Fundamentals of Power Electronics

Description

Fundamentals of Power Electronics, Second Edition, is an up-to-date and authoritative text and reference book on power electronics. This new edition retains the original objective and philosophy of focusing on the fundamental principles, models, and technical requirements needed for designing practical power electronic systems while adding a wealth of new material. Improved features of this new edition include: A new chapter on input filters, showing how to design single and multiple section filters; Major revisions of material on averaged switch modeling, low-harmonic rectifiers, and the chapter on AC modeling of the discontinuous conduction mode; New material on soft switching, active-clamp snubbers, zero-voltage transition full-bridge converter, and auxiliary resonant commutated pole. Also, new sections on design of multiple-winding magnetic and resonant inverter design; Additional appendices on Computer Simulation of Converters using averaged switch modeling, and Middlebrook's Extra Element Theorem, including four tutorial examples; and Expanded treatment of current programmed control with complete results for basic converters, and much more. This edition includes many new examples, illustrations, and exercises to guide students and professionals through the intricacies of power electronics design. Fundamentals of Power Electronics, Second Edition, is intended for use in introductory power electronics courses and related fields for both senior undergraduates and first-year graduate students interested in converter circuits and electronics, control systems, and magnetic and power systems. It will also be an invaluable reference for professionals working in power electronics, power conversion, and analogue and digital electronics. Preface 1 I 2 Contents xix Introduction 1 1.1 Introduction to Power Processing 1 1.2 Several Applications of Power Electronics 7 1.3 Elements of Power Electronics 9 References Converters in Equilibrium 11 Principles of Steady State Converter Analysis 13 2.1 Introduction 13 2.2 Inductor Volt-Second Balance, Capacitor Charge Balance, and the Small-Ripple Approximation 15 2.3 Boost Converter Example 22 2.4 uk Converter Example 27 2.5 Estimating the Output Voltage Ripple in Converters Containing Two-Pole Low-Pass Filters 31 2.6 Summary of Key Points 34 References 34 Problems 35 Steady-State Equivalent Circuit Modeling, Losses, and Efficiency 39 3.1 The DC Transformer Model 39 3.2 Inclusion of Inductor Copper Loss 42 3.3 Construction of Equivalent Circuit Model 45 3viii Contents 3.3.1 Inductor Voltage Equation 46 3.3.2 Capacitor Current Equation 46 3.3.3 Complete Circuit Model 47 3.3.4 Efficiency 48 3.4 How to Obtain the Input Port of the Model 50 3.5 Example: Inclusion of Semiconductor Conduction Losses in the Boost Converter Model 52 3.6 Summary of Key Points 56 References 56 Problems 57 Switch Realization 63 4.1 Switch Applications 65 4.1.1 Single-Quadrant Switches 65 4.1.2 Current-Bidirectional Two-Quadrant Switches 67 4.1.3 Voltage-Bidirectional Two-Quadrant Switches 71 4.1.4 Four-Quadrant Switches 72 4.1.5 Synchronous Rectifiers 73 4.2 A Brief Survey of Power Semiconductor Devices 74 4.2.1 Power Diodes 75 4.2.2 Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) 78 4.2.3 Bipolar Junction Transistor (BJT) 81 4.2.4 Insulated Gate Bipolar Transistor (IGBT) 86 4.2.5 Thyristors (SCR, GTO, MCT) 88 4.3 Switching Loss 92 4.3.1 Transistor Switching with Clamped Inductive Load 93 4.3.2 Diode Recovered Charge 96 4.3.3 Device Capacitances, and Leakage, Package, and Stray Inductances 