Fundamentals of Power Electronics

Description

This up-to-date textbook/reference provides a treatment of PWM converter steady-state and dynamic modelling, including averaged switch modelling, state-space averaging, the current-programmed mode, and the discontinuous conduction mode. Moving logically from theory to application-specific material, the book explains the fundamental principles, models, and technical requirements, allowing both students and professionals to construct working laboratory converters. In order to facilitate a concrete understanding of this material, examples on circuits and applications are introduced as well as step-by-step design techniques, mathematical problems, and real world examples. Preface 1 Introduction 1.1 Introduction to Power Processing 1.2 Several Applications of Power Electronics Elements of Power Electronics 1.3 1 7 9 References I Converters in Equilibrium 11 2 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 Boost Converter Example Cuk Converter Example 15 22 2.3 2.4 2.5 Estimating the Output Voltage Ripple in Converters Containing Two-Pole Low-Pass Filters 2.6 Summary of Key Points 31 Problems 34 34 35 Steady-State Equivalent Circuit Modeling, Losses, and Efficiency 39 References 3 27 3.1 The DC Transformer Model 39 3.2 Inclusion of Inductor Copper Loss 42 3.3 Construction of Equivalent Circuit Model 45viii Contents 3.3.1 3.3.2 3.3.3 3.3.4 4 3.4 How to Obtain the Input Port of the Model 3.5 Example: Inclusion of Semiconductor Conduction Losses in the Boost Converter Model 6 46 46 47 48 50 52 56 Summary of Key Points 3.6 References 56 Problems 57 Switch Realization 63 4.1 Switch Applications 65 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 65 67 71 72 73 4.2 5 Inductor Voltage Equation Capacitor Current Equation Complete Circuit Model Efficiency Single-Quadrant Switches Current-Bidirectional Two-Quadrant Switches Voltage-Bidirectional Two-Quadrant Switches Four-Quadrant Switches Synchronous Rectifiers A Brief Survey of Power Semiconductor Devices 74 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 75 78 81 86 88 Power Diodes Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) Bipolar Junction Transistor (BJT) Insulated Gate Bipolar Transistor (IGBT) Thyristors (SCR, GTO, MCT) 4.3 Switching Loss Transistor Switching with Clamped Inductive Load 4.3.1 4.3.2 Diode Recovered Charge 4.3.3 Device Capacitances, and Leakage, Package, and Stray Inductances Efficiency vs. Switching Frequency 4.3.4 4.4 Summary of Key Points References Problems 92 93 96 98 100 101 102 103 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 Inversion of Source and Load 6.1.1 Cascade Connection of Converters 6.1.2 6.1.3 Rotation of Three-Terminal Cell 132 132 134 137Contents 6.1.4 ix Differential Connection of the Load A Short List of Converters Transformer Isolation 6.3.1 Full-Bridge and Half-Bridge Isolated Buck Converters 6.3.2 Forward Converter 6.3.3 Push-Pull Isolated Buck Converter 6.3.4 Fly back Converter 6.3.5 Boost-Derived Isolated Converters 6.3.6 Isolated Versions of the SEPIC and the Cuk Converter 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 138 143 146 149 154 159 161 165 168 171 171 174 177 177 179 II Converter Dynamics and Control 185 7 AC Equivalent Circuit Modeling 187 7.1 7.2 187 192 193 194 196 197 197 201 202 204 204 213 213 216 217 221 226 228 229 232 235 242 244 247 248 6.2 6.3 7.3 7.4 7.5 Introduction The Basic AC Modeling Approach Averaging the Inductor Waveforms 7.2.1 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 7.2.7 Discussion of the Perturbation and Linearization Step 7.2.8 Results for Several Basic Converters 7.2.9 Example: A Nonideai Flyback Converter State-Space Averaging 7.3.1 The State Equations of a Network 7.3.2 The Basic State-Space Averaged Model 