• Author / Uploaded
• Anu Radha

Citation preview

•

I

E ements o Power E ectronics

THE OXFORD SERIES IN ELECTRICAL AND COMPUTER ENGINEERING Adel S. Sedra, Series Editor Allen and Holberg, CMOS Analog Circuit Design, 3rd edition Bobrow, Elementary Linear Circuit Analysis, 2nd edition Bobrow, Fundamentals of Electrical Engineering, 2nd edition Campbell, Fabrication Engineering at the Micro- and Nanoscale, 4th edition Chen, Digital Signal Processing Chen, Linear System Theory and Design, 4th edition Chen, Signals and Systems, 3rd edition Comer, Digital Logic and State Machine Design, 3rd edition Comer, Microprocessor-Based System Design Cooper and McGillem, Probabilistic Methods of Signal and System Analysis, 3rd edition Dimitrijev, Principles of Semiconductor Device, 2nd edition Dimitrijev, Understanding Semiconductor Devices Fortney, Principles of Electronics: Analog & Digital Franco, Electric Circuits Fundamentals Ghausi, Electronic Devices and Circuits: Discrete and Integrated Guru and Hiziroglu, Electric Machinery and Transformers, 3rd edition Houts, Signal Analysis in Linear Systems Jones, Introduction to Optical Fiber Communication Systems Krein, Elements of Power Electronics, 2nd edition Kuo, Digital Control Systems, 3rd edition Lathi, Linear Systems and Signals, 2nd edition Lathi, Signal Processing and Linear Systems Lathi and Ding, Modern Digital and Analog Communication Systems, 4th edition Martin, Digital Integrated Circuit Design Miner, Lines and Electromagnetic Fields for Engineers Parhami, Computer Architecture Parhami, Computer Arithmetic, 2nd edition Roberts and Sedra, SPICE, 2nd edition Roberts, Taenzler, and Burns, An Introduction to Mixed-Signal IC Test and Measurement, 2nd edition Roulston, An Introduction to the Physics of Semiconductor Devices Sadiku, Elements of Electromagnetics, 6th edition Santina, Stubberud, and Hostetter, Digital Control System Design, 2nd edition Sarma, Introduction to Electrical Engineering Schaumann, Xiao, and Van Valkenburg, Design ofAnalog Filters, 3rd edition Schwarz and Oldham, Electrical Engineering: An Introduction, 2nd edition Sedra and Smith, Microelectronic Circuits, 7th edition Stefani, Shahian, Savant, and Hostetter, Design of Feedback Control Systems, 4th edition Tsividis, Operation and Modeling of the MOS Transistor, 3rd edition Van Valkenburg, Analog Filter Design Warner and Grung, Semiconductor Device Electronics Wolovich, Automatic Control Systems Yariv and Yeh, Photonics: Optical Electronics in Modern Communications, 6th edition Zak, Systems and Control

• SECOND EDITION

Philip T. Krein University of Illinois Department of Electrical and Computer Engineering Urbana, Illinois

New York

Oxford

OXFORD UNIVERSITY PRESS

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Copyright© 2015, 1998 by Oxford University Press For titles covered by Section 112 of the US Higher Education Opportunity Act, please visit www.oup.com/us/he for the latest information about pricing and alternate formats. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016 http://www.oup.com Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Krein, Philip T., 1956- author. Elements of power electronics I Philip T. Krein, University of Illinois, Department of Electrical and Computer Engineering. 2nd ed. pages em ISBN: 978-0-19-938841-7 Includes bibliographical references and index. 1. Power electronics Textbooks. I. Title. TK7881.15.K74 2015 621.31'7 dc23 2014018905 Printing number: 9 8 7 6 5 4 3 2 1 Printed in the United States of America on acid-free paper

In memory of Theodore J. Krein 1929-2013

and Evelyn Leech Krein 7930-2014

....ontents

PREFACE xvii NOMENCLATURE xxi

PART 1:

PRINCIPLES Power Electronics and the Energy Revolution

CHAPTER 1

1.1 1.2 1.3 1.4

1.5

1.6

1.7

The Energy Basis of Electrical Engineering 3 What Is Power Electronics? 5 The Need for Electrical Conversion 7 History 8 1.4.1 Rectifiers and the Diode 8 1.4.2 Inverters and Power Transistors 9 1.4.3 Motor Drive Applications 11 1.4.4 Power Supplies and de- de Conversion 12 1.4.5 Alternative Energy Processing 15 1.4.6 The Energy Future: Power Electronics as a Revolution 1.4.7 Summary and Future Developments 18 Goals and Methods of Electrical Conversion 19 1.5.1 The Basic Objectives 19 1.5.2 The Efficiency Objective The Switch 20 1.5.3 The Reliability Objective Simplicity and Integration 1.5.4 Important Variables and Notation 21 Energy Analysis of Switching Power Converters 22 1.6.1 Conservation of Energy over Time 23 1.6.2 Energy Flows and Action in de- de Converters 25 1.6.3 Energy Flows and Action in Rectifiers 29 Power Electronics Applications: A Universal Energy Enabler 1.7.1 Solar Energy Architectures 32 1.7.2 Wind Energy Architectures 36 1.7.3 Tide and Wave Architectures 38 1.7.4 Electric Transportation Architectures 39

2

16

21

32

••

VII

•••

VIII

CONTENTS

1.8

CHAPTER 2

Recap Problems References

41 42 45

Switching Conversion and Analysis

48

2.1 2.2

Introduction 49 Combining Conventional Circuits and Switches 49 2.2.1 Organizing a Converter to Focus on Switches 49 2.2.2 Configuration-based Analysis 52 2.2.3 The Switch Matrix as a Design Tool 53 2.3 The Reality of Kirchhoff's Laws 56 2.3.1 The Challenge of Switching Violations 56 2.3.2 Interconnection of Voltage and Current Sources 58 2.3.3 Short-Term and Long-Term Violations 59 2.3.4 Interpretation of Average Inductor Voltage and Capacitor Current 2.3.5 Source Conversion 61 2.4 Switching Functions and Applications 63 2.5 Overview of Switching Devices 68 2.5.1 Real Switches 68 2.5.2 The Restricted Switch 69 2.5.3 Typical Devices and Their Functions 71 2.6 Methods for Diode Switch Circuits 75 2.7 Control of Converters Based on Switch Action 83 2.8 Equivalent Source Methods 84 2.9 Simulation 86 2.10 Summary and Recap 87 Problems 88 References 92

PART II: CONVERTERS AND APPLICATIONS CHAPTER 3

de-de Converters 3.1 3.2 3.3

3.4

3.5

94

The Importance of de- de Conversion 95 Why Not Voltage Dividers? 95 Linear Regulators 97 3.3.1 Regulator Circuits 97 3.3.2 Regulation Measures 99 Direct de- de Converters and Filters 100 3.4.1 The Buck Converter 100 3.4.2 The Boost Converter 105 3.4.3 Power Filter Design 107 3.4.4 Discontinuous Modes and Critical Inductance Indirect de- de Converters 121 3.5.1 The Buck-Boost Converter 121 3.5.2 The Boost-Buck Converter 124 3.5.3 The Flyback Converter 125

112

60

CONTENTS

3.5.4 SEPIC, Zeta, and Other Indirect Converters 129 3.5.5 Power Filters in Indirect Converters 131 3.5.6 Discontinuous Modes in Indirect Converters 133 3.6 Forward Converters and Isolation 139 3.6.1 Basic Transformer Operation 139 3.6.2 General Considerations in Forward Converters 141 3.6.3 Catch-Winding Forward Converter 142 3.6.4 Forward Converters with ac Links 143 3.6.5 Boost-Derived (Current-Fed) Forward Converters 3.7 Bidirectional Converters 147 3.8 de- de Converter Design Issues and Examples 149 3.8.1 The High-Side Switch Challenge 149 3.8.2 Limitations of Resistive and Forward Drops 150 3.8.3 Regulation 152 3.8.4 Solar Interface Converter 155 3.8.5 Electric Truck Interface Converter 157 3.8.6 Telecommunications Power Supply 158 3.9 Application Discussion 160 3.10 Recap 161 Problems 164 References 169

Rectifiers and Switched Capacitor Circuits

CHAPTER 4

4.1 4.2 4.3 4.4

4.5

4.6

4.7 4.8

Introduction 173 Rectifier Overview 173 The Classical Rectifier Operation and Analysis 175 Phase-Controlled Rectifiers 182 4.4.1 The Uncontrolled Case 182 4.4.2 Controlled Bridge and Midpoint Rectifiers 186 4.4.3 The Polyphase Bridge Rectifier 195 4.4.4 Power Filtering in Rectifiers 200 4.4.5 Discontinuous Mode Operation 202 Active Rectifiers 207 4.5.1 Boost Rectifier 207 4.5 .2 Discontinuous Mode Flyback and Related Converters as Active Rectifiers 213 4.5.3 Polyphase Active Rectifiers 215 Switched-Capacitor Converters 218 4.6.1 Charge Exchange between Capacitors 218 4.6.2 Capacitors and Switch Matrices 219 4.6.3 Doublers and Voltage Multipliers 221 Voltage and Current Doublers 223 Converter Design Examples 224 4.8.1 Wind Power Rectifier 224 4.8.2 Power System Control and High-Voltage de 226 4.8.3 Solid-State Lighting 228 4.8.4 Vehicle Active Battery Charger 230

