Preface xiii

Notation xv

1 Applications: Speed and Torque Control 1

1-1 History 1

1-2 Background 2

1-3 Types of ac Drives Discussed and the Simulation Software 2

1-4 Structure of this Textbook 3

1-5 “Test” Induction Motor 3

1-6 Summary 4

References 4

Problems 4

2 Induction Machine Equations in Phase Quantities: Assisted by Space Vectors 6

2-1 Introduction 6

2-2 Sinusoidally Distributed Stator Windings 6

2-2-1 Three-Phase, Sinusoidally Distributed Stator Windings 8

2-3 Stator Inductances (Rotor Open-Circuited) 9

2-3-1 Stator Single-Phase Magnetizing Inductance Lm,1-phase 9

2-3-2 Stator Mutual-Inductance Lmutual 11

2-3-3 Per-Phase Magnetizing-Inductance Lm 12

2-3-4 Stator-Inductance Ls 12

2-4 Equivalent Windings in a Squirrel-Cage Rotor 13

2-4-1 Rotor-Winding Inductances (Stator Open-Circuited) 13

2-5 Mutual Inductances between the Stator and the Rotor Phase Windings 15

2-6 Review of Space Vectors 15

2-6-1 Relationship between Phasors and Space Vectors in Sinusoidal Steady State 17

2-7 Flux Linkages 18

2-7-1 Stator Flux Linkage (Rotor Open-Circuited) 18

2-7-2 Rotor Flux Linkage (Stator Open-Circuited) 19

2-7-3 Stator and Rotor Flux Linkages (Simultaneous Stator and Rotor Currents) 20

2-8 Stator and Rotor Voltage Equations in Terms of Space Vectors 21

2-9 Making the Case for a dq -Winding Analysis 22

2-10 Summary 25

Reference 25

Problems 26

3 Dynamic Analysis of Induction Machines in Terms of dq Windings 28

3-1 Introduction 28

3-2 dq Winding Representation 28

3-2-1 Stator dq Winding Representation 29

3-2-2 Rotor dq Windings (Along the Same dq-Axes as in the Stator) 31

3-2-3 Mutual Inductance between dq Windings on the Stator and the Rotor 32

3-3 Mathematical Relationships of the dq Windings (at an Arbitrary Speed ωd) 33

3-3-1 Relating dq Winding Variables to Phase Winding Variables 35

3-3-2 Flux Linkages of dq Windings in Terms of Their Currents 36

3-3-3 dq Winding Voltage Equations 37

3-3-4 Obtaining Fluxes and Currents with Voltages as Inputs 40

3-4 Choice of the dqWinding Speed ωd 41

3-5 Electromagnetic Torque 42

3-5-1 Torque on the Rotor d -Axis Winding 42

3-5-2 Torque on the Rotor q -Axis Winding 43

3-5-3 Net Electromagnetic Torque Tem on the Rotor 44

3-6 Electrodynamics 44

3-7 d- and q-Axis Equivalent Circuits 45

3-8 Relationship between the dq Windings and the Per-Phase Phasor-Domain Equivalent Circuit in Balanced Sinusoidal Steady State 46

