Power electronics

Instantaneous power:

Energy:

Average power:

Average power for a dc voltage source:

rms voltage:

rms for v v1 v2 v3 . . . :

rms current for a triangular wave:

rms current for an offset triangular wave:

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

12

Irms B a Im

13

b

2

I 2

dc

Irms Im

13

Vrms 2V2

1,rms V 2

2,rms V2

3,rms Á

Vrms B

1

T3

T

0

v 2

(t)dt

Pdc Vdc Iavg

P W

T 1

T 3

t0T

t0

p(t) dt 1

T 3

t0T

t0

v(t)i(t) dt

W 3

t2

t1

p(t)dt

p(t) v(t)i(t)

Commonly used Power

and Converter Equations

har80679_FC.qxd 12/11/09 6:23 PM Page ii

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

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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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page ii

To my family, friends, and the many students

I have had the privilege and pleasure of guiding

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page iii

iv

Chapter 1

Introduction 1

Chapter 2

Power Computations 21

Chapter 3

Half-Wave Rectifiers 65

Chapter 4

Full-Wave Rectifiers 111

Chapter 5

AC Voltage Controllers 171

Chapter 6

DC-DC Converters 196

Chapter 7

DC Power Supplies 265

Chapter 8

Inverters 331

Chapter 9

Resonant Converters 387

Chapter 10

Drive Circuits, Snubber Circuits,

and Heat Sinks 431

Appendix A Fourier Series for Some

Common Waveforms 461

Appendix B State-Space Averaging 467

Index 473

BRIEF CONTENTS

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v

Chapter 1

Introduction 1

1.1 Power Electronics 1

1.2 Converter Classification 1

1.3 Power Electronics Concepts 3

1.4 Electronic Switches 5

The Diode 6

Thyristors 7

Transistors 8

1.5 Switch Selection 11

1.6 Spice, PSpice, and Capture 13

1.7 Switches in Pspice 14

The Voltage-Controlled Switch 14

Transistors 16

Diodes 17

Thyristors (SCRs) 18

Convergence Problems in

PSpice 18

1.8 Bibliography 19

Problems 20

Chapter 2

Power Computations 21

2.1 Introduction 21

2.2 Power and Energy 21

Instantaneous Power 21

Energy 22

Average Power 22

2.3 Inductors and Capacitors 25

2.4 Energy Recovery 27

2.5 Effective Values: RMS 34

2.6 Apparent Power and Power

Factor 42

Apparent Power S 42

Power Factor 43

2.7 Power Computations for Sinusoidal

AC Circuits 43

2.8 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

2.9 Power Computations Using

PSpice 51

2.10 Summary 58

2.11 Bibliography 59

Problems 59

Chapter 3

Half-Wave Rectifiers 65

3.1 Introduction 65

3.2 Resistive Load 65

Creating a DC Component

Using an Electronic Switch 65

3.3 Resistive-Inductive Load 67

3.4 PSpice Simulation 72

Using Simulation Software for

Numerical Computations 72

CONTENTS

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vi Contents

3.5 RL-Source Load 75

Supplying Power to a DC Source

from an AC Source 75

3.6 Inductor-Source Load 79

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

Resistive Load 94

RL Load 96

RL-Source Load 98

3.10 PSpice Solutions For

Controlled Rectifiers 100

Modeling the SCR in PSpice 100

3.11 Commutation 103

The Effect of Source Inductance 103

3.12 Summary 105

3.13 Bibliography 106

Problems 106

Chapter 4

Full-Wave Rectifiers 111

4.1 Introduction 111

4.2 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

Capacitance Output Filter 122

Voltage Doublers 125

LC Filtered Output 126

4.3 Controlled Full-Wave Rectifiers 131

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

4.4 Three-Phase Rectifiers 144

4.5 Controlled Three-Phase

Rectifiers 149

Twelve-Pulse Rectifiers 151

The Three-Phase Converter Operating

as an Inverter 154

4.6 DC Power Transmission 156

4.7 Commutation: The Effect of Source

Inductance 160

Single-Phase Bridge Rectifier 160

Three-Phase Rectifier 162

4.8 Summary 163

4.9 Bibliography 164

Problems 164

Chapter 5

AC Voltage Controllers 171

5.1 Introduction 171

5.2 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

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Contents vii

5.3 Three-Phase Voltage

Controllers 183

Y-Connected Resistive Load 183

Y-Connected RL Load 187

Delta-Connected Resistive Load 189

5.4 Induction Motor Speed Control 191

5.5 Static VAR Control 191

5.6 Summary 192

5.7 Bibliography 193

Problems 193

Chapter 6

DC-DC Converters 196

6.1 Linear Voltage Regulators 196

6.2 A Basic Switching Converter 197

6.3 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 Design Considerations 207

6.5 The Boost Converter 211

Voltage and Current Relationships 211

Output Voltage Ripple 215

Inductor Resistance 218

6.6 The Buck-Boost Converter 221

Voltage and Current Relationships 221

Output Voltage Ripple 225

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

6.11 Discontinuous-Current Operation 241

Buck Converter with Discontinuous

Current 241

Boost Converter with Discontinuous

Current 244

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 265

7.1 Introduction 265

7.2 Transformer Models 265

7.3 The Flyback Converter 267

Continuous-Current Mode 267

Discontinuous-Current Mode in the Flyback

Converter 275

Summary of Flyback Converter

Operation 277

7.4 The Forward Converter 277

Summary of Forward Converter

Operation 283

7.5 The Double-Ended (Two-Switch)

Forward Converter 285

7.6 The Push-Pull Converter 287

Summary of Push-Pull Operation 290

7.7 Full-Bridge and Half-Bridge DC-DC

Converters 291

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viii Contents

7.8 Current-Fed Converters 294

7.9 Multiple Outputs 297

7.10 Converter Selection 298

7.11 Power Factor Correction 299

7.12 PSpice Simulation of DC

Power Supplies 301

7.13 Power Supply Control 302

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 PWM Control Circuits 323

7.15 The AC Line Filter 323

7.16 The Complete DC Power Supply 325

7.17 Bibliography 326

Problems 327

Chapter 8

Inverters 331

8.1 Introduction 331

8.2 The Full-Bridge Converter 331

8.3 The Square-Wave Inverter 333

8.4 Fourier Series Analysis 337

8.5 Total Harmonic Distortion 339

8.6 PSpice Simulation of Square Wave

Inverters 340

8.7 Amplitude and Harmonic

Control 342

8.8 The Half-Bridge Inverter 346

8.9 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

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Contents ix

Chapter 9

Resonant Converters 387

9.1 Introduction 387

9.2 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

9.6 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

Appendix A Fourier Series for Some

Common Waveforms 461

Appendix B State-Space Averaging 467

Index 473

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xi

This book is intended to be an introductory text in power electronics, primar￾ily 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 chap￾ters 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), fol￾lowed 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 sug￾gested 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 supple￾ment 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 elec￾tronics 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

PREFACE

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page 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 hard￾ware lab. Variations in circuit performance for a change in components or oper￾ating parameters can be accomplished more easily with a computer simulation

than in a laboratory. PSpice circuits presented in this text do not necessarily rep￾resent 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.

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page xii

Preface xiii

Complete Online Solutions Manual Organization System (COSMOS). Pro￾fessors can benefit from McGraw-Hill’s COSMOS electronic solutions manual.

COSMOS enables instructors to generate a limitless supply of problem mate￾rial 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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page xiii