146

172

•

IX

X

CONTENTS

4.9 Application Discussion 4.10 Recap 234 Problems 238 References 243 CHAPTER 5

Inverters

233

246

5.1 5.2 5.3 5.4

Introduction 247 Inverter Considerations 247 Voltage-Sourced Inverters and Control 250 Pulse-Width Modulation 255 5.4.1 Introduction 255 5.4.2 Creating Pulse-Width Modulation Waveforms 258 5.4.3 Drawbacks of Pulse-Width Modulation 261 5.4.4 Multi-level Pulse-Width Modulation 262 5.4.5 Inverter Input Current under Pulse-Width Modulation 5.5 Three-Phase Inverters and Space Vector Modulation 266 5.6 Current-Sourced Inverters 273 5.7 Filters and Inverters 275 5.8 Inverter Design Examples 277 5.8.1 Solar Power Interface 277 5.8.2 Uninterruptible Power Supply 278 280 5.8.3 Electric Vehicle High-Performance Drive 5.9 Application Discussion 284 5.10 Recap 284 Problems 286 References 289

265

PART Ill: REAL COMPONENTS AND THEIR EFFECTS CHAPTER 6

Real Sources and Loads 6.1 6.2

6.3 6.4 6.5

6.6

292

Introduction 293 Real Loads 293 6.2.1 Quasi-Steady Loads 294 6.2.2 Transient Loads 296 6.2.3 Coping with Load Variation Dynamic Regulation Wire Inductance 299 Critical Values and Examples 301 Interfaces for Real Sources 305 6.5.1 Impedance Behavior of Sources 305 6.5.2 Interfaces for de Sources 306 6.5.3 Interfaces for ac Sources 309 Source Characteristics of Batteries 314 6.6.1 Lead-acid Cells 316 6.6.2 Nickel Batteries 317 6.6.3 Lithium-ion Batteries 318 6.6.4 Basis for Comparison 319

298

CONTENTS

6.7

Source Characteristics of Fuel Cells and Solar Cells 320 6.7.1 Fuel Cells 320 6.7.2 Solar Cells 322 6.8 Design Examples 324 6.8 .1 Wind Farm Interconnection Problems 324 6.8 .2 Bypass Capacitor Benefits 325 6.8 .3 Interface for a Boost Power Factor Correction Active Rectifier 326 6.8.4 Lithium-ion Battery Charger for a Small Portable Device 328 331 6.9 Application Discussion 6.10 Recap 332 Problems 334 References 337 CHAPTER 7

Capacitors and Resistors 7.1 7.2

7.3 7.4 7.5

7.6 7.7

7.8 7.9

CHAPTER 8

340

Introduction 341 Capacitors Types and Equivalent Circuits 341 341 7.2.1 Major Types 7.2.2 Equivalent Circuit 344 7.2.3 Impedance Behavior 346 7.2.4 Simple Dielectric Types and Materials 348 7.2.5 Electrolytics 349 7.2.6 Double-Layer Capacitors 352 Effects of Equivalent Series Resistance 353 Effects of Equivalent Series Inductance 356 Wire Resistance 358 7.5.1 Wire Sizing 358 361 7.5.2 Traces and Busbar 7.5.3 Temperature and Frequency Effects 363 Resistors 364 Design Examples 366 7.7.1 Single-phase Inverter Energy 366 7.7.2 Paralleling Capacitors in a Low-Voltage de- de Converter 7.7.3 Resistance Management in a Heat Lamp Application Application Discussion 370 Recap 372 Problems 373 References 376

Concepts of Magnetics for Power Electronics 8.1 8.2 8.3 8.4

Introduction 379 Maxwell's Equations with Magnetic Approximations Materials and Properties 380 Magnetic Circuits 382 8.4.1 The Circuit Analogy 382 8.4.2 Inductance 382 8.4.3 Ideal and Real Transformers 388

367 370

378 379

•

XI

••

XII

CONTENTS

8.5 8.6

8.7

8.8 8.9

CHAPTER 9

The Hysteresis Loop and Losses 391 Saturation as a Design Constraint 395 8.6.1 Saturation Limits 395 8.6.2 General Design Considerations 398 Design Examples 400 8.7.1 Core Materials and Geometries 400 8.7.2 Additional Discussion of Transformers 404 8.7.3 Hybrid Automobile Boost Inductor 405 8.7.4 Building-integrated Solar Energy Converter 406 8.7.5 Isolated Converter for Small Satellite Application 411 Application Discussion 414 417 Recap Problems 420 References 423

Power Semiconductors in Converters 9.1 9.2 9.3 9.4

9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13

9.14

9.15 9.16

424

Introduction 425 Switching Device States 425 Static Models 427 Switch Energy Losses and Examples 433 9.4.1 General Analysis of Losses 433 9.4.2 Losses during Commutation 435 9.4.3 Examples 439 Simple Heat Transfer Models for Power Semiconductors 443 The P-N Junction as a Power Device 448 P-N Junction Diodes and Alternatives 450 The Thyristor Family 452 Field-Effect Transistors 456 Insulated-Gate Bipolar Transistors 460 Integrated Gate-Commutated Thyristors and Combination Devices 464 Impact of Compound and Wide Bandgap Semiconductors Snubbers 466 9.13.1 Introduction 466 9.13.2 Lossy Turn-off Snubbers 467 9.13.3 Lossy Turn-on Snubbers 471 9.13.4 Combined and Lossless Snubbers 474 Design Examples 475 9.14.1 Boost Converter for Disk Drive 475 9.14.2 Loss Estimate for Electric Vehicle Inverter 481 9.14.3 Extreme Performance Devices 484 Application Discussion 485 Recap 487 Problems 491 References 494

464

CONTENTS

CHAPTER 10

Interfacing with Power Semiconductors

10.1 10.2

10.3 10.4 10.5

10.6

10.7 10.8

•••

XIII

496

Introduction 497 Gate Drives 497 10.2.1 Overview 497 10.2.2 Voltage-Controlled Gates 498 10.2.3 Pulsed-Current Gates 502 10.2.4 Other Thyristors 506 Isolation and High-Side Switching 507 P-channel Applications and Shoot-through 511 Sensors for Power Electronic Switches 513 10.5.1 Resistive Sensing 513 10.5.2 Integrating Sensing Functions with the Gate Drive 10.5.3 Noncontact Sensing 517 Design Examples 521 10.6.1 Gate Consideration on de- de-Based Battery Charger 10.6.2 Gate Drive Impedance Requirements 523 10.6.3 Hall Sensor Accuracy Interpretation 523 Application Discussion 524 Recap 524 Problems 526 References 529

515

521

PART IV: CONTROL ASPECTS CHAPTER 11

Overview of Feedback Control for Converters

11.1 11.2

11.3

11.4

11.5

532

Introduction 533 The Regulation and Control Problem 533 11.2.1 Introduction 533 11.2.2 Defining the Regulation Problem 533 11.2.3 The Control Problem 534 Review of Feedback Control Principles 535 11.3.1 Open-Loop and Closed-Loop Control 535 11.3.2 Block Diagrams 537 11.3.3 System Gain and Laplace Transforms 539 11.3.4 Transient Response and Frequency Domain 541 11.3.5 Stability 542 Converter Models for Feedback 546 11.4.1 Basic Converter Dynamics 546 11.4.2 Fast-Switching Models 547 11.4.3 Piecewise-Linear Models 547 11.4.4 Discrete-Time Models 550 Voltage-Mode and Current-Mode Controls for de- de Converters 551 11.5.1 Voltage-Mode Control 551 11.5.2 Current-Mode Control 555 11.5.3 Large-Signal Issues in Voltage-Mode and Current-Mode Control

558

•

XIV

CONTENTS

Comparator-Based Controls for Rectifier Systems 561 Proportional and Proportional-integral Control Applications Design Examples 566 11.8.1 Voltage-Mode Control and Performance 566 11.8 .2 Feedforward Compensation 567 11.8.3 Electric Vehicle Control Setup 568 11.9 Application Discussion 571 11.10 Recap 571 Problems 575 References 578

11.6 11.7 11.8

CHAPTER 12

Control Modeling and Design

12.1 12.2

12.3

12.4

12.5

12.6 12.7

564

580

Introduction 581 Averaging Methods and Models 581 12.2.1 Formulation of Averaged Models 581 12.2.2 Averaged Circuit Models 588 Small-Signal Analysis and Linearization 590 12.3.1 The Need for Linear Models 590 12.3.2 Obtaining Linear Models 590 12.3.3 Generalizing the Process 591 Control and Control Design Based on Linearization 12.4.1 Transfer Functions 594 12.4.2 Control Design Introduction 599 12.4.3 Compensation and Filtering 604 12.4.4 Compensated Feedback Examples 608 12.4.5 Challenges for Control Design 613 Design Examples 613 12.5.1 Boost Converter Control Example 613 12.5.2 Buck Converter with Current-Mode Control 12.5.3 Buck Converter with Voltage-Mode Control Application Discussion 623 Recap 625 Problems 627 References 629

594

618 620

PART V: ADVANCED TOPICS CHAPTER 13

ac to ac Conversion

13.1 13.2

13.3 13.4

632

Introduction 633 ac Regulators and Integral Cycle Control 633 13.2.1 Silicon-Conrolled Rectifier and Triac-Based ac Regulators 633 13.2.2 Integral Cycle Control 638 Frequency Matching Conditions 639 641 Matrix Converters 13.4.1 Slow-Switching Frequency Converters: The Choice !switch =hn - fout 641