7.3.3 Discussion of the State-Space Averaging Result 7.3.4 Example: State-Space Averaging of a Nonideal Buck-Boost Converter Circuit Averaging and Averaged Switch Modeling 7.4.1 Obtaining a Time-Invariant Circuit 7.4.2 Circuit Averaging 7.4.3 Perturbation and Linearization 7.4.4 Switch Networks 7.4.5 Example: Averaged Switch Modeling of Conduction Losses 7.4.6 Example: Averaged Switch Modeling of Switching Losses The Canonical Circuit Model 7.5.1 Development of the Canonical Circuit Modelx Contents 7.5.2 7.5.3 8 Example: Manipulation of the Buck-Boost Converter Model into Canonical Form Canonical Circuit Parameter Values for Some Common Converters 7.6 Modeling the Pulse-Width Modulator 253 7.7 Summary of Key Points 256 References 257 Problems 258 Converter Transfer Functions 265 8.1 Review of Bode Plots 267 8.1.1 8.1.2 8.1.3 8.1.4 8.1.5 8.1.6 8.1.7 8.1.8 269 275 276 277 278 282 287 289 8.2 Single Pole Response Single Zero Response Right Half-Plane Zero Frequency Inversion Combinations Quadratic Pole Response: Resonance The Low-Q Approximation Approximate Roots of an Arbitrary-Degree Polynomial Analysis of Converter Transfer Functions 8.2.1 8.2.2 8.2.3 Example: Transfer Functions of the Buck-Boost Converter Transfer Functions of Some Basic CCM Converters Physical Origins of the RHP Zero in Converters 293 294 300 300 8.3 Graphical Construction of Impedances and Transfer Functions 302 303 305 308 309 311 8.4 8.3.1 Series Impedances: Addition of Asymptotes Series Resonant Circuit Example 8.3.2 8.3.3 Parallel Impedances: Inverse Addition of Asymptotes Parallel Resonant Circuit Example 8.3.4 8.3.5 Voltage Divider Transfer Functions: Division of Asymptotes Graphical Construction of Converter Transfer Functions Measurement of AC Transfer Functions and Impedances 8.5 Summary of Key Points 8.6 References 9 250 252 313 317 321 322 Problems 322 Controller Design 331 9.1 Introduction 331 9.2 Effect of Negative Feedback on the Network Transfer Functions 334 9.2.1 9.2.2 Feedback Reduces the Transfer Functions from Disturbances to the Output 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 9.3 Construction of the Important Quantities 11( 1 + T) and Tl( 1 + T) and the Closed-Loop Transfer Functions 9.4 Stability 335 337 337 340Contents 9.4.1 9.4.2 9.4.3 9.5 9.6 9.7 10 The Phase Margin Test The Relationship Between Phase Margin and Closed-Loop Damping Factor Transient Response vs. Damping Factor 341 342 346 Regulator Design 347 9.5.1 9.5.2 9.5.3 9.5.4 348 351 353 354 Lead (PD) Compensator Lag (PI) Compensator Combined (P/D) Compensator Design Example Measurement of Loop Gains 362 9.6.1 9.6.2 9.6.3 364 367 368 Voltage Injection Current Injection Measurement of Unstable Systems Summary of Key Points 369 References 369 Problems 369 Input Filter Design 377 10.1 377 377 Introduction 10.1.1 10.1.2 Conducted EMI The Input Filter Design Problem 379 10.2 Effect of an Input Filter on Converter Transfer Functions 381 10.3 10.2.1 Discussion 10.2.2 Impedance Inequalities Buck Converter Example 382 384 385 10.3.1 Effect of Undamped Input Filter 10.3.2 Damping the Input Filter 10.4 Design of a Damped Input Filter 10.4.1 RrCb Parallel Damping 10.4.2 RrLb Parallel Damping 10.4.3 RrLb Series Damping 10.4.4 Cascading Filter Sections 10.4.5 Example: Two Stage Input Filter 10.5 Summary of Key Points References 11 xi 385 391 392 395 396 398 398 400 403 405 Problems 406 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode 409 11.1 DCM Averaged Switch Model 11.2 Small-Signal AC Modeling of the DCM Switch Network 11.2.1 Example: Control-to-Output Frequency Response of a DCM Boost Converter 11.2.2 Example: Control-to-Output Frequency Responses of a CCM/DCM SEPIC 410 420 428 429Contents xii 11.3 11.4 12 High-Frequency Dynamics of Converters in DCM Summary of Key Points 