Analysis of Electric Machinery and Drive Systems

Paul C. Krause is a former Professor at Purdue University School of Electrical and Computer Engineering. He is the founder of PC Krause and Associates Inc. and recipient of the 2010 IEEE Nikola Tesla Award. Oleg Wasynczuk is a Professor Emeritus of Electrical and Computer Engineering at Purdue University. He also served as Chief Technical Officer of PC Krause and Associates Inc. and is the recipient of the 2008 IEEE PES Cyril Veinott Electromechanical Energy Conversion Award. Scott D. Sudhoff is the Michael and Katherine Birck Distinguished Professor of Electrical and Computer Engineering at Purdue University. He is a former Editor-in-Chief of the IEEE Transactions on Energy Conversion and recipient of the 2024 IEEE Nikola Tesla Award. Steven D. Pekarek is the Edmund O. Schweitzer, III, Professor of Electrical and Computer Engineering at Purdue University. He has served as an Editor of the IEEE Transactions on Energy Conversion and the IEEE Transactions on Power Electronics, and is the recipient of the 2018 IEEE PES Cyril Veinott Electromechanical Energy Conversion Award.

• About the Authors xiPreface xiiiAcknowledgments xvAbout the Companion Website xvii1 Introductory Concepts 11.1 Introduction 11.2 Stationary Magnetically Coupled Circuits 11.2.1 Nonlinear Magnetic System 81.3 Energy Balance Relationships 131.4 Energy in Coupling Field 181.5 Electromagnetic Forces 241.6 Steady-State and Dynamic Performance of an Electromechanical System 27References 33Problems 332 Symmetrical Three-Phase Stator 372.1 Introduction 372.2 Stator Winding Configuration and Air-Gap mmf 372.3 Transformation Equations 412.4 Voltage Equations in Arbitrary Reference Frame 462.4.1 Electric Power 492.5 Transformation Between Reference Frames 492.6 P-Pole Machines 512.7 Transformation of a Balanced Set 522.8 Instantaneous and Steady-State Phasors 562.9 Variables Observed from Several Frames of Reference 57References 63Problems 633 Symmetrical Induction Machine 653.1 Introduction 653.2 Induction Machine 653.3 Transformation of Rotor Windings to the Arbitrary Reference Frame 673.4 Voltage, Flux-Linkage Equations, and Equivalent Circuit 703.5 Torque Expressed in Arbitrary Reference Frame Variables 753.6 Computer Simulation in the Arbitrary Reference Frame 773.7 Per Unit System 783.8 Steady-State Equivalent Circuit and Common Modes of Operation 813.9 Free-Acceleration Torque Versus Speed Characteristics 893.10 Free-Acceleration Characteristics Viewed from Various Reference Frames 973.11 Dynamic Performance During Sudden Changes in Load Torque 102References 105Problems 1054 Brushless DC Machine 1094.1 Introduction 1094.2 Voltage Equations in Machine Variables 1094.3 Voltage and Torque Equations in Rotor Reference Frame Variables 1134.4 Instantaneous and Steady-State Phasors 1164.5 Field Orientation of a Brushless DC Drive 1174.5.1 Brushless Dc Motor Operation with Φ V = 0 1184.5.2 Maximum-Torque-Per-Volt Operation of a Brushless dc Drive (φ V = Φ Vmt/v) 1214.5.3 Maximum-Torque-Per-Ampere Operation of a Brushless dc Drive (φ V = Φ Vmt/a) 124References 125Problems 1265 Synchronous Machines 1275.1 Introduction 1275.2 Windings of a Synchronous Machine 1285.3 Voltage Equations in Rotor Reference Frame Variables 1305.4 Torque Expressions Positive for Motor Action 1335.5 Time-Domain Block Diagram 1335.6 Rotor Angle and Angle Between Rotors 1365.7 Per Unit System 1375.8 Analysis of Steady-State Operation 1385.9 Stator Currents Positive out of Machine—Synchronous Generator Operation 1435.9.1 Dynamic Performance during a Sudden Change in Input Torque 1475.9.2 Dynamic Performance during a Three-Phase Fault at the Machine Terminals 153References 158Problems 1586 Neglecting Electric Transients 1636.1 Introduction 1636.2 Neglecting Stator Electric Transients 1636.3 Induction Machine with Stator Transients Neglected 1666.3.1 Free-Acceleration Characteristics 