98 4.3.4 Efficiency vs. Switching Frequency 100 4.4 Summary of Key Points 101 References 102 Problems 103 The Discontinuous Conduction Mode 107 5.1 Origin of the Discontinuous Conduction Mode, and Mode Boundary 108 5.2 Analysis of the Conversion Ratio M(D,K) 112 5.3 Boost Converter Example 117 5.4 Summary of Results and Key Points 124 Problems 126 Converter Circuits 131 6.1 Circuit Manipulations 132 6.1.1 Inversion of Source and Load 132 6.1.2 Cascade Connection of Converters 134 6.1.3 Rotation of Three-Terminal Cell 137 4 5 6 Contents ix 6.1.4 Differential Connection of the Load 138 6.2 A Short List of Converters 143 6.3 Transformer Isolation 146 6.3.1 Full-Bridge and Half-Bridge Isolated Buck Converters 149 6.3.2 Forward Converter 6.3.3 Push-Pull Isolated Buck Converter 6.3.4 Flyback Converter 6.3.5 Boost-Derived Isolated Converters 6.3.6 Isolated Versions of the SEPIC and the 6.4 Converter Evaluation and Design 6.4.1 Switch Stress and Utilization 6.4.2 Design Using Computer Spreadsheet 6.5 Summary of Key Points References Problems II Converter Dynamics and Control 7 AC Equivalent Circuit Modeling 7.1 Introduction 7.2 The Basic AC Modeling Approach 7.2.1 Averaging the Inductor Waveforms 7.2.2 Discussion of the Averaging Approximation 7.2.3 Averaging the Capacitor Waveforms 7.2.4 The Average Input Current 7.2.5 Perturbation and Linearization 7.2.6 Construction of the Small-Signal Equivalent Circuit Model 201 7.2.7 Discussion of the Perturbation and Linearization Step 202 7.2.8 Results for Several Basic Converters 204 7.2.9 Example: A Nonideal Flyback Converter 204 154 159 161 165 Converter 168 171 171 174 177 177 179 185 187 7.3 State-Space Averaging 213 7.3.1 The State Equations of a Network 213 7.3.2 The Basic State-Space Averaged Model 216 7.3.3 Discussion of the State-Space A veraging Result 217 7.3.4 Example: State-Space Averaging of a Nonideal Buck–Boost Converter 221 7.4 Circuit Averaging and Averaged Switch Modeling 226 7.4.1 Obtaining a Time-Invariant Circuit 228 7.4.2 Circuit Averaging 229 7.4.3 Perturbation and Linearization 232 7.4.4 Switch Networks 235 7.4.5 Example: Averaged Switch Modeling of Conduction Losses 242 7.4.6 Example: Averaged Switch Modeling of Switching Losses 244 7.5 The Canonical Circuit Model 247 7.5.1 Development of the Canonical Circuit Model 248 187 192 193 194 196 197 197 x Contents 7.5.2 Example: Manipulation of the Buck–Boost Converter Model into Canonical Form 250 7.5.3 Canonical Circuit Parameter Values for Some Common Converters 252 Modeling the Pulse-Width Modulator 253 Summary of Key Points 256 8 References 257 Problems 258 Converter Transfer Functions 265 8.1 Review of Bode Plots 267 8.1.1 Single Pole Response 269 8.1.2 Single Zero Response 275 8.1.3 Right Half-Plane Zero 276 8.1.4 Frequency Inversion 277 8.1.5 Combinations 278 8.1.6 Quadratic Pole Response: Resonance 282 8.1.7 The Low-Q Approximation 287 8.1.8 Approximate Roots of an Arbitrary-Degree Polynomial 289 8.2 Analysis of Converter Transfer Functions 293 8.2.1 Example: Transfer Functions of the Buck–Boost Converter 294 8.2.2 Transfer Functions of Some Basic CCM Converters 300 8.2.3 Physical Origins of the RHP Zero in Converters 300 8.3 Graphical Construction of Impedances and Transfer Functions 302 8.3.1 Series Impedances: Addition of Asymptotes 303 8.3.2 Series Resonant Circuit Example 305 8.3.3 Parallel Impedances: Inverse Addition of Asymptotes 308 8.3.4 Parallel Resonant Circuit Example 309 8.3.5 Voltage Divider Transfer Functions: Division of Asymptotes 311 8.4 Graphical Construction of Converter Transfer Functions 313 8.5 Measurement