power electronics - d.hart mcgraw, Exercises of Electric Machines

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Instantaneous power:

Energy:

Average power:

Average power for a dc voltage source:

rms voltage:

rms for v  v 1  v 2  v 3 ... :

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: V rms 

Vm 12

I rms  B

a

Im 13

b

2  I (^) dc^2

I rms 

I (^) m 13

V rms  2 V (^) 1,^2 rms  V (^) 2,^2 rms  V (^) 3,^2 rms  Á

V rms  B

T 3

T

0

v^2 ( t ) dt

P dc  V dc I avg

P 

W

T

T 3

t 0  T

t 0

p ( t ) dt 

T 3

t 0  T

t 0

v ( t ) i ( t ) dt

W 

t 2

t 1

p ( t ) dt

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

Commonly used Power

and Converter Equations

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.

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This book is printed on acid-free paper.

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ISBN 978-0-07-338067- MHID 0-07-338067-

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

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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—dc 2009047266

www.mhhe.com

iv

Contents vii

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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xi

T

his 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

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

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2 C H A P T E R 1 Introduction

Converters are classified by the relationship between input and output: ac input/dc output The ac-dc converter produces a dc output from an ac input. Average power is transferred from an ac source to a dc load. The ac-dc converter is specifically classified as a rectifier. For example, an ac-dc converter enables integrated circuits to operate from a 60-Hz ac line voltage by converting the ac signal to a dc signal of the appropriate voltage. dc input/ac output The dc-ac converter is specifically classified as an inverter. In the inverter, average power flows from the dc side to the ac side. Examples of inverter applications include producing a 120-V rms 60-Hz voltage from a 12-V battery and interfacing an alternative energy source such as an array of solar cells to an electric utility. dc input/dc output The dc-dc converter is useful when a load requires a specified (often regulated) dc voltage or current but the source is at a different or unregulated dc value. For example, 5 V may be obtained from a 12-V source via a dc-dc converter. ac input/ac output The ac-ac converter may be used to change the level and/or frequency of an ac signal. Examples include a common light-dimmer circuit and speed control of an induction motor. Some converter circuits can operate in different modes, depending on circuit and control parameters. For example, some rectifier circuits can be operated as inverters by modifying the control on the semiconductor devices. In such cases, it is the direction of average power flow that determines the converter classifica- tion. In Fig. 1-2, if the battery is charged from the ac power source, the converter is classified as a rectifier. If the operating parameters of the converter are changed and the battery acts as a source supplying power to the ac system, the converter is then classified as an inverter. Power conversion can be a multistep process involving more than one type of converter. For example, an ac-dc-ac conversion can be used to modify an ac source by first converting it to direct current and then converting the dc signal to an ac signal that has an amplitude and frequency different from those of the orig- inal ac source, as illustrated in Fig. 1-3.

Source

Input Output Converter Load

Figure 1-1 A source and load interfaced by a power electronics converter.

1.3 Power Electronics Concepts 3

Figure 1-2 A converter can operate as a rectifier or an inverter, depending on the direction of average power P.

Inverter

Rectifier

Converter

P

P

− (^) −

1.3 POWER ELECTRONICS CONCEPTS

Source

Input Output Converter 1 Converter 2 Load

Figure 1-3 Two converters are used in a multistep process.

To illustrate some concepts in power electronics, consider the design problem of creating a 3-V dc voltage level from a 9-V battery. The purpose is to supply 3 V to a load resistance. One simple solution is to use a voltage divider, as shown in Fig. 1-4. For a load resistor RL , inserting a series resistance of 2 RL results in 3 V across RL. A problem with this solution is that the power absorbed by the 2 R (^) L resistor is twice as much as delivered to the load and is lost as heat, making the circuit only 33.3 percent efficient. Another problem is that if the value of the load resistance changes, the output voltage will change unless the 2RL resistance changes proportionally. A solution to that problem could be to use a transistor in place of the 2 RL resistance. The transistor would be controlled such that the volt- age across it is maintained at 6 V, thus regulating the output at 3 V. However, the same low-efficiency problem is encountered with this solution. To arrive at a more desirable design solution, consider the circuit in Fig. 1-5 a. In that circuit, a switch is opened and closed periodically. The switch is a short circuit when it is closed and an open circuit when it is open, making the voltage

9 V 3 V

−

R (^) L

2 RL

−

Figure 1-4 A simple voltage divider for creating 3 V from a 9-V source.