431 References Problems 434 434 435 Current Programmed Control 439 12.1 Oscillation forD> 0.5 441 12.2 A Simple First-Order Model 12.2.1 Simple Model via Algebraic Approach: Buck-Boost Example 12.2.2 Averaged Switch Modeling 12.3 A More Accurate Model 12.3.1 Current-Programmed Controller Model 12.3.2 Solution of the CPM Transfer Functions 12.3.3 Discussion 12.3.4 Current-Programmed Transfer Functions of the CCM Buck Converter 12.3.5 Results for Basic Converters 12.3.6 Quantitative Effects of Current-Programmed Control on the Converter Transfer Functions 449 450 454 459 12.4 Discontinuous Conduction Mode 12.5 Summary of Key Points References Problems 459 462 465 466 469 471 473 480 481 482 III Magnetics 489 13 Basic Magnetics Theory 491 13.1 491 491 498 501 502 502 504 506 506 508 508 508 512 514 515 518 520 522 13.2 13.3 13.4 Review of Basic Magnetics 13.1.1 Basic Relationships 13.1.2 Magnetic Circuits Transformer Modeling 13.2.1 The Ideal Transformer 13.2.2 The Magnetizing Inductance 13.2.3 Leakage Inductances Loss Mechanisms in Magnetic Devices 13.3.1 Core Loss 13.3.2 Low-Frequency Copper Loss Eddy Currents in Winding Conductors 13.4.1 Introduction to the Skin and Proximity Effects 13.4.2 Leakage Flux in Windings 13.4.3 Foil Windings and Layers 13.4.4 Power Loss in a Layer 13.4.5 Example: Power Loss in a Transformer Winding 13.4.6 Interleaving the Windings 13.4.7 PWM Waveform HarmonicsContents xiii Several Types of Magnetic Devices, Their B-H Loops, and Core vs. Copper Loss 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 525 525 527 528 529 530 531 532 533 Inductor Design 539 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 Kg 539 541 542 542 543 543 14.2 14.3 A Step-by-Step Procedure Multiple-Winding Magnetics Design via the Kg Method 544 545 14.3.1 Window Area Allocation 14.3.2 Coupled Inductor Design Constraints 14.3.3 Design Procedure 14.4 Examples 14.4.1 Coupled Inductor for a Two-Output Forward Converter 14.4.2 CCM Fly back Transformer 14.5 Summary of Key Points References Problems 545 550 552 554 554 557 562 562 563 Transformer Design 565 15.1 565 566 566 567 568 569 570 573 573 576 580 580 582 13.5 14 15 15.2 15.3 15.4 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. till 15.1.5 Optimum Flux Density A Step-by-Step Transformer Design Procedure Examples 15.3.1 Example 1: Single-Output Isolated Cuk Converter 15.3.2 Example 2: Multiple-Output Full-Bridge Buck Converter AC Inductor Design 15.4.1 Outline of Derivation 15.4.2 Step-by-Step AC Inductor Design Procedurexiv Contents 15.5 Summary 583 Problems 584 IV Modern Rectifiers and Power System Harmonics 16 Power and Harmonics in Nonsinusoidal Systems 16.1 Average Power 16.2 Root-Mean-Square (RMS) Value of a Waveform 16.3 Power Factor 16.3.1 Linear Resistive Load, Nonsinusoidal Voltage 16.3.2 Nonlinear Dynamic Load, Sinusoidal Voltage 589 590 593 594 594 595 16.4 Power Phasors in Sinusoidal Systems 598 Harmonic Currents in Three-Phase Systems 599 16.6 Harmonic Currents in Three-Phase Four-Wire Networks Harmonic Currents in Three-Phase Three-Wire Networks Harmonic Current Flow in Power Factor Correction Capacitors AC Line Current Harmonic Standards 16.6.1 16.6.2 Bibliography Problems International Electrotechnical Commission Standard 1000 IEEE/ ANSI Standard 519 Line-Commutated Rectifiers 17.1 17.2 The Single-Phase Full-Wave Rectifier 17.1.1 Continuous Conduction Mode 17.1.2 Discontinuous Conduction Mode 17.1.3 Behavior when Cis Large 17.1.4 Minimizing THD when C is Small The Three-Phase Bridge Rectifier 17.2.1 Continuous Conduction Mode 17.2.2 Discontinuous Conduction Mode 599 601 602 603 603 604 605 605 609 609 610 611 612 613 615 615 616 617 17.4 Phase Control 17.3.1 Inverter Mode 17.3.2 Harmonics and Power Factor 17.3.3 Commutation Harmonic Trap Filters 622 