Power Electronics,Daniel W. Hart PDF

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har80679_FC.qxd 12/11/09 6:23 PM Page ii Commonly used Power and Converter Equations Instantaneous power: p(t) ⫽ v(t)i(t) t2 Energy: W ⫽ p(t)dt 3 t1 t0 ⫹T t0 ⫹T W 1 1 Average power: P ⫽ ⫽ p(t) dt ⫽ v(t)i(t) dt T T3 T3 t0 t0 Average power for a dc voltage source: Pdc ⫽ Vdc Iavg 1 T 2 rms voltage: Vr...

Description

Commonly used Power and Converter Equations Instantaneous power: p(t) ⫽ v(t)i(t) t2

Energy: W ⫽

3

p(t)dt

t1

t0 ⫹T

t0 ⫹T

t0

t0

W 1 1 p(t) dt ⫽ v(t)i(t) dt Average power: P ⫽ ⫽ T T3 T3 Average power for a dc voltage source: Pdc ⫽ Vdc Iavg rms voltage: Vrms ⫽

1 T 2 v (t)dt BT3 0

rms for v ⫽ v1 ⫹ v2 ⫹ v3 ⫹ . . . : Vrms ⫽ 2V 1,2 rms ⫹ V 2,2 rms ⫹ V 3,2 rms ⫹ Á rms current for a triangular wave: Irms ⫽

Im 13

rms current for an offset triangular wave: Irms ⫽

a

Im 2 2 b ⫹ I dc B 13

rms voltage for a sine wave or a full-wave rectified sine wave: Vrms ⫽

Vm 12

rms voltage for a half-wave rectified sine wave: Vrms ⫽ Power factor: pf ⫽

P P ⫽ S Vrms Irms

Aa Total harmonic distortion: THD ⫽ n⫽2 I1 q

Distortion factor: DF ⫽ Form factor ⫽

Irms Iavg

Crest factor ⫽

Ipeak Irms

I 2n

1 A 1 ⫹ (THD)2

Buck converter: Vo ⫽ Vs D Boost converter: Vo ⫽

Vs 1⫺D

´ converters: Vo ⫽ ⫺ Vs a Buck-boost and Cuk

SEPIC: Vo ⫽ Vs a

D b 1⫺D

Flyback converter: Vo ⫽ Vs a

D N b a 2b 1 ⫺ D N1

Forward converter: Vo ⫽ Vs D a

N2 b N1

D b 1⫺D

Vm 2

Power Electronics Daniel W. Hart Valparaiso University Valparaiso, Indiana

POWER ELECTRONICS Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOC/DOC 1 0 9 8 7 6 5 4 3 2 1 0 ISBN 978-0-07-338067-4 MHID 0-07-338067-9 Vice President & Editor-in-Chief: Marty Lange Vice President, EDP: Kimberly Meriwether-David Global Publisher: Raghothaman Srinivasan Director of Development: Kristine Tibbetts Developmental Editor: Darlene M. Schueller Senior Marketing Manager: Curt Reynolds Project Manager: Erin Melloy Senior Production Supervisor: Kara Kudronowicz Senior Media Project Manager: Jodi K. Banowetz Design Coordinator: Brenda A. Rolwes Cover Designer: Studio Montage, St. Louis, Missouri (USE) Cover Image: Figure 7.5a from interior Compositor: Glyph International Typeface: 10.5/12 Times Roman Printer: R. R. Donnelley All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. This book was previously published by: Pearson Education, Inc. Library of Congress Cataloging-in-Publication Data Hart, Daniel W. Power electronics / Daniel W. Hart. p. cm. Includes bibliographical references and index. ISBN 978-0-07-338067-4 (alk. paper) 1. Power electronics. I. Title. TK7881.15.H373 2010 621.31'7—dc22 2009047266 www.mhhe.com

To my family, friends, and the many students I have had the privilege and pleasure of guiding