CONTENTS

13.4.2 Unrestricted Frequency Converters: The Choicefswitch =hn + fout 13.4.3 Unifying the Direct Switching Methods: Linear Phase Modulation 646 13.5 The Cycloconverter 648 651 13.6 Pulse-Width Modulation ac- ac Conversion 13.7 de Link Converters 653 13.8 ac Link Converters 656 13.9 Design Examples 657 13.9.1 Heater Control with Triac ac Regulator 657 13.9.2 Aircraft Interface Converter 658 660 13.9.3 Sizing a de Link ac- ac Converter 661 13.10 Application Discussion 13.11 Recap 662 Problems 663 References 666 CHAPTER14

Resonance in Converters

14.1 14.2

14.3

14.4

14.5 14.6

14.7 14.8

CHAPTER 15

668

Introduction 669 Review of Resonance 669 14.2.1 Characteristic Equations 669 14.2.2 Step Function Excitation 671 14.2.3 Series Resonance 675 14.2.4 Parallel Resonance 677 Soft Switching Techniques Introduction 681 14.3.1 Soft Switching Principles 681 14.3.2 Inverter Configurations 681 14.3.3 Parallel capacitor as a de-de Soft Switching Element 683 Soft switching in de-de Converters 684 14.4.1 Description of Quasi-resonance 684 14.4.2 Zero-Current Switching Transistor Action 685 14.4.3 Zero-Voltage Switching Transistor Action 691 Resonance Used for Control Forward Converters 696 Design Examples 697 14.6.1 Limitations of Antiresonant Filters 697 14.6.2 Creating an ac Link for a de- de Converter 699 14.6.3 Resonant Boost Converter for Solar Application 699 Application Discussion 702 Recap 702 Problems 705 References 710

Hysteresis and Geometric Control for Power Converters

15.1 15.2

Introduction 713 Hysteresis Control

712 713

644

XV

•

XVI

CONTENTS

15.3

15.4 15.5

15.6 15.7

15.2.1 Definition and Basic Behavior 713 15.2.2 Hysteresis Control in de- de Converters 714 15.2.3 Hysteresis Power Factor Correction Control 721 15.2.4 Inverters 725 15.2.5 Design Approaches 726 Switching Boundary Control 727 15.3.1 Behavior Near a Switching Boundary 727 15.3.2 Possible Behavior 729 15.3.3 Choosing a Switching Boundary 730 Frequency Control in Geometric Methods 734 Design Examples 736 15.5.1 Designing Hysteresis Controllers 736 15.5.2 Switching Boundary Control Combination for Battery Charging Management 737 15.5.3 Boost Converter with Switching Boundary Control Application Discussion 742 Recap 742 Problems 744 References 747

APPENDICES A.

B.

c. D.

Some Useful Trigonometric Identities Unit Systems 753 Fourier Series 757 Three-Phase Circuits 765

INDEX 773

751

740

Pre ace

ower electronics drives the 21st century energy revolution by providing essential energy enablers for computer systems, portable digital products, solid -state lighting, transportation electrification, motor control, renewable and alternative resources, battery management, home appliances, energy-efficient buildings, and a host of other applications. Motors with integrated power electronics are commonplace today. Wind and solar energy use power electronics to interconnect with grid resources. Electric and hybrid cars and trucks reduce emissions and enhance fuel economy. Data centers and cloud computing resources draw an increasing share of global electricity. Power electronics is being integrated with digital and analog electronics in high-performance integrated circuits. The field has emerged as an important topic of study for students in electrical and computer • • eng1neenng. The second edition of Elements of Power Electronics presents power electronics in its many facets. The objective is to lay a foundational base from which engineers can examine the field and practice its unusual and challenging design problems. It provides a framework that leads to families of conversion types and shows how various circuits branch out from this foundation. It includes supporting material about real devices and components, addressing issues that include magnetics design and applications of passive components. These issues are fundamental for practicing designers. Power semiconductors and other power devices have reached the point at which almost any application challenges can be addressed. Imaginative circuit designers have found a huge variety of solutions to many types of power electronics problems. A system-level understanding is valuable for assessing new applications or addressing vital applications in new ways. There is much more to do to prepare solutions that are more efficient, more reliable, more cost effective, and more functional than known approaches. ••

XVII

•••

XVIII

PREFACE

Why study power electronics? First, because it is fun. Power electronic circuits and systems are the basic energy blocks behind things that light up, move, take us from place to place, manage information, use batteries, communicate, cook a meal, or store data. These are changing the world in profound ways. Second, because it is a broad field that makes use of all of a student's knowledge of electrical engineering while seeking a new depth of understanding. Working knowledge of circuits, semiconductor devices, digital and analog design, electromagnetics, power systems, electromechanics, and control will benefit a power electronics engineer. Third, because it brings life, vitality, and breadth to abstract concepts. To the power electronics engineer, Kirchhoff's laws are the beacons that guide design and the snares that catch the unwary or careless. Since power processing is a universal need, power electronics designers often work across wide power ranges (microwatts to megawatts, for instance) and in many application domains.

New in the Second Edition The second edition has been revised extensively on the basis of student and reader feedback. The organization is sequential to match the teaching sequence that is being used. Power conversion examples are developed in Chapter 1, based on more comprehensive coverage of energy methods. Converter concepts and other foundational information have been wrapped in with circuit analysis and design to link the applications. There are more examples on power filters and their design. Implementation issues such as high-side switching now appear with converter design. Basic material such as Fourier series and three-phase circuits has been moved into the Appendixes. Aspects of circuit operation such as discontinuous modes are included with converter analysis and design. A new objective of this edition is to provide fundamental text material on renewable and alternative energy. Many power electronics engineers entered the field because it gives them the tools to make profound changes to energy systems, energy infrastructure, and global standards of living. Expanded design examples, with application discussion and emphasis on emerging energy advances, have been added to almost every chapter. Alternative energy, solid-state lighting, and electric transportation are just three typical application domains expanded here in examples and problem sets. There is enhanced emphasis here on growing circuit applications such as active rectifiers, which are rapidly supplanting passive and classical rectifiers even in small power supplies. The treatment of pulse width modulation has been expanded to address space-vector modulation. The chapter on sources and loads includes new sections about source characteristics of batteries, fuel cells, and solar cells. The power semiconductor device material emphasizes power MOSFETs and IGBTS, which have become the mainstream devices for energy conversion. Emerging devices based on wide bandgap semiconductors, especially SiC and GaN, are introduced. The chapters on control have been restructured with more examples. Advanced topics that include ac-ac converters, resonant circuits, and geometric controls are presented near the end. The net result is a more concise version that emphasizes power conversion circuits and enhances material on applications. The reference lists and problem sets at the end of each chapter have been expanded. Some problems in each chapter have been labeled explicitly as advanced material with an icon. They are intended for readers seeking in-depth challenges. Many of these and other problems emphasize design and encourage readers to develop judgment about power electronics in context. There are many options for design problem approaches, and many of the advanced problems do not have unique solutions.

PREFACE

•

XIX

Organization and supplements The book is organized into six parts. In the first part, two chapters on principles lay out the applications and tools of switching power conversion. In the second part, three chapters on converters present general energy conversion circuits and their operation. The third part provides five chapters that present real components and their functions in energy processes, ranging from ways to model and evaluate real sources and loads, capacitors, inductors, power semiconductors, and interface circuits for power devices. The fourth part provides two chapters on control in power electronics. The fifth part presents advanced topics in three chapters, including ac-ac converters and resonant circuits. An undergraduate course in power electronics might cover Chapters 1-8 in depth, with more limited coverage of Chapters 9-10. An accompanying lab course covers additional applications. The graduate course covers Chapters 9-15. Prior courses in circuits, electronics, and electromagnetics are assumed. Prior courses in electromechanics, analog and digital filter design, and power systems are not vital but make sense in the context of a broad curriculum on modern power and energy issues. Several readers have asked about laboratory experiments and exercises. A supplemental laboratory manual, with complete details and a comprehensive set of experiments, is freely available electronically on the textbook website at www.oup.com/us/krein. The equipment used in our laboratory has been designed and built through the open source Blue Box project at the University of Illinois. All circuit designs, drawings, fabrication details, and documents are available for public use under open-source licenses. Instructors should request access to presentation slides and additional course materials by contacting Oxford University Press. Power electronic circuits can be a challenge to simulate, and many readers ask about tools and methods. In this book, many simulations are developed through Mathcad® or through direct equations implemented in Mathematica®. In addition to these, some of the most respected industry tools include PSIM® (powersimtech.com) and the freeware tool PowereSIM (www.poweresim.com). While many designers use PSpice®, this tool requires special techniques, especially if closed-loop converter controls are to be explored. Professional-grade tools include Transim® (www.transim.com) and proprietary power electronics toolboxes developed for MATLAB® and Simulink® (www.mathworks.com). Sample simulations can be found on the textbook website. Given the rapid evolution of power electronics simulators, the text does not emphasize specific tools.

Acknowledgments I am grateful to the many hundreds of students who have provided feedback on the first edition and its use. The classroom and laboratory experiences of these undergraduate and graduate students have guided the revisions in the second edition. Many sections were inspired by challenging questions from students. Their enthusiasm for energy advances is the main motivation for this book. The comments of the external reviewers have been valuable in completing the second edition. I deeply appreciate both the encouragements and criticisms. The changes to this edition owe much to these reviewers. Osama Abdel-Rahman, University of Central Florida Robert Balog, Texas A & M University Radian Belu, Drexel University

XX

PREFACE

Simon Foo, Florida State University Rob Frohne, Walla Walla University Shih-Min Hsu, University of Alabama at Birmingham Roger King, University of Toledo Brad Lehman, Northeastern University Maciej Noras, UNC Charlotte Martin Ordonez, University of British Columbia William L. Schultz, Case Western Reserve University Wajiha Shireen, University of Houston Russ Tatro, CSU Sacramento Hamid A. Toliyat, Texas A & M University Zia Yamayee, University of Portland Zhaoxian Zhou, University of Southern Mississippi

Credits and caveats Many power conversion circuits and control techniques are the subject of active patent protection. The author cannot guarantee that specific circuits or methods described in the text are available for general use. This is especially true of resonant conversion material in Chapter 8. Power electronics by its nature is an excellent subject for laboratory study. However, it brings many more hazards than more familiar areas of electronics. Readers who plan experimental work in the field should take proper safety precautions in the laboratory. Mathcad is a registered trademark of Mathsoft, Inc. Mathematica is a registered trademark of Wolfram Research, Inc. PSPICE is a registered trademark of MicroSim Corporation. Matlab is a registered trademark of The MathWorks, Inc. Xantrex, Lambda, Kyosan, Magnetek, Semikron, Vicar, Tektronix, and Motorola are registered trademarks of their respective companies.