17.5 Transformer Connections 628 17.6 Summary Problems 630 631 632 Pulse-Width Modulated Rectifiers 637 17.3 References 18 587 16.5 16.5.1 16.5.2 16.5.3 17 583 References 18.1 Properties of the Ideal Rectifier 619 619 620 638Contents 18.2 Realization of a Near-Ideal Rectifier xv 640 CCM Boost Converter DCM Flyback Converter 642 646 18.3 Control of the Current Waveform 648 18.4 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 Single-Phase Converter Systems Incorporating Ideal Rectifiers 648 654 657 659 663 663 668 18.5 18.4.1 Energy Storage 18.4.2 Modeling the Outer Low-Bandwidth Control System RMS Values of Rectifier Waveforms 674 676 18.6 18.5.1 Boost Rectifier Example 18.5.2 Comparison of Single-Phase Rectifier Topologies Modeling Losses and Efficiency in CCM High-Quality Rectifiers 679 681 683 684 18.7 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 11 18.6.4 Design Example Ideal Three-Phase Rectifiers 18.8 Summary of Key Points 691 18.2.1 18.2.2 673 678 685 References 692 Problems 696 v Resonant Converters 703 19 Resonant Conversion 705 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 M = V!Vg 709 710 711 713 714 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 715 715 717 718 721 19.3.1 19.3.2 19.4 Operation of the Full Bridge Below Resonance: Zero-Current Switching Operation of the Full Bridge Above Resonance: Zero-Voltage Switching 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 722 723 726 727 729 734xvi Contents 19.4.4 20 Another Example 19.5 Exact Characteristics of the Series and Parallel Resonant Converters 19.6 19.5.1 Series Resonant Converter 19.5.2 Parallel Resonant Converter Summary of Key Points 737 740 740 748 References 752 752 Problems 755 Soft Switching 761 20.1 Soft-Switching Mechanisms of Semiconductor Devices 762 763 765 768 20.2 20.1.1 Diode Switching 20.1.2 MOSFET Switching 20.1.3 IGBT Switching The Zero-Current-Switching Quasi-Resonant Switch Cell 20.2.1 20.2.2 20.2.3 Waveforms of the Half-Wave ZCS Quasi-Resonant Switch Cell The Average Terminal Waveforms The Full-Wave ZCS Quasi-Resonant Switch Cell 768 770 774 779 20.3 Resonant Switch Topologies 781 783 784 787 20.4 20.3.1 The Zero-Voltage-Switching Quasi-Resonant Switch 20.3.2 The Zero-Voltage-Switching Multi-Resonant Switch 20.3.3 Quasi-Square-Wave Resonant Switches Soft Switching in PWM Converters 20.4.1 The Zero-Voltage Transition Full-Bridge Converter 20.4.2 The Auxiliary Switch Approach 20.4.3 Auxiliary Resonant Commutated Pole 20.5 Summary of Key Points References Problems Appendices Appendix A 790 791 794 796 797 798 800 803 RMS Values of Commouly-Observed Converter Waveforms 805 A.l Some Common Waveforms 805 A.2 General Piecewise Waveform 809 Appendix B B.l B.2 Simulation of Converters Averaged Switch Models for Continuous Conduction Mode B.l.l Basic CCM Averaged Switch Model B.l.2 CCM Subcircuit Model that Includes Switch Conduction Losses B.l.3 Example: SEPIC DC Conversion Ratio and Efficiency B.l.4 Example: Transient Response of a Buck-Boost Converter Combined CCM/DCM Averaged Switch Model B.2.l Example: SEPIC Frequency Responses B.2.2 Example: Loop Gain and Closed-Loop Responses of a Buck Voltage Regulator 813 815 815 816 818 819 822 825 827Contents B.2.3 Example: DCM Boost Rectifier Current Programmed Control Current Programmed Mode Model for Simulation B.3.1 B.3.2 Example: Frequency Responses of a Buck Converter with Current Programmed Control References B.3 AppendixC Middlebrook's Extra Element Theorem Basic Result Derivation Discussion Examples A Simple Transfer Function C.4.1 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 References C.l C.2 C.3 C.4 AppendixD Magnetics Design Tables Pot Core Data D.l 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 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