ADVANCED ELECTRIC DRIVES ADVANCED ELECTRIC DRIVES Analysis, Control, and Modeling Using MATLAB/Simulink® Ned Mohan Copyright © 2014 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See www.mathworks.com/trademarks for a list of additional trademarks. The MathWorks Publisher Logo identifies books that contain MATLAB® content. Used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book or in the software downloadable from http://www.wiley.com/WileyCDA/WileyTitle/productCd-047064477X.html and http://www.mathworks.com/ matlabcentral/fileexchange/?term=authorid%3A80973. 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TK4058.M5783 2014 621.460285'53–dc23 2014005496 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 CONTENTS 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 9 m,1-phase 2-3-2 Stator Mutual-Inductance L 11 mutual 2-3-3 Per-Phase Magnetizing-Inductance L 12 m 2-3-4 Stator-Inductance L  12 s 2-4 Equivalent Windings in a Squirrel-Cage Rotor 13 2-4-1 Rotor-Winding Inductances (Stator Open-Circuited) 13 v vi CONTENTS 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 ω ) 33 d 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 CONTENTS vii 3-3-4 Obtaining Fluxes and Currents with Voltages as Inputs 40 3-4 Choice of the dq Winding Speed ω   41 d 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 on em 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 viii CONTENTS 4-6 Torque, Speed, and Position Control 72 4-6-1 The Reference Current i* (t) 72 sq 4-6-2 The Reference Current i* (t) 73 sd 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 (cid:31) Rotor Flux Linkage λ-Axis 79 r 5-1-1 Calculation of ω   81 dA 5-1-2 Calculation of T   81 em 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 τ  97 r 6-2 Steady-State Analysis 101 6-2-1 Steady-State i /i* 104 sd sd 6-2-2 Steady-State i /i* 104 sq sq