MEN . . . LATURE

Symbol a

fj D

A B

c D E F G H I J K L M

Meaning Phase delay angle Turn-off angle; transistor current gain Difference angle, for relative phase control Electric permittivity; thermal emissivity Efficiency, Pou/Pin Angle Flux linkage, Wb-turns Magnetic permeability Time constant ratio, tiT; damping factor Resistivity Electrical conductivity; Stefan-Boltzman constant Time constant, L/R or RC Flux; phase angle Radian frequency; radian shaft rotational speed Permeance Reluctance

Area Magnetic flux density Capacitance Duty ratio Electric field Force Open-loop transfer function; conductance Magnetic field intensity; feedback transfer function Current Current density Closed-loop transfer function Inductance Modulating function •

XXI

•• XXII

NOMENCLATURE

N P Q R

S T V W X Y Z a b

Number of turns Power Reactive power; quality factor; charge Resistance Apparent power Period; temperature Voltage Work; energy Reactance Admittance Impedance Turns ratio; commutation parameter Fourier sine coefficient Constant (in general); Fourier component amplitude Time-varying duty ratio Control error Frequency Gap length; transconductance Heat transfer coefficient Time-varying current

c

d e

f g h i j

"-1

k l m n

p

q s t u v x y

Modulation index; gain; thermal conductivity Length Integer index Integer index Integer index; instantaneous power Switching function; heat flow Laplace operator Time System input; Heaviside's step function; commutation interval Time-varying voltage State variable Output variable

Special Circuit Symbols

_l_ Ideal de voltage source

Ideal ac voltage source

Ideal de current source

Ideal ac current source

T

Voltage source (ac or de)

~

£

Generic transistor (BJT, FET, IGBT)

•

•

CHAPTER 1

Power Electronics and The Energy Revolution 2

CHAPTER 2

Switching Conversion and Analysis 48

1

CHAPTER

P

ER ELE TR Nl

AND

THE ENERGY REV LUTI

N

The magnificent energy of Niagara Falls readily converts to electricity for transport to users far away. (Top: Niagara Falls. Bottom: Marimbondo Hydroelectric Power Plant, courtesy of Furnas Centrais Electricas, Brazil.) FIGURE 1.1

2

THE ENERGY BASIS OF ELECTRICAL ENGINEERING

3

1.1 THE ENERGY BASIS OF ELECTRICAL ENGINEERING In 1748, Benjamin Franklin used his remarkable new invention, the electric motor, to roast a turkey for a riverbank party [1]. Since then, electricity has become the dominant way to convert, transport, and use energy. Growing electricity production and consumption are indicators of economic development and well-being. The intensity, convenience, and flexibility of electricity make power grids one of the largest global businesses. In electrical form, the energy needs of a city can be carried by a few wires of modest size. Energy is readily controlled for needs ranging from nanoscale medical implants and mobile phones to steel mills and national rail transport systems. What are the alternatives? Moving water has driven industry for centuries. Today, it is cheaper and easier to use water to produce electricity, as shown in Figure 1.1, than to divert a river to deliver energy to hundreds of factories and businesses in a city. Hydroelectric resources in Canada, Brazil, Egypt, China, and other places supply vast regions because of the flexibility and intensity of electricity. Hydrocarbon fuels offer another approach, and they are shipped thousands of kilometers through pipelines for transportation and heating. Fuel is difficult to convert efficiently to meet wider needs. Energy in thermal form is also common. In many large cities, low-pressure steam from power plants is distributed to buildings for winter heat, but the temperature is modest and limitations of Carnot cycles make it difficult to use for other purposes. Even a large steam-based power plant has conversion efficiency below 40%. Electricity circumvents Carnot limits: a 1 V battery has energy intensity that corresponds to a 50,000°C heat source. Electric motors can exceed 98% conversion efficiency. Electricity serves as an "energy currency" because it is so convenient to prepare, distribute, control, convert, and use. It takes a wide range of different forms, a few listed in Table 1.1, with contrasting characteristics. We see electrical energy in de batteries or ac outlets, single-phase or three-phase circuits, 5 V or 1 V logic levels, bipolar 12 V levels, 15 kV neighborhood distribution lines, transmission systems rated at a million volts, and a variety of frequencies. Each application is best matched to a particular type of source. Some examples of devices that require and include conversion processes are shown in Figure 1.2. Even so, people do not really use electricity; they use its tangible end results in the form of heat, light, information, communications, and mechanical work. There are limitations in spite of the fundamental properties. Electricity works so quickly that problems can propagate over a large region faster than engineers can react. It takes on a wide diversity of forms. The best forms for transport, for instance, are not best for most applications. Because it is difficult to store, it is the ultimate "real time" resource; generation and consumption must match on millisecond time scales. Direct electrical storage involves capacitors (batteries store chemical energy), and these are bulky. The following example illustrates the limited energy storage capabilities of typical capacitors1.

1 Appendix

B lists many of the important SI units.

TABLE 1.1 Examples of Electrical Energy Forms Purpose

1)rpical Form of Electricity

Expected "Ideal Form"

High-power generation Bulk energy transport Domestic wiring

Three-phase ac, 50-60Hz, 10-30 kV Three-phase ac, up to 765 kV or more Split single-phase ac, 120 V (Americas), 230 V (Europe, Asia) Single-phase ac, three-phase ac +3.3 V de and less

Polyphase ac de, 500 kV and up Low-voltage de

Electric motors Digital electronics Analog electronics Fluorescent lighting Solid-state lighting Storage battery applications Medical and industrial magnetic devices Photovoltaic energy Mobile power systems

Electric transportation Telephone and other communication systems Underground power cable Portable equipment

FIGURE 1.2

+12 V, ±12 V, lower levels Single-phase ac, approximately 230 V Controlled de current Load dependent

Polyphase ac, with frequency control Low-voltage de (0.5 V and below are discussed) Bipolar de High-frequency ac Controlled de current Controlled de current

Depends on available sources

High-current de

Fixed de load or large inverter +12 V de (automotive), +28 V de (aircraft), 400Hz ac (aircraft, marine), variable-frequency ac (aircraft) 700 V de and other levels 48 V de and other de levels

Matched to peak power transfer de at 300 V and higher levels

Polyphase ac 1.5 V to 20 V battery levels

Bipolar de Highest possible efficiency, with multiple de voltage levels for digital, analog, radio-frequency, and display electronics

Electrical applications. Each uses a different form of electricity.

Medium-voltage de Low-voltage de

WHAT IS POWER ELECTRON ICS?

5

The capacitor is the only device capable of direct electrical energy storage. The device here, rated at 2700 J.LF at 375 V, can keep a 20 W lamp burning for less than 10 s. FIGURE 1.3

Example 1.1.1 A 2700 J.lF capacitor like the one shown in Figure 1.3 is connected across a 375 V de source. How much energy does this capacitor store? How long will this energy support a20 Wlamp? A 2700 J.lF capacitor in a 375 V circuit stores 1/2 CV2 , or 190 J of energy. A 20 W lamp uses energy at the rate of 20 J/s. The energy stored in this capacitor will keep the bulb burning for (190 J)/(20 J/s) = 9.5 s. Higher voltages and capacitances will add only a few more seconds. It is challenging to support more than a few seconds of energy needs with capacitors. A liter of gasoline delivers about 10 MJ as burned in a typical engine, far more energy than a similar volume of capacitors or batteries.

In the example, keep in mind the distinction between energy, which ultimately represents useful work, and power as the rate of energy flow. Although people often use "power" and "energy" interchangeably when discussing the electricity grid, the flow intensity in watts should not be confused with the work effort in joules. They have far different engineering impacts on design.

1.2 WHAT IS POWER ELECTRONICS? Most electrical engineers work on information, control, and communications or they create and operate the electricity grid itself. What about the conversion and control of energy? This is the domain of power electronics. The objective is to apply electronics technology directly to energy processing. Here is a more specific definition:

Definition: Power electronics involves the study of electronic circuits intended to control the flow of electrical energy and their applications. These circuits handle power flow at levels much higher than the individual device ratings.

In practice, power electronics is a peer of analog electronics, digital electronics, and radio-frequency electronics as a field of study, as suggested in Figure 1.4. A distinctive

6

POWER ELECTRONICS AND THE ENERGY REVOLUTION

FIGURE 1.4

Advanced topics in electronics.

