Power Magnetic Devices

Author Biography xiii Preface xv About the Companion Site xix 1 Optimization-Based Design 1 1.1 Design Approach 1 1.2 Mathematical Properties of Objective Functions 3 1.3 Single-Objective Optimization Using Newton’s Method 5 1.4 Genetic Algorithms: Review of Biological Genetics 7 1.5 The Canonical Genetic Algorithm 10 1.6 Real-Coded Genetic Algorithms 15 1.7 Multi-Objective Optimization and the Pareto-Optimal Front 25 1.8 Multi-Objective Optimization Using Genetic Algorithms 27 1.9 Formulation of Fitness Functions for Design Problems 31 1.10 A Design Example 33 References 39 Problems 40 2 Magnetics and Magnetic Equivalent Circuits 43 2.1 Ampere’s Law, Magnetomotive Force, and Kirchhoff’s MMF Law for Magnetic Circuits 43 2.2 Magnetic Flux, Gauss’s Law, and Kirchhoff’s Flux Law for Magnetic Circuits 46 2.3 Magnetically Conductive Materials and Ohm’s Law For Magnetic Circuits 48 2.4 Construction of the Magnetic Equivalent Circuit 56 2.5 Translation of Magnetic Circuits to Electric Circuits: Flux Linkage and Inductance 59 2.6 Representing Fringing Flux in Magnetic Circuits 64 2.7 Representing Leakage Flux in Magnetic Circuits 68 2.8 Numerical Solution of Nonlinear Magnetic Circuits 80 2.9 Permanent Magnet Materials and Their Magnetic Circuit Representation 95 2.10 Closing Remarks 98 References 98 Problems 99 3 Introduction to Inductor Design 103 3.1 Common Inductor Architectures 103 3.2 DC Coil Resistance 105 3.3 DC Inductor Design 108 3.4 Case Study 113 3.5 Closing Remarks 119 References 120 Problems 120 4 Force and Torque 123 4.1 Energy Storage in Electromechanical Devices 123 4.2 Calculation of Field Energy 125 4.3 Force from Field Energy 127 4.4 Co-Energy 128 4.5 Force from Co-Energy 132 4.6 Conditions for Conservative Fields 133 4.7 Magnetically Linear Systems 134 4.8 Torque 135 4.9 Calculating Force Using Magnetic Equivalent Circuits 135 References 139 Problems 139 5 Introduction to Electromagnet Design 141 5.1 Common Electromagnet Architectures 141 5.2 Magnetic, Electric, and Force Analysis of an Ei-Core Electromagnet 141 5.3 EI-Core Electromagnet Design 151 5.4 Case Study 155 References 162 Problems 163 6 Magnetic Core Loss and Material Characterization 165 6.1 Eddy Current Losses 165 6.2 Hysteresis Loss and the B–H Loop 172 6.3 Empirical Modeling of Core Loss 177 6.4 Magnetic Material Characterization 183 6.5 Measuring Anhysteretic Behavior 188 6.6 Characterizing Behavioral Loss Models 197 6.7 Time-Domain Loss Modeling: the Preisach Model 201 6.8 Time-Domain Loss Modeling: the Extended Jiles–Atherton Model 205 References 211 Problems 212 7 Transformer Design 215 7.1 Common Transformer Architectures 215 7.2 T-Equivalent Circuit Model 217 7.3 Steady-State Analysis 221 7.4 Transformer Performance Considerations 223 7.5 Core-Type Transformer Configuration 231 7.6 Core-Type Transformer MEC 238 7.7 Core Loss 244 7.8 Core-Type Transformer Design 245 7.9 Case Study 251 7.10 Closing Remarks 259 References 260 Problems 260 8 Distributed Windings and Rotating Electric Machinery 263 8.1 Describing Distributed Windings 263 8.2 Winding Functions 271 8.3 Air-Gap Magneto Motive Force 276 8.4 Rotating MMF 278 8.5 Flux Linkage and Inductance 280 8.6 Slot Effects and Carter’s Coefficient 282 8.7 Leakage Inductance 284 8.8 Resistance 289 8.9 Introduction