BRIEF CONTENTS

Chapter 1 Introduction

Chapter 7 DC Power Supplies

1

265

Chapter 2 Power Computations 21

Chapter 8 Inverters 331

Chapter 3 Half-Wave Rectifiers 65

Chapter 9 Resonant Converters 387

Chapter 4 Full-Wave Rectifiers 111

Chapter 10 Drive Circuits, Snubber Circuits, and Heat Sinks 431

Chapter 5 AC Voltage Controllers

Appendix A Fourier Series for Some Common Waveforms 461

171

Appendix B State-Space Averaging Index Chapter 6 DC-DC Converters 196

iv

473

467

CONTENTS

Chapter 1 Introduction 1.1 1.2 1.3 1.4

2.5 2.6

1

Power Electronics 1 Converter Classification 1 Power Electronics Concepts 3 Electronic Switches 5 The Diode 6 Thyristors 7 Transistors 8

1.5 1.6 1.7

1.8

Bibliography 19 Problems 20

Chapter 2 Power Computations 21 2.1 2.2

Introduction 21 Power and Energy 21 Instantaneous Power 21 Energy 22 Average Power 22

2.3 2.4

Apparent Power S 42 Power Factor 43

2.7 2.8

Inductors and Capacitors 25 Energy Recovery 27

Power Computations for Sinusoidal AC Circuits 43 Power Computations for Nonsinusoidal Periodic Waveforms 44 Fourier Series 45 Average Power 46 Nonsinusoidal Source and Linear Load 46 Sinusoidal Source and Nonlinear Load 48

Switch Selection 11 Spice, PSpice, and Capture 13 Switches in Pspice 14 The Voltage-Controlled Switch Transistors 16 Diodes 17 Thyristors (SCRs) 18 Convergence Problems in PSpice 18

Effective Values: RMS 34 Apparent Power and Power Factor 42

14

Power Computations Using PSpice 51 2.10 Summary 58 2.11 Bibliography 59 Problems 59 2.9

Chapter 3 Half-Wave Rectifiers 65 3.1 3.2

Introduction 65 Resistive Load 65 Creating a DC Component Using an Electronic Switch 65

3.3 3.4

Resistive-Inductive Load 67 PSpice Simulation 72 Using Simulation Software for Numerical Computations 72

v

vi

3.5

Contents

Capacitance Output Filter 122 Voltage Doublers 125 LC Filtered Output 126

RL-Source Load 75 Supplying Power to a DC Source from an AC Source 75

3.6

Inductor-Source Load 79

4.3

Resistive Load 131 RL Load, Discontinuous Current 133 RL Load, Continuous Current 135 PSpice Simulation of Controlled Full-Wave Rectifiers 139 Controlled Rectifier with RL-Source Load 140 Controlled Single-Phase Converter Operating as an Inverter 142

Using Inductance to Limit Current 79

3.7

The Freewheeling Diode 81 Creating a DC Current 81 Reducing Load Current Harmonics 86

3.8

Half-Wave Rectifier With a Capacitor Filter 88 Creating a DC Voltage from an AC Source 88

3.9

The Controlled Half-Wave Rectifier 94

4.4 4.5

Resistive Load 94 RL Load 96 RL-Source Load 98

3.10 PSpice Solutions For Controlled Rectifiers 100 Modeling the SCR in PSpice 100

4.6 4.7

4.1 4.2

Introduction 111 Single-Phase Full-Wave Rectifiers 111 The Bridge Rectifier 111 The Center-Tapped Transformer Rectifier 114 Resistive Load 115 RL Load 115 Source Harmonics 118 PSpice Simulation 119 RL-Source Load 120

DC Power Transmission 156 Commutation: The Effect of Source Inductance 160 Single-Phase Bridge Rectifier 160 Three-Phase Rectifier 162

The Effect of Source Inductance 103

Chapter 4 Full-Wave Rectifiers 111

Three-Phase Rectifiers 144 Controlled Three-Phase Rectifiers 149 Twelve-Pulse Rectifiers 151 The Three-Phase Converter Operating as an Inverter 154