of AC Transfer Functions and Impedances 317 8.6 Summary of Key Points 321 References 322 Problems 322 Controller Design 331 9.1 Introduction 331 9.2 Effect of Negative Feedback on the Network Transfer Functions 334 9.2.1 Feedback Reduces the Transfer Functions from Disturbances to the Output 335 9.2.2 Feedback Causes the Transfer Function from the Reference Input to the Output to be Insensitive to Variations in the Gains in the Forward Path of the Loop 337 9.3 Construction of the Important Quantities 1/(1 + T) and T/(1 + T) and the Closed-Loop Transfer Functions 337 9.4 Stability 340 9 7.6 7.7 Contents xi 9.4.1 The Phase Margin Test 341 9.4.2 The Relationship Between Phase Margin and Closed-Loop Damping Factor 342 9.4.3 Transient Response vs. Damping Factor 346 9.5 Regulator Design 347 9.5.1 Lead (PD) Compensator 348 9.5.2 Lag (PI) Compensator 351 9.5.3 Combined (PID) Compensator 353 9.5.4 Design Example 354 9.6 Measurement of Loop Gains 362 9.6.1 Voltage Injection 364 9.6.2 Current Injection 367 9.6.3 Measurement of Unstable Systems 368 9.7 Summary of Key Points 369 References 369 Problems 369 10 Input Filter Design 377 10.1 Introduction 377 10.1.1 Conducted EMI 377 10.1.2 The Input Filter Design Problem 379 10.2 Effect of an Input Filter on Converter Transfer Functions 381 10.2.1 Discussion 382 10.2.2 Impedance Inequalities 384 10.3 Buck Converter Example 385 10.3.1 Effect of Undamped Input Filter 385 10.3.2 Damping the Input Filter 391 10.4 Design of a Damped Input Filter 392 Parallel Damping 395 Parallel Damping 396 Series Damping 398 Cascading Filter Sections 398 10.4.1 10.4.2 10.4.3 10.4.4 10.4.5 11 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode 409 11.1 DCM Averaged Switch Model 410 11.2 Small-Signal AC Modeling of the DCM Switch Network 420 11.2.1 Example: Control-to-Output Frequency Response of a DCM Boost Converter 428 11.2.2 Example: Control-to-output Frequency Responses of a CCM/DCM SEPIC 429 Example: Two Stage Input Filter 400 10.5 Summary of Key Points 403 References 405 Problems 406 xii 12 Contents 11.3 High-Frequency Dynamics of Converters in DCM 431 11.4 Summary of Key Points 434 References 434 Problems 435 Current Programmed Control 439 12.1 Oscillation for D > 0.5 441 12.2 A Simple First-Order Model 449 12.2.1 Simple Model via Algebraic Approach: Buck–Boost Example 450 12.2.2 Averaged Switch Modeling 454 12.3 A More Accurate Model 459 12.3.1 Current-Programmed Controller Model 459 12.3.2 Solution of the CPM Transfer Functions 462 12.3.3 Discussion 465 12.3.4 Current-Programmed Transfer Functions of the CCM Buck Converter 466 12.3.5 Results for Basic Converters 469 12.3.6 Quantitative Effects of Current-Programmed Control on the Converter Transfer Functions 471 12.4 Discontinuous Conduction Mode 473 12.5 Summary of Key Points 480 References 481 Problems 482 III Magnetics 489 13 Basic Magnetics Theory 491 13.1 Review of Basic Magnetics 491 13.1.1 Basic Relationships 491 13.1.2 Magnetic Circuits 498 13.2 Transformer Modeling 501 13.2.1 The Ideal Transformer 502 13.2.2 The Magnetizing Inductance 502 13.2.3 Leakage Inductances 504 13.3 Loss Mechanisms in Magnetic Devices 506 13.3.1 Core Loss 506 13.3.2 Low-Frequency Copper Loss 508 13.4 Eddy Currents in Winding Conductors 508 13.4.1 Introduction to the Skin and Proximity Effects 508 13.4.2 Leakage Flux in Windings 512 13.4.3 Foil Windings and Layers 514 13.4.4 Power Loss in a Layer 515 13.4.5 Example: Power Loss in a Transformer Winding 518 13.4.6 Interleaving the Windings 520 13.4.7 PWM Waveform Harmonics 522 14 13.5.1 Filter Inductor 13.5.2 AC Inductor 13.5.3 Transformer 