxDensityConstraints 373
8.7 CurrentDensityConstraints 376
8.8 ChoiceofAspectRatio 377
8.9 EddyCurrentIronLosses 377
8.9.1 EddyCurrentToothIronLosses 378
8.9.2 EddyCurrentYokeIronLosses 379
8.10 EquivalentCircuitParameters 380
8.10.1 MagnetizingInductance 381
8.10.2 CurrentSource 382
8.10.3 EddyCurrentIronLossResistance 382
8.10.4 AlternateEquivalentCircuit 383
8.11 TemperatureConstraintsandCoolingCapability 383
8.12 MagnetProtection 384
8.12.1 MagnetProtectionforMaximumSteady-StateCurrent 384
8.12.2 MagnetProtectionforTransientConditions 386
8.13 DesignforFluxWeakening 387
8.14 PMMotorwithInsetMagnets 389
8.14.1 Short-CircuitProtection 392
8.14.2 FluxWeakening 392
8.15 CoggingTorque 393
8.16 RippleTorque 394
8.17 DesignUsingFerriteMagnets 394
8.18 PermanentMachineswithBuriedMagnets 395
8.18.1 PMMachineswithBuriedCircumferentialMagnets 396
8.19 Conclusion 399
Acknowledgment 400
References 400
CHAPTER9 ELECTROMAGNETICDESIGNOFSYNCHRONOUSMACHINES 401
9.1 CalculationofUsefulFluxPerPole 401
9.2 CalculationofDirectandQuadratureAxisMagnetizingInductance 402
9.3 DeterminationofFieldMagnetizingInductance 411
9.4 Determinationofd-AxisMutualInductances 418
9.5 CalculationofRotorPoleLeakagePermeances 420
9.6 StatorLeakageInductancesofaSalientPoleSynchronousMachine 424
9.6.1 ZigzagorTooth-TopLeakageInductanceofSalientPoleMachines 424
9.7 TheAmortisseurWindingParameters 428