3.11 Commutation 103 3.12 Summary 105 3.13 Bibliography 106 Problems 106

Controlled Full-Wave Rectifiers 131

4.8 4.9

Summary 163 Bibliography 164 Problems 164

Chapter 5 AC Voltage Controllers 5.1 5.2

171

Introduction 171 The Single-Phase AC Voltage Controller 171 Basic Operation 171 Single-Phase Controller with a Resistive Load 173 Single-Phase Controller with an RL Load 177 PSpice Simulation of Single-Phase AC Voltage Controllers 180

Contents

5.3

Three-Phase Voltage Controllers 183

6.11 Discontinuous-Current Operation 241 Buck Converter with Discontinuous Current 241 Boost Converter with Discontinuous Current 244

Y-Connected Resistive Load 183 Y-Connected RL Load 187 Delta-Connected Resistive Load 189

5.4 5.5 5.6 5.7

Induction Motor Speed Control 191 Static VAR Control 191 Summary 192 Bibliography 193 Problems 193

Chapter 6 DC-DC Converters 196 6.1 6.2 6.3

Linear Voltage Regulators 196 A Basic Switching Converter 197 The Buck (Step-Down) Converter 198 Voltage and Current Relationships 198 Output Voltage Ripple 204 Capacitor Resistance—The Effect on Ripple Voltage 206 Synchronous Rectification for the Buck Converter 207

6.4 6.5

Design Considerations 207 The Boost Converter 211 Voltage and Current Relationships 211 Output Voltage Ripple 215 Inductor Resistance 218

6.6

6.12 Switched-Capacitor Converters 247 The Step-Up Switched-Capacitor Converter 247 The Inverting Switched-Capacitor Converter 249 The Step-Down Switched-Capacitor Converter 250

6.13 PSpice Simulation of DC-DC Converters 251 A Switched PSpice Model 252 An Averaged Circuit Model 254

6.14 Summary 259 6.15 Bibliography 259 Problems 260

Chapter 7 DC Power Supplies 7.1 7.2 7.3

´ 6.7 The Cuk Converter 226 6.8 The Single-Ended Primary Inductance Converter (SEPIC) 231 6.9 Interleaved Converters 237 6.10 Nonideal Switches and Converter Performance 239 Switch Voltage Drops 239 Switching Losses 240

Introduction 265 Transformer Models 265 The Flyback Converter 267 Continuous-Current Mode 267 Discontinuous-Current Mode in the Flyback Converter 275 Summary of Flyback Converter Operation 277

The Buck-Boost Converter 221 Voltage and Current Relationships 221 Output Voltage Ripple 225

265

7.4

The Forward Converter 277 Summary of Forward Converter Operation 283

7.5 7.6

The Double-Ended (Two-Switch) Forward Converter 285 The Push-Pull Converter 287 Summary of Push-Pull Operation 290

7.7

Full-Bridge and Half-Bridge DC-DC Converters 291

vii

viii

Contents

Current-Fed Converters 294 Multiple Outputs 297 Converter Selection 298 Power Factor Correction 299 PSpice Simulation of DC Power Supplies 301 7.13 Power Supply Control 302 7.8 7.9 7.10 7.11 7.12

Control Loop Stability 303 Small-Signal Analysis 304 Switch Transfer Function 305 Filter Transfer Function 306 Pulse-Width Modulation Transfer Function 307 Type 2 Error Amplifier with Compensation 308 Design of a Type 2 Compensated Error Amplifier 311 PSpice Simulation of Feedback Control 315 Type 3 Error Amplifier with Compensation 317 Design of a Type 3 Compensated Error Amplifier 318 Manual Placement of Poles and Zeros in the Type 3 Amplifier 323

7.14 7.15 7.16 7.17

PWM Control Circuits 323 The AC Line Filter 323 The Complete DC Power Supply 325 Bibliography 326 Problems 327