13.5.4 Coupled Inductor 13.5.5 Flyback Transformer 13.6 Summary of Key Points References Problems Inductor Design 14.1 Filter Inductor Design Constraints 14.1.1 Maximum Flux Density 14.1.2 Inductance 14.1.3 Winding Area 14.1.4 Winding Resistance 14.1.5 The Core Geometrical Constant 14.2 A Step-by-Step Procedure 14.3 Multiple-Winding Magnetics Design via the 14.3.1 Window Area Allocation 14.3.2 Coupled Inductor Design Constraints 14.3.3 Design Procedure 15 14.4 Examples 14.4.1 Coupled Inductor for a Two-Output Forward Converter 14.4.2 CCM Flyback Transformer 14.5 Summary of Key Points References Problems Transformer Design 15.1 Transformer Design: Basic Constraints 15.1.1 Core Loss 15.1.2 Flux Density 15.1.3 Copper Loss 15.1.4 Total Power Loss vs. 15.1.5 Optimum Flux Density 15.2 A Step-by-Step Transformer Design Procedure 15.3 Examples 13.5 Several Types of Magnetic Devices, Their B–H Loops, and Core vs. Copper Loss Contents xiii 525 525 527 528 529 530 531 532 533 539 539 541 542 542 543 543 544 545 545 550 552 554 554 557 562 562 563 565 565 566 566 567 568 569 570 573 573 576 580 580 582 Method 15.3.1 Example 1: Single-Output Isolated Converter 15.3.2 Example 2: Multiple-Output Full-Bridge Buck Converter 15.4 AC Inductor Design 15.4.1 Outline of Derivation 15.4.2 Step-by-Step AC Inductor Design Procedure xiv IV 16 Contents 15.5 Summary 583 References 583 Problems 584 Modern Rectifiers and Power System Harmonics 587 Power and Harmonics in Nonsinusoidal Systems 589 16.1 Average Power 590 16.2 Root-Mean-Square (RMS) Value of a Waveform 593 16.3 Power Factor 594 16.3.1 Linear Resistive Load, Nonsinusoidal Voltage 594 16.3.2 Nonlinear Dynamic Load, Sinusoidal Voltage 595 16.4 Power Phasors in Sinusoidal Systems 598 16.5 Harmonic Currents in Three-Phase Systems 599 16.5.1 Harmonic Currents in Three-Phase Four-Wire Networks 599 16.5.2 Harmonic Currents in Three-Phase Three-Wire Networks 601 16.5.3 Harmonic Current Flow in Power Factor Correction Capacitors 602 16.6 AC Line Current Harmonic Standards 603 16.6.1 International Electrotechnical Commission Standard 1000 603 16.6.2 IEEE/ANSI Standard 519 604 17 Line-Commutated Rectifiers 609 17.1 The Single-Phase Full-Wave Rectifier 609 17.1.1 Continuous Conduction Mode 610 17.1.2 Discontinuous Conduction Mode 611 17.1.3 Behavior when C is Large 612 17.1.4 Minimizing THD when C is Small 613 17.2 The Three-Phase Bridge Rectifier 615 17.2.1 Continuous Conduction Mode 615 17.2.2 Discontinuous Conduction Mode 616 17.3 Phase Control 617 17.3.1 Inverter Mode 619 17.3.2 Harmonics and Power Factor 619 17.3.3 Commutation 620 17.4 Harmonic Trap Filters 622 17.5 Transformer Connections 628 17.6 Summary 630 References 631 Problems 632 Pulse-Width Modulated Rectifiers 637 18.1 Properties of the Ideal Rectifier 638 18 Bibliography Problems 605 605 18.2 Realization of a Near-Ideal Rectifier 18.2.1 CCM Boost Converter 18.2.2 DCM Flyback Converter 18.3 Control of the Current Waveform 18.3.1 Average Current Control 18.3.2 Current Programmed Control 18.3.3 Critical Conduction Mode and Hysteretic Control 18.3.4 Nonlinear Carrier Control 18.4 Single-Phase Converter Systems Incorporating Ideal Rectifiers 18.4.1 Energy Storage 18.4.2 Modeling the Outer Low-Bandwidth Control System 18.5 RMS Values of Rectifier Waveforms 18.5.1 Boost Rectifier Example 18.5.2 Comparison of Single-Phase Rectifier Topologies 18.6 Modeling Losses and Efficiency in CCM High-Quality Rectifiers 18.6.1 Expression for Controller Duty Cycle d(t) 18.6.2 Expression for the DC Load Current 18.6.3 Solution for Converter Efficiency 18.6.4 Design Example 18.7 Ideal