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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 L m,1-phase 9 2-3-2 Stator Mutual-Inductance L mutual 11 2-3-3 Per-Phase Magnetizing-Inductance L m 12 2-3-4 Stator-Inductance L s 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 Ï? d) 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 dq Winding Speed Ï? d 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 T em 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 = 0â??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 Ï? dA 81 5-1-2 Calculation of T em 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 Ï? r 97 6-2 Steady-State Analysis 101 6-2-1 Steady-State i sd / i s* d 104 6-2-2 Steady-State i sq / i s* q 104 6-2-3 Steady-State θ err 105 6-2-4 Steady-State T em / T e* 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 ^ V s 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 λ s , λ r , T em, and Ï? m 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 T em 134 9-4-4 Calculation of the Rotor Speed Ï? m 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 T em 159 11-2-2 Induced Back-EMF e a 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