Chapter 8 Inverters 331 8.1 8.2 8.3 8.4 8.5 8.6

Introduction 331 The Full-Bridge Converter 331 The Square-Wave Inverter 333 Fourier Series Analysis 337 Total Harmonic Distortion 339 PSpice Simulation of Square Wave Inverters 340

8.7 8.8 8.9

Amplitude and Harmonic Control 342 The Half-Bridge Inverter 346 Multilevel Inverters 348 Multilevel Converters with Independent DC Sources 349 Equalizing Average Source Power with Pattern Swapping 353 Diode-Clamped Multilevel Inverters 354

8.10 Pulse-Width-Modulated Output 357 Bipolar Switching 357 Unipolar Switching 358

8.11 PWM Definitions and Considerations 359 8.12 PWM Harmonics 361 Bipolar Switching 361 Unipolar Switching 365

8.13 Class D Audio Amplifiers 366 8.14 Simulation of Pulse-Width-Modulated Inverters 367 Bipolar PWM 367 Unipolar PWM 370

8.15 Three-Phase Inverters 373 The Six-Step Inverter 373 PWM Three-Phase Inverters 376 Multilevel Three-Phase Inverters 378

8.16 PSpice Simulation of Three-Phase Inverters 378 Six-Step Three-Phase Inverters 378 PWM Three-Phase Inverters 378

8.17 Induction Motor Speed Control 379 8.18 Summary 382 8.19 Bibliography 383 Problems 383

ix

Contents

Chapter 9 Resonant Converters 387 9.1 9.2

Introduction 387 A Resonant Switch Converter: Zero-Current Switching 387 Basic Operation 387 Output Voltage 392

9.3

A Resonant Switch Converter: Zero-Voltage Switching 394 Basic Operation 394 Output Voltage 399

9.4

The Series Resonant Inverter 401 Switching Losses 403 Amplitude Control 404

9.5

The Series Resonant DC-DC Converter 407 Basic Operation 407 Operation for ωs ⬎ ωo 407 Operation for ω0 /2 ⬍ ωs⬍ ω0 413 Operation for ωs ⬍ ω0 / 2 413 Variations on the Series Resonant DC-DC Converter 414

The Parallel Resonant DC-DC Converter 415 9.7 The Series-Parallel DC-DC Converter 418 9.8 Resonant Converter Comparison 421 9.9 The Resonant DC Link Converter 422 9.10 Summary 426 9.11 Bibliography 426 Problems 427

Chapter 10 Drive Circuits, Snubber Circuits, and Heat Sinks 431 10.1 Introduction 431 10.2 MOSFET and IGBT Drive Circuits 431 Low-Side Drivers 431 High-Side Drivers 433

10.3 Bipolar Transistor Drive Circuits 437 10.4 Thyristor Drive Circuits 440 10.5 Transistor Snubber Circuits 441 10.6 Energy Recovery Snubber Circuits 450 10.7 Thyristor Snubber Circuits 450 10.8 Heat Sinks and Thermal Management 451 Steady-State Temperatures 451 Time-Varying Temperatures 454

10.9 Summary 457 10.10 Bibliography 457 Problems 458

9.6

Appendix A Fourier Series for Some Common Waveforms 461 Appendix B State-Space Averaging Index