ELECTRONIC CIRCUITS AND NETWORKS

RADIO-FREQUENCY ELECTRONICS

DIGITAL ELECTRONICS

ANALOG ELECTRONICS

POWER ELECTRONICS

Control, energy, and power electronics are interrelated. Adapted from [2]. FIGURE 1.5

Circuits Magnetics Power Semiconductors

ELECTRONICS

and DEVICES

feature is breadth of scope. As in Figure 1.5 [2], the field combines aspects of energy systems, electronics, and control with many specialized disciplines. The breadth and variety of power electronics appeal to the generalist, and many engineers in the discipline explain that their interest is based on wide connections across electrical engineering topics. The challenges, however, are unique because power converters are large-signal nonlinear networks. The circuits and many of the devices do not lend themselves to familiar tools and approaches. This offers opportunities for new ways of thinking and for innovation. Here are some examples. Example 1.2.1 An audio amplifier is an electronic circuit that often handles considerable energy levels. In North America, a typical stereo receiver draws 60 Hz ac energy, detects low-power FM electromagnetic signals, and delivers substantial power levels at audio frequency. Is this power electronics? Maybe. However, many amplifier circuits do not handle high relative energy levels. Conventional class AB amplifiers are not considered examples of power electronics. A 100 W amplifier of this type is designed with transistors and heat sinks big enough to dissipate at least 100 W. The devices are used primarily to reconstruct audio information rather than to control and convert energy, and the efficiency is usually well below 50%. Switching class D

THE NEED FOR ELECTRICAL CONVERSION

7

1N4004 170cos(120 nt)

v FIGURE 1.6

170Q 5000 J.lF

Half-wave rectifier for Example 1.2.2.

amplifiers [3] are power electronic circuits, and these are used in portable communications products, automotive systems, telephone products, and many home theater systems. A class D circuit for 100 W audio output is designed for energy conversion. It might use transistors rated for only 20 W dissipation and can readily exceed 80% efficiency. The ratio of energy handled to energy consumed is 4:1 or higher.

Example 1.2.2 A half-wave rectifier circuit is built with a standard 1N4004 diode and a capacitor, as shown in Figure 1.6. This device is specified for peak reverse voltage of 400 V, average forward current of 1 A, and power dissipation of 1 W. The circuit input is 60 Hz, 120 V ac RMS, and the output is 170 V de at up to 1 A. Is this a power electronic circuit? Yes. The diode is rated for 1 W but is controlling up to 170 V and 1 A (yielding a product of 170 W) at the circuit output. The circuit controls 170 times as much energy as its devices consume. Rectifiers are typical examples of power electronic circuits. Example 1.2.3 The FDP26N40 is a metal oxide-semiconductor field-effect transistor (MOSFET). Its manufacturer reports that it has a maximum continuous drain current rating of 26 A, maximum drain-source breakdown voltage of 400 V, and rated power dissipation of 265 W. In power electronic applications, this device can be used to control up to 26 A x 400 V = 10.4 kW. This transistor is rated to dissipate up to 265 W, yet it can control the flow in a 10 kW circuit. Several manufacturers have developed power electronic controllers for domestic refrigerators, air conditioners, and even electric vehicles based on this device and its relatives. Power electronics designers look mainly at voltage and current ratings of a device. The power handling rating is an important factor in setting up design requirements and is much different (and higher) than the device power dissipation rating:

Definition: The power handling rating of a given device is the product of the voltage rating and the current rating.

The power handling rating sets up a target; there should be a way to use a device to manage energy flow at a level that approaches this value. One drawback of using devices close to their power handling ratings is that small problems can have large consequences. Many engineers find out the hard way that power semiconductors make fast, but expensive, fuses.

1.3 THE NEED FOR ELECTRICAL CONVERSION In the earliest days of electricity grids in the 1880s and 1890s, there were public arguments back and forth between Edison, who advocated de distribution, and Westinghouse and Tesla, who advocated ac distribution [4]. Although many would claim that Tesla "won," based on advantages that have led to domination of three-phase ac power systems, the outcome is more

8

POWER ELECTRON ICS AND THE ENERGY REVO LUTION

subtle to a power electronics engineer. Because of the early systems, there has always been a need for ac-dc and dc-ac conversion. It can be argued that the downfall of the original Edison system was the lack of good methods for de-de conversion. Today, technology has caught up. Even so, the Edison system did not really disappear. In much of the world, there are actually two overlaid electricity grids. One, the familiar ac system using Tesla's technologies, serves energy needs of industrial and residential customers. The other is a de system that serves the needs of the telephone and communications infrastructure. Many modern applications are not a good match to either the Tesla or the Edison systems, and this makes power electronics ubiquitous. A desktop personal computer consumes power provided at about 1 V de, 3 V de, 5 V de, 12 V de, and three or four more levels, not the ±150 V de provided in the Edison system. The motor in an electric car, industrial robot, manufacturing line, disk drive, or even a modern washing machine does not operate directly from a fixed-voltage, constant-frequency ac supply as envisioned by Tesla. The ultimate result is that the best forms of electricity for generation, bulk transmission, distribution, and end use differ in many ways. The job of the power electronics engineer is to make it practical to exchange energy among all the different electrical forms building bridges between what were once seen as mutually exclusive domains. Table 1.1 suggests long-term ideal forms. Based on Tesla's innovations, for instance, three-phase ac is probably the best form for electricity generation. It has been found that high -voltage de (HVDC) is the best form for large-scale long-distance transmission. Inside a school, factory, or home the situation is less clear: de power offers better safety and higher efficiency, while ac power is easier to protect. It is a matter of present debate whether de should return to wider use within homes and buildings. At the point of end use, the variety of needs is huge. Electronic appliances such as computers and flat-screen televisions require low-voltage de power. Fluorescent lamps need high-frequency ac with controls that account for their nonlinear behavior, although many still operate directly from the grid if the voltage is suitable. Ovens and heating appliances are flexible but benefit from relatively high voltage. Motors in home appliances, heating ventilation, and air-conditioning systems, and robots often use power electronic inverters that operate in turn from de. This wide variety presents unending challenges to power electronics engineers. An expert might work one day on the complex power distribution inside a smart phone, the next on a multi-kilowatt battery charger and management unit for an electric vehicle, and the next on a generation interface for a wind turbine. The challenges range from microwatts to megawatts, and the needs range from electronic devices operating at hundreds of millivolts to utility grid devices at hundreds of kilovolts.

1.4 HISTORY 1.4.1 Rectifiers and the Diode There has been a need for energy exchange between de and ac systems since the dawn of the electricity grid. The rectifier, a general term for acto de conversion, was served originally with an ac motor driving a de generator. The rectifying diode is a device that conducts asymmetrically based on polarity and also can support ac-dc conversion. The basic form of the diode rectifier circuit was discussed in the nineteenth century, and it is interesting that rectifier diodes were discovered during the 1880s [5]. The solid-state electronics era began

HISTORY

FIGURE 1.7

Circuit symbol for the silicon-controlled rectifier.

Gate

9

G

Anode

Cathode

A

K

long before the modern semiconductor age. Originally it was based on selenium, copper oxide, and other nonlinear materials that remained important for diodes into the 1950s. The vacuum diode initiated the tube electronics era in about 1901 [6]. Today, silicon diodes are available that block 6 kV or more and can carry thousands of amps [7]. Schottky diodes built with SiC [8], GaN [9], and other materials [10] can achieve even more extreme ratings. Rectifier diodes, as two-terminal devices, respond to circuit conditions and are not subject to direct control. Controlled rectifiers to produce adjustable voltages and currents for smelters, welders, motors, electrochemical processes, and battery chargers have been important from the beginning. Vacuum tubes with small amounts of mercury and extra control grids were invented by Hewitt in 1902 [6], [11]. A 1905 paper by C. P. Steinmetz [12] shows essentially the entire suite of methods and waveforms of controlled rectifiers. They support more direct rectifier control. Mercury arc tubes were the mainstay of industrial controlled rectifiers well into the 1960s, and they dominated in HVDC transmission even after that time. Some observers associate the birth of power electronics with the invention of the silicon-controlled rectifier (SCR) in 1957 [13], [14]. This three-terminal device, with the symbol shown in Figure 1.7, acts like a diode only when a pulse is applied to its third gate terminal, producing the basic function of an arc tube with a solid-state device. The SCR is the most basic device in the thyristor family and remains the device of choice for industrial rectifiers. When control is not needed, semiconductor diodes can do the job. Modern SCRs and diodes individually reach about 10 MW power handling ratings. Series and parallel sets extend this all the way up to HVDC transmission levels, as exemplified by Figure 1.8. A major link from the Columbia River to Southern California on the U.S. Pacific coast is rated at ±500 kV and 3100 MW. The HVDC links from the Itaipu power plant in Brazil to Sao Paulo are rated at ±600 kV and 6300 MW. Even larger lines have been discussed for transferring solar power from the Sahara Desert to cities in Europe and across continents. A more recent development is the active rectifier, an ac-dc conversion circuit fundamentally different from a diode or SCR bridge. An active rectifier controls energy flow between an ac source and a de load dynamically, adjusting rapidly to track a desirable sinusoidal current on the ac side. The general approach is common in small de power supplies and electric vehicle chargers, and it is in growing use in industrial motor controllers.

1.4.2 Inverters and Power Transistors An inverter is a general term for a de to ac converter. Although this function has been just as important as rectification since the beginning, diodes do not support it, and it has been fundamentally more challenging. Mercury arc tubes and SCRs can support inverter operation with auxiliary circuits. A few engineers developed this as early as the 1920s [15], [16], but practical auxiliary circuits appeared only after the introduction of the SCR. Early leaders in the field such as McMurray [17] and Hoft [18] were famous for their SCR-based inverter designs. By 1964, General Motors had demonstrated electric cars that used ac motors controlled by these types of inverters [19].