3-9 Computer Simulation 47

3-9-1 Calculation of Initial Conditions 48

3-10 Summary 56

Reference 56

Problems 57

4 Vector Control of Induction-Motor Drives: A Qualitative Examination 59

4-1 Introduction 59

4-2 Emulation of dc and Brushless dc Drive Performance 59

4-2-1 Vector Control of Induction-Motor Drives 61

4-3 Analogy to a Current-Excited Transformer with a Shorted Secondary 62

4-3-1 Using the Transformer Equivalent Circuit 65

4-4 d- and q -Axis Winding Representation 66

4-5 Vector Control with d-Axis Aligned with the Rotor Flux 67

4-5-1 Initial Flux Buildup Prior to t = 0−67

4-5-2 Step Change in Torque at t = 0+68

4-6 Torque, Speed, and Position Control 72

4-6-1 The Reference Current isq t * ( ) 72

4-6-2 The Reference Current isd t ( ) 73

4-6-3 Transformation and Inverse-Transformation of Stator Currents 73

4-6-4 The Estimated Motor Model for Vector Control 74

4-7 The Power-Processing Unit (PPU) 75

4-8 Summary 76

References 76

Problems 77

5 Mathematical Description of Vector Control in Induction Machines 79

5-1 Motor Model with the d-Axis Aligned Along the Rotor Flux Linkage λ r-Axis 79

5-1-1 Calculation of ωdA 81

5-1-2 Calculation of Tem 81

5-1-3 d-Axis Rotor Flux Linkage Dynamics 82

5-1-4 Motor Model 82

5-2 Vector Control 84

5-2-1 Speed and Position Control Loops 86

5-2-2 Initial Startup 89

5-2-3 Calculating the Stator Voltages to Be Applied 89

5-2-4 Designing the PI Controllers 90

5-3 Summary 95

Reference 95

Problems 95

6 Detuning Effects in Induction Motor Vector Control 97

6-1 Effect of Detuning Due to Incorrect Rotor Time Constant τr 97

6-2 Steady-State Analysis 101

6-2-1 Steady-State isd /is*d 104

6-2-2 Steady-State isq /is*q 104

6-2-3 Steady-State θerr 105

6-2-4 Steady-State Tem /Te*m 106

6-3 Summary 107

References 107

Problems 108

7 Dynamic Analysis of Doubly Fed Induction Generators and Their Vector Control 109

7-1 Understanding DFIG Operation 110

7-2 Dynamic Analysis of DFIG 116

7-3 Vector Control of DFIG 116

7-4 Summary 117

References 117

Problems 117

8 Space Vector Pulse Width-Modulated (SV-PWM) Inverters 119

8-1 Introduction 119

8-2 Synthesis of Stator Voltage Space Vector vsa 119

8-3 Computer Simulation of SV-PWM Inverter 124

8-4 Limit on the Amplitude ˆVs of the Stator Voltage Space Vectov sa 125

Summary 128

References 128

Problems 129

9 Direct Torque Control (DTC) and Encoderless Operation of Induction Motor Drives 130

9-1 Introduction 130

9-2 System Overview 130

9-3 Principle of Encoderless DTC Operation 131

9-4 Calculation of λs, λ r, Tem, and ωm 132

9-4-1 Calculation of the Stator Flux λ s 132

9-4-2 Calculation of the Rotor Flux λ r 133

9-4-3 Calculation of the Electromagnetic Torque Tem 134

9-4-4 Calculation of the Rotor Speed ωm 135

9-5 Calculation of the Stator Voltage Space Vector 136

9-6 Direct Torque Control Using dq-Axes 139

9-7 Summary 139

References 139

Problems 139

Appendix 9-A 140

Derivation of Torque Expressions 140

10 Vector Control of Permanent-Magnet Synchronous Motor Drives 143

10-1 Introduction 143

10-2 d-q Analysis of Permanent Magnet (Nonsalient-Pole) Synchronous Machines 143

10-2-1 Flux Linkages 144

10-2-2 Stator dq Winding Voltages 144

10-2-3 Electromagnetic Torque 145

10-2-4 Electrodynamics 145

10-2-5 Relationship between the dq Circuits and the Per-Phase Phasor-Domain Equivalent Circuit in Balanced Sinusoidal Steady State 145

10-2-6 dq-Based Dynamic Controller for “Brushless DC” Drives 147

10-3 Salient-Pole Synchronous Machines 151

10-3-1 Inductances 152

10-3-2 Flux Linkages 153

10-3-3 Winding Voltages 153

10-3-4 Electromagnetic Torque 154

10-3-5 dq-Axis Equivalent Circuits 154

10-3-6 Space Vector Diagram in Steady State 154

10-4 Summary 156

References 156

Problems 156

11 Switched-Reluctance Motor (SRM) Drives 157

11-1 Introduction 157

11-2 Switched-Reluctance Motor 157

11-2-1 Electromagnetic Torque Tem 159

11-2-2 Induced Back-EMF ea 161

11-3 Instantaneous Waveforms 162

11-4 Role of Magnetic Saturation 164

11-5 Power Processing Units for SRM Drives 165

11-6 Determining the Rotor Position for Encoderles Operation 166

11-7 Control in Motoring Mode 166

11-8 Summary 167

References 167

Problems 167

Index 169

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