Three-Phase Rectifiers 18.8 Summary of Key Points References Problems V Resonant Converters 19 Resonant Conversion 19.1 Sinusoidal Analysis of Resonant Converters 19.1.1 Controlled Switch Network Model 19.1.2 Modeling the Rectifier and Capacitive Filter Networks 19.1.3 Resonant Tank Network 19.1.4 Solution of Converter Voltage Conversion Ratio 19.2 Examples 19.2.1 Series Resonant DC–DC Converter Example 19.2.2 Subharmonic Modes of the Series Resonant Converter 19.2.3 Parallel Resonant DC–DC Converter Example 19.3 Soft Switching 19.3.1 Operation of the Full Bridge Below Resonance: Zero-Current Switching 19.3.2 Operation of the Full Bridge Above Resonance: Zero-Voltage Switching 19.4 Load-Dependent Properties of Resonant Converters 19.4.1 Inverter Output Characteristics 19.4.2 Dependence of Transistor Current on Load 19.4.3 Dependence of the ZVS/ZCS Boundary on Load Resistance Contents xv 640 642 646 648 648 654 657 659 663 663 668 673 674 676 678 679 681 683 684 685 691 692 696 703 705 709 710 711 713 714 715 715 717 718 721 722 723 726 727 729 734 xvi Contents 19.4.4 Another Example 737 19.5 Exact Characteristics of the Series and Parallel Resonant Converters 740 19.5.1 Series Resonant Converter 740 19.5.2 Parallel Resonant Converter 748 19.6 Summary of Key Points 752 References 752 Problems 755 Soft Switching 761 20.1 Soft-Switching Mechanisms of Semiconductor Devices 762 20.1.1 Diode Switching 763 20.1.2 MOSFET Switching 765 20.1.3 IGBT Switching 768 20.2 The Zero-Current-Switching Quasi-Resonant Switch Cell 768 20.2.1 Waveforms of the Half-Wave ZCS Quasi-Resonant Switch Cell 770 20.2.2 The Average Terminal Waveforms 774 20.2.3 The Full-Wave ZCS Quasi-Resonant Switch Cell 779 20.3 Resonant Switch Topologies 781 20.3.1 The Zero-Voltage-Switching Quasi-Resonant Switch 783 20.3.2 The Zero-Voltage-Switching Multi-Resonant Switch 784 20.3.3 Quasi-Square-Wave Resonant Switches 787 20.4 Soft Switching in PWM Converters 790 20.4.1 The Zero-Voltage Transition Full-Bridge Converter 791 20.4.2 The Auxiliary Switch Approach 794 20.4.3 Auxiliary Resonant Commutated Pole 796 20.5 Summary of Key Points 797 References 798 Problems 800 20 Appendices 803 Appendix A A.1 A.2 RMS Values of Commonly-Observed Converter Waveforms 805 Some Common Waveforms 805 General Piecewise Waveform 809 Appendix B Simulation of Converters 813 B.1 Averaged Switch Models for Continuous Conduction Mode 815 B.1.1 Basic CCM Averaged Switch Model 815 B.1.2 CCM Subcircuit Model that Includes Switch Conduction Losses 816 B.1.3 Example: SEPIC DC Conversion Ratio and Efficiency 818 B.1.4 Example: Transient Response of a Buck–Boost Converter 819 B.2 Combined CCM/DCM Averaged Switch Model 822 B.2.1 Example: SEPIC Frequency Responses 825 B.2.2 Example: Loop Gain and Closed-Loop Responses of a Buck Voltage Regulator 827 B.2.3 Example: DCM Boost Rectifier B.3 Current Programmed Control B.3.1 Current Programmed Mode Model for Simulation B.3.2 Example: Frequency Responses of a Buck Converter with Contents xvii 832 834 834 837 840 843 843 846 849 850 850 855 857 859 861 863 864 865 866 866 867 868 869 871 References Appendix C C.1 C.2 C.3 C.4 References Appendix D Magnetics Design Tables Current Programmed Control Middlebrook’s Extra Element Theorem Basic Result Derivation Discussion Examples C.4.1 A Simple Transfer Function C.4.2 An Unmodeled Element C.4.3 Addition of an Input Filter to a Converter C.4.4 Dependence of Transistor Current on Load in a Resonant Inverter D.1 Pot Core Data D.2 EE Core Data D.3 EC Core Data D.4 ETD Core Data D.5 PQ Core Data D.6 American Wire Gauge Data References Index