10

POWER ELECTRONICS AND THE ENERGY REVOLUTION

A rectifier-inverter set for the Pacific Intertie high-voltage line between Oregon and Southern California. Courtesy of Los Angeles Department of Water and Power. Photographer: Peter S. Garra. FIGURE 1.8

Although inverters can be built with SCRs, power transistors offer more flexibility and control capability. During the 1970s, power bipolar junction transistors (BJTs) came into use for inverters, at least up to several tens of kilowatts. Spurred on by space power systems and industrial motor controllers, extensive development in the 1970s and 1980s led to many mature designs. However, power BJTs have limited gain, and it quickly became clear that high power ratings would be hard to support. The largest devices reached 1 MW power handling ratings, although 250 kW devices were more practical. The power MOSFET, introduced in the late 1970s, is a voltage-controlled device that proved easy to operate. The power MOSFET quickly supplanted the BJT in applications up to about 1 kW. Today, it has become vital in inverters for solar energy and a whole host of high-performance applications. Inverters for radio-frequency transmitters, audio amplifiers, and small motor controllers generally use MOSFETs. Typical individual devices can handle up to 10 kW, and packages containing multiple dies extend this. Unique to power electronics is the insulated-gate bipolar transistor (IGBT). This device, commercialized in the late 1980s, adds benefits of voltage control to power BJTs. It dominates mid-range inverters, through about 500 kW or more, and is the reason hybrid and electric vehicles have enjoyed renewed success. IGBTs have reached ratings beyond 4 kV and 2000 A, with power handling ratings above 200 kW. Six are used in a typical motor controller such as the one in Figure 1.9. They have become the component of choice for most motor control applications. At the very highest power levels, above 1 MW, IGBTs and even SCRs are not always the best choice. This is the province of the gate turn-off SCR (GTO), a device with high ratings

HISTORY

FIGURE 1.9

11

Industrial motor controller rated for 100 kW.

that provides some of the control capability of transistors. Although GTOs are not as easy to use as IGBTs, they have ratings suitable for wind turbines and locomotives. An enhanced device called the gate-commutated thyristor (GCT) is now implemented in complete integrated gate-commutated thyristor (IGCT) modules. The IGCT is a printed circuit board that includes a large GCT or GTO and a substantial gate control circuit. These assemblies allow power electronics to support motor drives and converters rated at several megawatts.

1.4.3 Motor Drive Applications Motor control and motor drives are sometimes considered a separate application field related to power electronics. In a typical commercial ac motor controller, the incoming ac power is rectified to create a de voltage source. This de voltage supplies an inverter, often built with IGBTs. Control of ac motors has been an important technological objective since Tesla introduced the polyphase induction motor in the late 1880s [20]. De motors previously were common in control applications, because their speed can be altered by adjusting the input de voltage level, and their output torque can be manipulated through control of their main winding current. They have major disadvantages in cost and reliability: a true de motor has brushes and a mechanical commutator to maintain. Ac motors, and especially induction motors, are inherently cheaper to build and maintain than de machines. They have better power-to-weight ratios than de machines and can operate at higher speeds. Moving parts are few, and only the bearings themselves require upkeep if motor ratings are observed. However, the speed of an ac machine is tied to the input frequency, and the torque is adjusted by altering the magnetic field levels in the device. The challenge of providing adjustable magnetic field and input frequency makes ac motors difficult to control. Before about 1980, the extra cost of power electronics exceeded the cost disadvantage of de machines, and de systems were used when control of motor speed or torque was needed. In a few cases, the reliability advantages of ac machines were critically important. Rotating machines were used to provide adjustable frequency for these applications. Inverters built from power MOSFETs or IGBTs meet the functional requirements of ac motor control. In the mid-1990s, the cost of these electronic drives began to drop so

12

POWER ELECTRONICS AND THE ENERGY REVOLUTION

•

,.

,__

FIGURE 1.10

T

L

........ -,..................... . JAPAN AIRLINES ·

The Boeing 787, a highly electric aircraft.

dramatically that the combination of a power electronic circuit and an ac motor became cheaper than an equivalent de motor system. Advanced ac motion control equipment can address almost any automation application. The emergence of high-performance rare-earth permanent magnets (PMs) plays into this history. Modern PM machines offer performance and efficiency advantages but must operate with inverters. MOSFETs support PM motors in small robot actuators and in many devices, including disk drives and DVD players. IGBTs support PM motors in industrial applications and electric vehicles. Sometimes the combination of an inverter and a PM ac machine is called a "brushless de machine" to emphasize the control capability. Electronic drives can manipulate wing flaps in a jetliner like the one in Figure 1.10, operate a power steering system, support a quiet light rail commuter train, or accelerate a race car.

1.4.4 Power Supplies and de-de Conversion Power supply circuits for computers, portable communications, television sets, electrical appliances, home theater equipment, and so on are a commonplace element of electrical equipment. Some typical supplies intended as components of larger systems are illustrated in Figure 1.11. The earliest power supplies for vacuum tube electronics employed rectifiers followed by filtering circuits to create a smooth de output. Until about 2000, most power supplies took this same general form, with the addition of a transformer at the ac input to set the correct voltage level. This conventional power supply style matured after about 1970, when monolithic integrated series regulator circuits [21] were introduced. A series regulator is an amplifier that provides a fixed power output even from a somewhat noisy rectified signal. The combination of transformer, rectifier, and regulator is called a linear power supply since the output circuit that maintains fixed voltage is based on a linear amplifier (the system as a whole is still nonlinear). These circuits are being supplanted by more comprehensive power electronics. Late in the 1960s, use of de sources in aerospace applications motivated the development of de-de conversion circuits for power supplies. The basic circuits are much older and grew out of early rectifier applications. Power semiconductors make these circuits inexpensive and reliable. In a typical arrangement, an ac source from a wall outlet is rectified without a transformer; the resulting high de voltage is converted through a de-de circuit to the 12 V,

HISTORY

FIGURE 1.11

13

A typical computer power supply and two fixed-output switching supplies.

5 V, 1 V, or other level required by the application. These switched-mode power supplies are widespread. A personal computer often requires power supplies that deliver 1 V, 3.3 V, 5 V, 12 V, -12 V, 24 V, and other levels. There are additional power supply requirements for video displays, power-over-Ethernet applications, and other peripheral devices. Only a switched-mode supply can support such complex requirements without high costs. The bulk and weight of linear power supplies make them infeasible for personal computers, hand held communication devices, calculators, notebook computers, tablets, flat-panel televisions, and many small appliances. Switched-mode supplies often use power MOSFETs. Trends toward high reliability, low cost, and miniaturization have reached the point at which a 12 V power supply sold today might last a million hours (more than 100 years!) and provide 100 W of output in a package with volume of less than 10 cm3, for a price of less than US$0.10 per watt. Power supplies rated up to a few watts can be built right into an ac plug, as in Figure 1.12. Beyond power supplies, which draw energy from the ac grid, de-de converters provide important building blocks for many conversion functions. Energy exchange among disparate de voltage and current levels became important in telephone systems and space programs. It can be argued that de-de power electronics is one of the most important spinoffs of the 1960s-era U.S. space program. When Stanley and Westinghouse developed the commercial magnetic transformer in 1886 [22], it was to allow convenient energy exchange among ac voltage levels. Electricity produced from a generator at a few kilovolts can be stepped up to hundreds of kilovolts for transmission, back to a few kilovolts for distribution, and ultimately to about 240 V or less for a customer. For de-de conversion, a "transformer" is not so direct. Magnetic transformers

14

POWER ELECTRONICS AND THE ENERGY REVOLUTION

FIGURE 1.12

This 5 W power supply fits into the ac plug itself.

require time-varying signals. Today most high-power de-de converters are really dc-ac-dc converters, with a small high-frequency transformer embedded inside to alter the voltage level. The size of a transformer is inversely proportional to operating frequency. A 50 kHz device is about a factor of 1000 smaller than a 50 Hz transformer with similar ratings. It is also possible to interconnect switches and inductors to perform de-de conversion without a transformer. Some examples will be considered in Section 1.6. The necessary converter circuits were known by the 1940s and implemented with vacuum tubes. In the 1960s power BJTs made implementation simpler. An Apollo lunar spacecraft combined 28 V de and 400 Hz ac to manage its subsystems, but it also needed de-de converters for electronics [23]. The International Space Station is a highly complex de power system, using a variety of de-de converters and other power electronics [24]. These converters gained momentum in the 1980s and 1990s as power MOSFETs matured. Stand-alone de-de converters, in the form of "power bricks," came into wide use in communications applications in the early 1990s. They are building blocks for cellular phone towers, data centers, and many high-performance applications. During the 2000s, de-de converters packaged with rectifier bridges began to blur distinctions from power supplies and to replace older types of rectifier supplies. Today, miniature power supplies such as the integrated USB device in Figure 1.12 are designed around a de-de conversion circuit. The cost has dropped to the point that practical "de transformers" are now common. These circuits are essential enablers of modern battery-based devices. More sophisticated de-de converters are used in advanced computers and large data centers. A server blade or computer workstation uses a comprehensive de power distribution architecture previously found only in satellites. In a de-based data center, distribution uses de voltages at hundreds or thousands of volts and then converts to 12 V or 48 Vat individual boards or computers. From there, electricity is delivered to many point-of-load de-de converters that step up or step down to the local desired voltage. Device technology for power supplies and de-de converters is being driven by expanding needs in the automotive industry, the telecommunications industry, renewable energy, personal portable devices, medical equipment, and other applications. The amount and complexity of electronic hardware and computer control in a typical automobile continue to increase. Power

HISTORY

15

conversion for this industry must be cost effective yet rugged enough to survive high vibration and a wide temperature range. Global communications are possible only when sophisticated equipment can be used almost anywhere in the world; however, electrical supplies are neither reliable nor consistent in much of the world. In North America, voltage swings are often less than ±5% around a nominal value. In many developing nations, the swing can be ±25% when power is available; battery chargers and computers must tolerate these swings. Portability challenges designers to obtain the best possible performance from small batteries, so equipment must use as little energy as possible. The low voltages used for portable battery packs, which range from less than 2 V up to only about 20 V, produce difficult conversion requirements when they need to accommodate differing ac supplies around the world. Beyond silicon power semiconductors, wide bandgap materials, most notably SiC and GaN, are of interest for power electronic devices [25]. These materials are beneficial because in principle they can be more efficient than silicon devices, they can function at higher temperatures and voltages, and they support more effective thermal designs to remove heat. Less material can be used to meet device performance objectives. The ultimate material is probably carbon, either as diamond or as a graphene structure. Diamond and graphene are far better heat conductors than other known solids [26] a substantial benefit in energy-intensive power converters. Diamond is difficult to implement in power devices, however [27].