to Reference Frame Theory 290 8.10 Expressions for Torque 294 References 299 Problems 299 9 Introduction to Permanent Magnet AC Machine Design 303 9.1 Permanent Magnet Synchronous Machines 303 9.2 Operating Characteristics of PMAC Machines 305 9.3 Machine Geometry 312 9.4 Stator Winding 317 9.5 Material Parameters 320 9.6 Stator Currents and Control Philosophy 320 9.7 Radial Field Analysis 321 9.8 Lumped Parameters 326 9.9 Ferromagnetic Field Analysis 327 9.10 Formulation of Design Problem 332 9.11 Case Study 336 9.12 Extensions 344 References 345 Problems 346 10 Introduction to Thermal Equivalent Circuits 349 10.1 Heat Energy, Heat Flow, and the Heat Equation 349 10.2 Thermal Equivalent Circuit of One-Dimensional Heat Flow 352 10.3 Thermal Equivalent Circuit of a Cuboidal Region 358 10.4 Thermal Equivalent Circuit of a Cylindrical Region 361 10.5 Inhomogeneous Regions 367 10.6 Material Boundaries 373 10.7 Thermal Equivalent Circuit Networks 376 10.8 Case Study: Thermal Model of Electromagnet 380 References 396 Problems 397 11 Alternating Current Conductor Losses 399 11.1 Skin Effect in Strip Conductors 399 11.2 Skin Effect in Cylindrical Conductors 405 11.3 Proximity Effect in a Single Conductor 409 11.4 Independence of Skin and Proximity Effects 411 11.5 Proximity Effect in a Group of Conductors 413 11.6 Relating Mean-Squared Field and Leakage Permeance 416 11.7 Mean-Squared Field for Select Geometries 417 11.8 Conductor Losses in Rotating Machinery 422 11.9 Conductor Losses in a UI-Core Inductor 426 11.10 Closing Remarks 431 References 431 Problems 432 12 Parasitic Capacitance 433 12.1 Modeling Approach 433 12.2 Review of Electrostatics 434 12.3 Turn-to-Turn Capacitance 442 12.4 Coil-to-Core Capacitance 446 12.5 Layer-to-Layer Capacitance 449 12.6 Capacitance in Multi-Winding Systems 452 12.7 Measuring Capacitance 455 References 458 Problems 459 13 Buck Converter Design 461 13.1 Buck Converter Analysis 461 13.2 Semiconductors 469 13.3 Heat Sink 472 13.4 Capacitors 474 13.5 UI-Core Input Inductor 476 13.6 UI-Core Output Inductor 477 13.7 Operating Point Analysis 488 13.8 Design Paradigm 492 13.9 Case Study 495 13.10 Extensions 501 References 501 Problems 501 14 Three-Phase Inductor Design 503 14.1 System Description 503 14.2 Inductor Geometry 516 14.3 Magnetic Equivalent Circuit 518 14.4 Magnetic Analysis 529 14.5 Inductor Design Paradigm 533 14.6 Case Study 537 References 541 Problems 541 15 Common-Mode Inductor Design 543 15.1 Common-Mode Voltage and Current 543 15.2 System Description 545 15.3 Common-Mode Equivalent Circuit 546 15.4 Common-Mode Inductor Specification 552 15.5 UR-Core Common-Mode Inductor 557 15.6 UR-Core Common-Mode Inductor Magnetic Analysis 562 15.7 Common-Mode Inductor Design Paradigm 564 15.8 Common-Mode Inductor Case Study 566 References 571 Problems 571 16 Finite Element Analysis 573 16.1 Maxwell’s and Poisson’s Equations 573 16.2 Finite Element Analysis Formulation 575 16.3 Finite Element Analysis Implementation 580 16.4 Closing Remarks 587 References 588 Problems 588 Appendix A Conductor Data and Wire Gauges 589 Appendix B Selected Ferrimagnetic Core Data 593 Appendix C Selected Magnetic Steel Data 595 Appendix D Selected Permanent Magnet Data 599 Appendix E Phasor Analysis 601 Appendix F Trigonometric Identities 607 Index 609