Introduction to AC Machine Design

PREFACE AND ACKNOWLEDGMENTS xiii LIST OF PRINCIPAL SYMBOLS xv ABOUT THE AUTHOR xxiii CHAPTER 1 MAGNETIC CIRCUITS 1 1.1 Biot-Savart Law 1 1.2 The Magnetic Field B 2 1.3 Example--Computation of Flux Density B 3 1.4 The Magnetic Vector Potential A 5 1.5 Example--Calculation of Magnetic Field from the Magnetic Vector Potential 6 1.6 Concept of Magnetic Flux 7 1.7 The Electric Field E 9 1.8 Ampere's Law 10 1.9 Magnetic Field Intensity H 12 1.10 Boundary Conditions for B and H 15 1.11 Faraday's Law 17 1.12 Induced Electric Field Due to Motion 18 1.13 Permeance, Reluctance, and the Magnetic Circuit 19 1.14 Example--Square Toroid 23 1.15 Multiple Circuit Paths 23 1.16 General Expression for Reluctance 24 1.17 Inductance 27 1.18 Example--Internal Inductance of a Wire Segment 28 1.19 Magnetic Field Energy 29 1.20 The Problem of Units 31 1.21 Magnetic Paths Wholly in Iron 33 1.22 Magnetic Materials 35 1.23 Example--Transformer Structure 37 1.24 Magnetic Circuits with Air Gaps 40 1.25 Example--Magnetic Structure with Saturation 42 1.26 Example--Calculation for Series-Parallel Iron Paths 43 1.27 Multiple Winding Magnetic Circuits 44 1.28 Magnetic Circuits Applied to Electrical Machines 46 1.29 Effect of Excitation Coil Placement 48 CHAPTER 2 THE MMF AND FIELD DISTRIBUTION OF AN AC WINDING 51 2.1 MMF and Field Distribution of a Full-Pitch Winding for a Two Pole Machine 51 2.2 Fractional Pitch Winding for a Two-Pole Machine 54 2.3 Distributed Windings 56 2.4 Concentric Windings 62 2.5 Effect of Slot Openings 64 2.6 Fractional Slot Windings 67 2.7 Winding Skew 70 2.8 Pole Pairs and Circuits Greater than One 73 2.9 MMF Distribution for Three-Phase Windings 73 2.10 Concept of an Equivalent Two-Phase Machine 76 CHAPTER 3 MAIN FLUX PATH CALCULATIONS USING MAGNETIC CIRCUITS 79 3.1 The Main Magnetic Circuit of an Induction Machine 79 3.2 The Effective Gap and Carter's Coefficient 80 3.3 The Effective Length 84 3.4 Calculation of Tooth Reluctance 86 3.5 Example 1--Tooth MMF Drop 89 3.6 Calculation of Core Reluctance 94 3.7 Example 2--MMF Drop Over Main Magnetic Circuit 102 3.8 Magnetic Equivalent Circuit 111 3.9 Flux Distribution in Highly Saturated Machines 112 3.10 Calculation of Magnetizing Reactance 116 3.11 Example 3--Calculation of Magnetizing Inductance 120 CHAPTER 4 USE OF MAGNETIC CIRCUITS IN LEAKAGE REACTANCE CALCULATIONS 125 4.1 Components of Leakage Flux in Induction Machines 125 4.2 Specific Permeance 127 4.3 Slot Leakage Permeance Calculations 129 4.4 Slot Leakage Inductance of a Single-Layer Winding 134 4.5 Slot Leakage Permeance of Two-Layer Windings 135 4.6 Slot Leakage Inductances of a Double-Cage Winding 137 4.7 Slot Leakage Inductance of a Double-Layer Winding 139 4.8 End-Winding Leakage Inductance 144 4.9 Stator Harmonic or Belt Leakage 156 4.10 Zigzag Leakage Inductance 159 4.11 Example 4--Calculation of Leakage Inductances 164 4.12 Effective Resistance and Inductance Per Phase of Squirrel-Cage Rotor 171 4.13 Fundamental Component of Rotor Air Gap MMF 175 4.14 Rotor Harmonic Leakage Inductance 177 4.15 Calculation of Mutual Inductances 181 4.16 Example 5--Calculation of Rotor Leakage Inductance Per Phase 186 4.17 Skew Leakage Inductance 187 4.18 Example 6--Calculation of Skew Leakage Effects 189 CHAPTER 5 CALCULATION OF INDUCTION MACHINE LOSSES 193 5.1 Introduction 193 5.2 Eddy Current Effects in Conductors 194 5.3 Calculation of Stator Resistance 203 5.4 Example 7--Calculation of Stator and Rotor