1.4.5 Alternative Energy Processing Most electrical forms linked to alternative and renewable energy are incompatible with the power grid. Photovoltaic (PV) panels and fuel cells deliver de power. Wind turbines, ocean wave generators, and small gas turbines usually deliver variable-frequency ac output. Many renewable resources benefit from battery energy storage, which must be interconnected with them. Power electronics is a vital enabler for all these resources. Simply put, alternative energy is not possible without power electronics. Power electronics must provide all the control functions necessary for safe delivery of electricity from alternative sources to a utility grid or other load. The PV arrays in Figure 1.13, for example, should be controlled to deliver the highest possible power to the

-

FIGURE 1.13

utility grid.

These solar panel arrays deliver de power to inverters, which convert it and deliver it into the

16

POWER ELECTRONICS AND THE ENERGY REVOLUTION

Large wind turbines are a cost-effective electricity resource, but they cannot deliver energy to the grid without power electronics. FIGURE 1.14

grid at any moment; the panels are expensive, and the owner should settle for nothing less. This maximum power control is a difficult problem, since a panel sees clouds, motion of the sun, dirt, temperature changes, and other variations as it operates. Wind turbines like those in Figure 1.14 are also controlled for maximum power, but in addition must have dynamic limiting controls to make sure strong gusts and storms do not cause damage. The microturbine shown in Figure 1.15 spins a small ac generator at extreme speed (50,000 RPM or more). These units can burn exhaust gases from landfills or biowaste. Power electronics for microturbines usually rectify the generator output and then connect to the utility grid through an inverter. The inverter in this case, as well as for PV and wind applications, must produce the correct frequency and voltage and disconnect if something goes wrong in the grid or in the alternative resource.

1.4.6 The Energy Future: Power Electronics as a Revolution In 2003, the U.S. National Academy of Engineering listed electrification as the greatest engineering achievement of the 20th century [28]. Electricity seems commonplace in the developed world, but virtually all commerce and activity stops when power is out. Electrification remains an urgent priority in much of the world as an essential enabler of economic growth, water processing and delivery, health, education, and information. The electrification revolution of the 20th century made limited use of power electronics. The most fundamental energy innovations of the present and future, including electrification of transportation, dramatic improvements in efficient energy use, renewable resources, and personalized electronics, all rely on power electronics to make them work. An emerging second electrical revolution, driven by power electronics, is readily apparent around us as hybrid and electric cars enter mass markets, compact fluorescent and solid-state light-emitting diode (LED) lighting take over from incandescent lamps, electronics become small and portable, and demand grows for wind and solar power.

HISTORY

17

-

-

..

A microturbine is a modest-size device that delivers a few tens of kilowatts from natural gas, waste methane, or biowaste gas products. An internal rectifier and inverter process power for delivery to the grid. This unit is less than 2 m tall. FIGURE 1.15

Today, most electricity is processed by power electronics at some point between original generation and final use. The old debate between Edison's de system and Tesla's ac system becomes moot power electronics can take in the most convenient available electricity form and deliver the desired result. The choice of ac or de for the network is secondary, governed by safety, protection, and reliability rather than by the generators or loads. Modern energy requirements and electricity demands are far different from the incandescent lights, simple electric stoves, and line-connected electric motors that dominated the first wave of electrification. The circuit in Figure 1.16 is designed to operate a set of LEDs for a solid-state lamp [29] and is based on de-de converters. The growth of electric transportation will have an enormous and unpredictable impact on grids and patterns of energy use. It is likely that some parts of the world will skip wired grids and opt for direct local use of renewables. Energy challenges and the impact of energy production and consumption on the environment have been concerns for many decades. Although power electronics does not solve the challenges directly, it facilitates higher efficiency, better control, and renewable resources and enables new types of solutions. The transportation system of the future is likely to benefit from a wide range of flexible energy resources. Energy users will seek more efficient products that reduce costs but do not compromise performance. Electricity provides

18

POWER ELECTRONICS AND THE ENERGY REVOLUTION

Vline

85-265 Vac

"v

EMI filter

PFC

de-de (flyback)

~-------------------------,

~----------------------------,

y

y

y

..... ...

........ I::;

r

==

\.\.

Vsense Isense

PFC controller

de-de controller ------- -- -------- - ------- ---

FIGURE 1.16

LED driver circuit arrangement (courtesy of B. Lehman).

the energy currency with the flexibility for exchange between nearly unlimited sources and loads. Power electronics is the physical means of "currency exchange" in this context, opening broad new possibilities for the energy future.

1.4.7 Summary and Future Developments Not long ago, power semiconductor devices were the limiting factors in converter design. Today's power electronic components routinely reach power handling levels needed by household appliances, industrial processes, and automobiles. A designer chooses a circuit and device to match the application, and many alternatives are often available. The field has become an "applications-driven" subject. A few fast-growing applications are shown in Figure 1.17. The chronology is summarized in Table 1.2.

A few of many growth areas for power electronic applications: renewable energy, integrated power, heavy vehicles, data centers, and electric transportation. FIGURE 1.17

GOA LS AND METHODS OF ELECTRICAL CONVERS ION

19

TABLE 1.2 Summary of Chronology of Electronic Power Conversion Dates

Device or Technology

Conversion Technologies

1880s

Transformers, motor-generator sets

1900s 1920s

Vacuum diodes Mercury-arc tubes

1930s 1940s

Selenium rectifiers, grid control Magnetic amplifiers

1950s

Semiconductor diodes

1960s

Silicon-controlled rectifiers (SCRs)

1970s

Power bipolar transistors

1980s

Power field-effect transistors

1990s

IGBT

2000s

Power electronics building blocks, SiC devices GaN devices

Electromechanical units for ac-dc conversion Voltage level shifting for ac Development of major applications Controlled rectification Electronic circuits for ac-dc and dc-ac conversion Basic techniques worked out for ac-ac conversion "Semiconductor" rectifier technologies in regular production Electronic power amplifiers Further advances in electronic conversion Inception of electronic conversion for high-voltage de power transmission Growing need for small power supplies for electronic gear High-power semiconductor devices, which quickly replaced mercury tubes and made controllable ac-dc converters practical Substantial simplification of dc-ac and de-de conversion techniques Emergence of power electronics as a separate discipline New methods for de-de conversion Rapid expansion of markets for miniature power supplies Nearly any application now possible Emphasis on the best alternative for a given application Designers consider more aspects of a complete system Rapid growth of vehicle applications Rapid growth of solid-state lighting Growth of renewable resources

2010s

Modern power electronic methods are being applied to audio amplifiers, smart phones, medical implants, microprocessors, sensors that harvest vibrational energy from their surroundings, and intelligent power grids. There is need for skilled engineers who can apply the methods in unconventional ways.

1.5 GOALS AND METHODS OF ELECTRICAL CONVERSION 1.5.1 The Basic Objectives The objective in power electronics is to control energy flow between an electrical source and a load with a power converter, as depicted in Figure 1.18. The converter must manipulate flow but should not consume energy. The reason is simple: any energy used within the converter is lost to the overall system. To be useful, a converter should have high input-output energy efficiency, 1J =Pou/Pin· This is the first and primary design objective in power electronics: EFFICIENCY TARGET ---7 100 % We seek lossless processes to implement converters. A power converter connected between a source and a load affects system reliability. A failure in the converter affects the user (the load) just as if the energy source fails. An unreliable power converter creates an unreliable system. To put this in perspective, consider that

20

POWER ELECTRONICS AND THE ENERGY REVOLUTION

FIGURE 1.18 Electric energy source

Basic electric power conversion

system.

•

Power converter

•

Electrical load

a typical U.S. household loses electric power only a few minutes a year. Energy is available 99.999% of the time ("five nines"). A converter must be better than this to avoid degrading the system. As high efficiency is achieved, this second reliability objective grows in importance: RELIABILITY TARGET ---7 NO FAILURES OVER APPLICATION LIFETIME Reliability can be a more difficult objective than efficiency. Imagine trying to prove that a circuit will not fail over decades of use.