473

467

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PREFACE

T

his book is intended to be an introductory text in power electronics, primarily for the undergraduate electrical engineering student. The text assumes that the student is familiar with general circuit analysis techniques usually taught at the sophomore level. The student should be acquainted with electronic devices such as diodes and transistors, but the emphasis of this text is on circuit topology and function rather than on devices. Understanding the voltage-current relationships for linear devices is the primary background required, and the concept of Fourier series is also important. Most topics presented in this text are appropriate for junior- or senior-level undergraduate electrical engineering students. The text is designed to be used for a one-semester power electronics course, with appropriate topics selected or omitted by the instructor. The text is written for some flexibility in the order of the topics. It is recommended that Chap. 2 on power computations be covered at the beginning of the course in as much detail as the instructor deems necessary for the level of students. Chapters 6 and 7 on dc-dc converters and dc power supplies may be taken before Chaps. 3, 4, and 5 on rectifiers and voltage controllers. The author covers chapters in the order 1, 2 (introduction; power computations), 6, 7 (dc-dc converters; dc power supplies), 8 (inverters), 3, 4, 5 (rectifiers and voltage controllers), followed by coverage of selected topics in 9 (resonant converters) and 10 (drive and snubber circuits and heat sinks). Some advanced material, such as the control section in Chapter 7, may be omitted in an introductory course. The student should use all the software tools available for the solution to the equations that describe power electronics circuits. These range from calculators with built-in functions such as integration and root finding to more powerful computer software packages such as MATLAB®, Mathcad®, Maple™, Mathematica®, and others. Numerical techniques are often suggested in this text. It is up to the student to select and adapt all the readily available computer tools to the power electronics situation. Much of this text includes computer simulation using PSpice® as a supplement to analytical circuit solution techniques. Some prior experience with PSpice is helpful but not necessary. Alternatively, instructors may choose to use a different simulation program such as PSIM® or NI Multisim™ software instead of PSpice. Computer simulation is never intended to replace understanding of fundamental principles. It is the author’s belief that using computer simulation for the instructional benefit of investigating the basic behavior of power electronics circuits adds a dimension to the student’s learning that is not possible from strictly manipulating equations. Observing voltage and current waveforms from a computer simulation accomplishes some of the same objectives as those xi

xii

Preface

of a laboratory experience. In a computer simulation, all the circuit’s voltages and currents can be investigated, usually much more efficiently than in a hardware lab. Variations in circuit performance for a change in components or operating parameters can be accomplished more easily with a computer simulation than in a laboratory. PSpice circuits presented in this text do not necessarily represent the most elegant way to simulate circuits. Students are encouraged to use their engineering skills to improve the simulation circuits wherever possible. The website that accompanies this text can be found at www.mhhe .com/hart, and features Capture circuit files for PSpice simulation for students and instructors and a password-protected solutions manual and PowerPoint® lecture notes for instructors. My sincere gratitude to reviewers and students who have made many valuable contributions to this project. Reviewers include Ali Emadi Illinois Institute of Technology Shaahin Filizadeh University of Manitoba James Gover Kettering University Peter Idowu Penn State, Harrisburg Mehrdad Kazerani University of Waterloo Xiaomin Kou University of Wisconsin-Platteville Alexis Kwasinski The University of Texas at Austin Medhat M. Morcos Kansas State University Steve Pekarek Purdue University Wajiha Shireen University of Houston Hamid Toliyat Texas A&M University Zia Yamayee University of Portland Lin Zhao Gannon University A special thanks to my colleagues Kraig Olejniczak, Mark Budnik, and Michael Doria at Valparaiso University for their contributions. I also thank Nikke Ault for the preparation of much of the manuscript.

Preface

Complete Online Solutions Manual Organization System (COSMOS). Professors can benefit from McGraw-Hill’s COSMOS electronic solutions manual. COSMOS enables instructors to generate a limitless supply of problem material for assignment, as well as transfer and integrate their own problems into the software. For additional information, contact your McGraw-Hill sales representative. Electronic Textbook Option. This text is offered through CourseSmart for both instructors and students. CourseSmart is an online resource where students can purchase the complete text online at almost one-half the cost of a traditional text. Purchasing the eTextbook allows students to take advantage of CourseSmart’s Web tools for learning, which include full text search, notes and highlighting, and e-mail tools for sharing notes among classmates. To learn more about CourseSmart options, contact your McGraw-Hill sales representative or visit www.CourseSmart.com. Daniel W. Hart Valparaiso University Valparaiso, Indiana

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C H A P T E R

1

Introduction

1.1 POWER ELECTRONICS Power electronics circuits convert electric power from one form to another using electronic devices. Power electronics circuits function by using semiconductor devices as switches, thereby controlling or modifying a voltage or current. Applications of power electronics range from high-...