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11‐9 MAKING A CASE FOR A dq‐WINDING ANALYSIS 11‐10 SUMMARY PROBLEMS 12 Dynamic Analysis of Induction Machines in Terms of dq‐Windings 12‐1 INTRODUCTION 12‐2 dq‐WINDING REPRESENTATION 12‐3 MATHEMATICAL RELATIONSHIPS OF THE dq‐WINDINGS (AT AN ARBITRARY SPEED ω_d) 12‐4 CHOICE OF THE dq‐WINDING SPEED ω_d 12‐5 ELECTROMAGNETIC TORQUE 12‐6 ELECTRODYNAMICS 12‐7 d‐ AND q‐AXIS EQUIVALENT CIRCUITS 12‐8 RELATIONSHIP BETWEEN THE dq‐WINDINGS AND THE PER‐PHASE PHASOR‐DOMAIN EQUIVALENT CIRCUIT IN BALANCED SINUSOIDAL STEADY STATE 12‐9 COMPUTER SIMULATION 12‐10 Phasor Analysis 12‐11 SUMMARY FURTHER READING PROBLEMS Test Machine 13 Mathematical Description of Vector Control in Induction Machines 13‐1 INTRODUCTION 13‐2 MOTOR MODEL WITH THE d‐AXIS ALIGNED ALONG THE ROTOR FLUX LINKAGE

‐AXIS 13‐3 VECTOR CONTROL 13‐4 HARDWARE PROTOTYPING OF VECTOR CONTROL OF INDUCTION MOTOR 13‐5 SUMMARY REFERENCE PROBLEMS 14 Speed‐Sensorless Vector Control of Induction Motor 14‐1 INTRODUCTION 14‐2 OPEN‐LOOP SPEED ESTIMATOR 14‐3 MODEL‐REFERENCE ADAPTIVE SYSTEM (MRAS) ESTIMATOR 14‐4 PARAMETER SENSITIVITY OF OPEN‐LOOP ESTIMATOR AND MRAS ESTIMATOR 14‐5 PRACTICAL IMPLEMENTATION 14‐6 SUMMARY REFERENCES FURTHER READING PROBLEMS 14‐A APPENDIX 15 Analysis of Doubly Fed Generators (DFIGs) in Steady State and Their Vector Control 15‐1 INTRODUCTION 15‐2 STEADY‐STATE ANALYSIS 15‐3 UNDERSTANDING DFIG OPERATION IN dq AXIS 15‐4 DYNAMIC ANALYSIS OF DFIG 15‐5 VECTOR CONTROL OF DFIG 15‐6 SUMMARY REFERENCES FURTHER READING PROBLEMS 16 Direct Torque Control (DTC) and Encoder‐Less Operation of Induction Motor Drives 16‐1 INTRODUCTION 16‐2 SYSTEM OVERVIEW 16‐3 PRINCIPLE OF ENCODER‐LESS DTC OPERATION 16‐4 CALCULATION OF

_s,

_r, T_em, AND ω_m 16‐5 CALCULATION OF THE STATOR VOLTAGE SPACE VECTOR 16‐6 DIRECT TORQUE CONTROL USING dq‐AXES 16‐7 SUMMARY REFERENCE FURTHER READING PROBLEMS TEST MACHINE 16‐A APPENDIX 17 Vector Control of Permanent‐Magnet Synchronous Motor Drives 17‐1 INTRODUCTION 17‐2 dq‐ANALYSIS OF PERMANENT‐MAGNET SYNCHRONOUS MACHINES 17‐3 NON‐SALIENT POLE SYNCHRONOUS MACHINES 17‐4 SALIENT‐POLE SYNCHRONOUS MACHINES 17‐5 HARDWARE PROTOTYPING OF VECTOR CONTROL OF SPM SYNCHRONOUS MOTOR 17‐6 SUMMARY REFERENCES PROBLEMS 17‐A APPENDIX 18 Reluctance Drives: Stepper‐Motors and Switched‐Reluctance Drives 18‐1 INTRODUCTION 18‐2 THE OPERATING PRINCIPLE OF RELUCTANCE MOTORS 18‐3 STEPPER‐MOTOR DRIVES 18‐4 SRM DRIVES

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