Resistance 205 5.5 Rotor Parameters of Irregularly Shaped Bars 212 5.6 Categories of Electrical Steels 216 5.7 Core Losses Due to Fundamental Flux Component 217 5.8 Stray Load and No-Load Losses 222 5.9 Calculation of Surface Iron Losses Due to Stator Slotting 228 5.10 Calculation of Tooth Pulsation Iron Losses 237 5.11 Friction and Windage Losses 244 5.12 Example 8--Calculation of Iron Loss Resistances 244 CHAPTER 6 PRINCIPLES OF DESIGN 251 6.1 Design Factors 251 6.2 Standards for Machine Construction 252 6.3 Main Design Features 255 6.4 The D2L Output Coefficient 258 6.5 The D3L Output Coefficient 269 6.6 Power Loss Density 277 6.7 The D2.5L Sizing Equation 277 6.8 Choice of Magnetic Loading 278 6.9 Choice of Electric Loading 281 6.10 Practical Considerations Concerning Stator Construction 287 6.11 Rotor Construction 293 6.12 The Design Process 295 6.13 Effect of Machine Performance by a Change in Dimension 299 CHAPTER 7 THERMAL DESIGN 305 7.1 The Thermal Problem 305 7.2 Temperature Limits and Maximum Temperature Rise 306 7.3 Heat Conduction 307 7.4 Heat Convection on Plane Surfaces 325 7.5 Heat Flow Across the Air Gap 327 7.6 Heat Transfer by Radiation 328 7.7 Cooling Methods and Systems 329 7.8 Thermal Equivalent Circuit 333 7.9 Example 10--Heat Distribution of 250 HP Induction Machine 338 7.10 Transient Heat Flow 353 CHAPTER 8 PERMANENT MAGNET MACHINES 359 8.1 Magnet Characteristics 359 8.2 Hysteresis 362 8.3 Permanent Magnet Materials 364 8.4 Determination of Magnet Operating Point 366 8.5 Sinusoidally FED Surface PM Motor 369 8.6 Flux Density Constraints 373 8.7 Current Density Constraints 376 8.8 Choice of Aspect Ratio 377 8.9 Eddy Current Iron Losses 377 8.10 Equivalent Circuit Parameters 380 8.11 Temperature Constraints and Cooling Capability 383 8.12 Magnet Protection 384 8.13 Design for Flux Weakening 387 8.14 PM Motor with Inset Magnets 389 8.15 Cogging Torque 393 8.16 Ripple Torque 394 8.17 Design Using Ferrite Magnets 394 8.18 Permanent Machines with Buried Magnets 395 CHAPTER 9 ELECTROMAGNETIC DESIGN OF SYNCHRONOUS MACHINES 401 9.1 Calculation of Useful Flux Per Pole 401 9.2 Calculation of Direct and Quadrature Axis Magnetizing Inductance 402 9.3 Determination of Field Magnetizing Inductance 411 9.4 Determination of d-Axis Mutual Inductances 418 9.5 Calculation of Rotor Pole Leakage Permeances 420 9.6 Stator Leakage Inductances of a Salient Pole Synchronous Machine 424 9.7 The Amortisseur Winding Parameters 428 9.8 Mutual and Magnetizing Inductances of the Amortisseur Winding 435 9.9 Direct Axis Equivalent Circuit 435 9.10 Referral of Rotor Parameters to the Stator 438 9.11 Quadrature Axis Circuit 441 9.12 Power and Torque Expressions 446 9.13 Magnetic Shear Stress 449 9.14 Field Current Profile 451 CHAPTER 10 FINITE-ELEMENT SOLUTION OF MAGNETIC CIRCUITS 455 10.1 Formulation of the Two-Dimensional Magnetic Field Problem 455 10.2 Significance of the Vector Potential 458 10.3 The Variational Method 459 10.4 Nonlinear Functional and Conditions for Minimization 460 10.5 Description of the Finite-Element Method 465 10.6 Magnetic Induction and Reluctivity in the Triangle Element 467 10.7 Functional Minimization 468 10.8 Formulation of the Stiffness Matrix Equation 472 10.9 Consideration of Boundary Conditions 474 10.10 Step-By-Step Procedure for Solving the Finite-Element Problem 476 10.11 Finite-Element Modeling of Permanent Magnets 482 10.A Appendix 486 APPENDIX A COMPUTATION OF BAR CURRENT 489 APPENDIX B FEM EXAMPLE 493 INDEX 505