1666.4 The Synchronous Machine with Stator Transients Neglected 1706.4.1 Three-Phase Fault at Machine Terminals 171References 175Problems 1757 Machine Equations in Operational Impedances and Time Constants 1777.1 Introduction 1777.2 Park’s Equations in Operational form 1787.3 Operational Impedances and G(P) for a Synchronous Machine with Four Rotor Windings 1787.4 Standard Synchronous Machine Reactances 1827.5 Standard Synchronous Machine Time Constants 1847.6 Derived Synchronous Machine Time Constants 1857.7 Parameters from Short-Circuit Characteristics 1887.8 Parameters from Frequency-Response Characteristics 196References 202Problems 2048 Eigenvalues and Voltage-Behind-Reactance Machine Equations 2078.1 Introduction 2078.2 Machine Equations to be Linearized 2088.2.1 Induction Machine 2088.2.2 Synchronous Machine 2098.3 Linearization of Machine Equations 2108.3.1 Induction Machine 2118.3.2 Synchronous Machines 2138.4 Small-Displacement Stability—Eigenvalues 2168.5 Eigenvalues of Typical Induction Machines 2168.6 Eigenvalues of Typical Synchronous Machines 2208.7 Detailed Voltage-Behind-Reactance Model 2218.8 Reduced-Order Voltage-Behind-Reactance Model 230References 231Problems 2329 Semi-Controlled Bridge Converters 2339.1 Introduction 2339.2 Single-Phase Load Commutated Converter 2339.3 Three-Phase Load Commutated Converter 2459.4 Conclusions and Extensions 256References 257Problems 25810 Fully Controlled Three-Phase Bridge Converters 25910.1 Introduction 25910.2 The Three-Phase Bridge Converter 25910.3 Six-Step Operation 26510.4 Six-Step Modulation 27310.5 Sine-Triangle Modulation 27810.6 Extended Sine-Triangle Modulation 28310.7 Space-Vector Modulation 28510.8 Hysteresis Modulation 28910.9 Delta Modulation 29210.10 Open-Loop Voltage and Current Regulation 29310.11 Closed-Loop Voltage and Current Regulation 296References 300Problems 30211 Direct-Current Machine and Drive 30511.1 Introduction 30511.2 Commutation 30611.3 Voltage and Torque Equations 30911.4 Permanent-Magnet dc Machine 31111.5 dc Drive 31311.5.1 Average-Value Time-Domain Block Diagram 31611.5.2 Torque Control 318Reference 319Problems 31912 Torque Control of Permanent-Magnet and Synchronous Reluctance Machines 32112.1 Introduction 32112.2 Torque Control of a Permanent-Magnet AC Machine 32212.2.1 Maximum Steady-State Torque Versus Speed 32412.3 Simulation of a Permanent-Magnet AC Machine with Torque Control 33112.3.1 Electrical Dynamics 33312.3.2 Mechanical Dynamics 33312.3.3 System-Level Simulation Block Diagram 33412.3.4 System Studies 33512.3.5 Reduced-Order Simulation 33912.4 Torque Control of a Synchronous Reluctance Machine 339References 347Problems 34813 Induction Motor Drives 35113.1 Introduction 35113.2 Volts-Per-Hertz Control 35113.3 Constant Slip Current Control 35813.4 Field-Oriented Control 36513.5 Direct Field-Oriented Control 36913.6 Robust Direct Field-Oriented Control 37113.7 Indirect Rotor Field-Oriented Control 37613.8 Direct Torque Control 37913.9 Slip Energy Recovery Drives 38313.10 Conclusions 386References 386Problems 38714 Permanent-Magnet AC Motor Drives 38914.1 Introduction 38914.2 Voltage-Source Inverter Drives 39014.3 Equivalence of Voltage-Source Inverters to an Idealized Source 39114.4 Average-Value Analysis of Voltage-Source Inverter Drives 40014.5 Steady-State Performance of Voltage-Source Inverter Drives 40314.6 Transient and Dynamic Performance of Voltage-Source Inverter Drives 40614.7 Case Study: Voltage-Source Inverter-Based Speed Control 41114.8 Current-Regulated Inverter Drives 41714.9 Voltage Limitations of Current-Regulated Inverter Drives 42114.10 Current Command Synthesis 42314.11 Average-Value Modeling of Current-Regulated Inverter Drives 42614.12 Case Study: Current-Regulated Inverter-Based Speed Controller 428References 431Problems 431Appendix A Abbreviations, Constants, Conversions, and Identities 433Appendix B Phasors and Phasor Diagrams 437Index 441