1.5.2 The Efficiency Objective

The Switch

As simple a circuit element as a light switch, like the one in Figure 1.19, is a reminder that the extreme requirements in power electronics are not especially novel. Ideally, when a switch is on, it exhibits v switch = 0 and will carry any current imposed on it. When a switch is off, it blocks the flow of current (i switch = 0), regardless of the voltage across it. The device power, Pdevice = v switch iswitch' is identically zero at all times. The switch controls energy flow with no loss. Reliability can be high too. Well-made household light switches perform over decades of use and can survive about 100,000 operations. A mechanical light switch does not meet all the practical needs, though. A switch in a power supply often functions 100,000 times each second. Even the best mechanical switch will not last beyond a few million cycles. A circuit built from ideal switches will be lossless. Many people equate power electronics with the study of switching power converters. Other lossless elements such as capacitors, inductors, and conventional transformers will also be useful for conversion. The complete concept is shown in Figure 1.20, which illustrates a power electronic system. The system consists of an energy source, an electrical load, a lossless power converter, and control functions. The converter is a power electronic circuit with switches, lossless

A switch and its electrical terminal values. FIGURE 1.19

+ V switch

•

1 switch

GOALS AND METHODS OF ELECTRICAL CONVERSION

FIGURE 1.20

21

A basic power electronic system.

Control

energy storage elements, and magnetic transformers. The controls take information from the source, load, and designer. Then they determine how the switches operate to achieve the desired conversion. Usually, the controls are built up with conventional low-power analog and digital electronics.

1.5.3 The Reliability Objective

Simplicity and Integration

It is well established in systems engineering that more parts make a system more likely to fail [30]. Power electronic circuits tend to have few parts, especially in the main energy flow paths. The necessary operations must be carried out through shrewd use of those parts. Often, this means that sophisticated control strategies are applied to seemingly simple conversion circuits. One way to avoid the reliability-complexity tradeoff is to use highly integrated components. A high-end microprocessor, for example, contains billions of parts. Since all interconnections and signals flow within a single chip, the reliability is nearly that of a single part. An important parallel trend in power electronic devices is the integrated module. Manufacturers seek ways to package several switching devices, their interconnections, protection components, and filtering devices together as a unit. Control circuits for converters are also integrated as much as possible to keep reliability high.

1.5.4 Important Variables and Notation In a power electronic system, several electrical quantities are of special interest. Efficiency has already been identified. Maximum values of currents and voltages will be needed to determine necessary device ratings. Energy flow is the underlying objective, and power and energy levels in each part of the system are important. We are most interested in energy flow over reasonable intervals of time. The power electronic circuit must control the flow from source to load. The average energy flow rate, or average power, is therefore of particular interest. Some important quantities: Average power at a specified location. This represents useful energy flow. Peak values of voltages and currents. These determine device ratings. Average values of voltages and currents, the de values in a circuit. Root mean square (RMS) voltages and currents. The average power in a resistor is determined by RMS voltage or current. RMS values often govern the losses in a converter. Waveforms. Power electronic circuits often have clear graphical properties. Study of waveforms is often a direct way to evaluate a circuit's operation. Device power. Switches are not quite ideal, and some residual power will be lost in them.

22

POWER ELECTRONICS AND THE ENERGY REVOLUTION

TABLE 1.3 Nomenclature Summary Notation

Description

v(t), i(t), etc.

Instantaneous values of voltage, current, power, or other quantities, given in lower-case notation. Time is usually shown explicitly. Angle bracket notation for average or de quantities. Averages are defined over some time period Tin integral form. Upper-case form. Used for explicit de source values as well as an alternative notation for averages, especially for average power. The true root mean square value associated with a given time function. RMS quantities are defined over a time period Tin integral form. In conventional power systems practice, a given voltage or current is an RMS value unless explicitly stated otherwise. Moving-average quantities. An average form that retains time dependence by moving the "integral window" as a function oft. A simple alternative P(t) will usually be used to indicate the moving average of power. Complex phasor quantity, with magnitude given in RMS units.

(v), (i) V, I, p

-

v(t), i (t)

V, I

-

v(t), i (t)

Small-signal perturbation or ripple. A small change around a constant level.

These quantities are crucial to an understanding of power electronics and the circuits studied in it. Notation for average and RMS values of some periodic function v(t) will be given as

V =

(v)

iT

1 v(t)dt, VRMs = =T o

iT

-1 v 2 (t)dt T o

(1.1)

Table 1.3 summarizes the notational practices in this text. The SI system of units is preferred in this book [31], although in the context of energy, other units are common. For example, electrical energy is often measured in kilowatt-hours rather than the preferred joules. Since a joule is equivalent to a watt-second, the conversion is 3.6 MJ/kW-h. Appendix B lists some relevant units and the associated conversion factors. Many problems in energy systems and power electronics involve cost analysis. The wide range and rapid fluctuations in global energy costs make it impossible to perform detailed cost analysis here, but valuable relative comparisons can be performed. Efficiency is also a helpful tool for comparison.

1.6 ENERGY ANALYSIS OF SWITCHING POWER CONVERTERS The analysis of circuits that contain switches and energy storage is, by necessity, indirect. Loop and node equations cannot be written consistently when switches are in place. Since a switch is either on or off, such a circuit has many configurations. Three methods are used for this type of analysis. In direct piecewise analysis approaches, individual configurations are studied separately. The current and voltage solutions must match at the times when switches operate. When this match is enforced, the solutions are assembled like puzzle pieces to give a complete answer. This method is often applied in simulation tools, but can be lengthy for hand solutions. The second approach is energy analysis, in which energy flows are examined during each configuration, and conservation of energy takes the place of time-based matching. Based on energy analysis, a third method, averaging, is widely used. This section

ENERGY ANALYSIS OF SWITCHING POWER CONVERTERS

23

presents energy analysis, which will lead to the development and use of averaging in later chapters.

1.6.1 Conservation of Energy over Time Since power electronic circuits are intended to be 100% efficient, energy conservation over an extended time interval is useful for analysis. Usually, energy is drawn in and stored part of the time and then removed from storage and delivered to the load part of the time. Energy goes in and out, but since none is to be lost, the converter input and output must match over a suitable time interval. Most power electronic circuits operate with periodic switching. Over a full period, the net energy flow in such a circuit should be zero. Energy conservation is always valid, so it can be used at any consistent location in a circuit. It can be used to treat the whole converter or applied to any single component within the converter. Energy analysis is usually informative when the focus is on an energy storage component that experiences the most change during operation. The circuit of Figure 1.21 provides a useful example of energy analysis. The semiconductors are used as switches, and the circuit normally operates with periodic switching with the switching devices working in alternation. Part of the time, the left switch is on and the circuit configuration is that of Figure 1.22. The rest of the time, the right switch is on and the configuration in Figure 1.23 is present. The inductor inside the converter is exposed to large changes in its voltage (and thus power and energy flows). Energy analysis based on the inductor is a good strategy for studying the circuit. In energy analysis, the energy flows are

•

/

/

l;n

...........

...........

~

,

~

•

1out

..-

r

+

+ -

Gate control

L

Gate control

R

c

IL

FIGURE 1.21

Candidate power converter.

•

Energy transfer switching circuit configuration, left switch on. FIGURE 1.22

1out

+ R

L

c

•

Energy transfer switching circuit configuration, right switch on. FIGURE 1.23

lout

+ R

L

c

24

POWER ELECTRONICS AND THE ENERGY REVOLUTION

quantified and compared. The equations for energy must balance. Since energy is the time integral of power, integrals of voltage-current products provide the equations.

Example 1.6.1 In the circuit of Figure 1.21, the switching period is T. The switches act in alternation, and each is on half of the period. The input and output voltages are approximately constant, as is the inductor current. Use energy analysis to find the values of Vout' lv and iout in terms of vin and the circuit parameters. When the left switch is on, the inductor input power is Vin!L. Over the time interval T/2, the energy into the inductor is ~n(left)

_ fT/2 _ ~n/LT - Jo ~nlL dt2

(1.2)

When the right switch is on, the inductor input power is VoulL. Therefore, over the remainder of the period, the energy into the inductor is W in(right) --

fTT/2 v outI L d t -- voulLT 2

(1.3)

Since energy is conserved, the energy going in must match that going out. Equivalently, the total energy into the inductor over a full period must be zero, and (1.4)

This requires (1.5)

Provided that the period Tis not zero (true when switching is taking place) and that IL is not zero (true provided there is nonzero energy flow in the circuit), this simplifies to vout =- ~n

(1.6)

What about the value of the current? Since iout was not connected to the inductor, it did not enter the analysis. Energy analysis based on the capacitor provides a second equation for the currents. First, the current iout must be Vou!R by Ohm's Law. Energy into the capacitor is as follows (watch the current polarities): (1.7)

(1.8)

~n(total) = -

Vou/LT

2

(1.9)

ENERGY ANALYSIS OF SWITCHING POWER CONVERTERS

25

This requires (1.10)

and therefore __ 2Vout IL R

(1.11)

which, from (1.6), becomes (1.12)

The circuit of Figure 1.21 is a polarity reverser: the output is the negative of the input. Here, the inductor current is twice the load current. An important assumption in this analysis was that the voltages and currents do not change much. This would seem highly limiting, since the stored energy cannot change unless currents and voltages change, but it turns out that the results are unaffected if the currents and voltages are allowed to change by a modest amount. Careful attention to signs is essential during energy analysis. It is vital to choose an energy direction and stick with it. For the capacitor, for example, positive input energy implies positive input current. The negative signs in equations (1.7) and (1.8) are required because the current direction defined in the figure flows out of the capacitor.

1.6.2 Energy Flows and Action in de-de Converters The circuit in Example 1.6.1 is one example of a de-de converter. In this case, it reverses the voltage polarity given a nonzero load. Let us generalize to a wider range of forms of de-de conversion. Figure 1.24 shows a similar two-switch converter. The switches act in alternation. This time, let us assume that the left switch is on for a fraction D of each period, called the duty ratio, and the right switch is on the rest of the time. Energy analysis can tell us the function of the converter.

L

•

...........

h

lout

/

,,

+ + -

FIGURE 1.24

Gate control

... .....

/\

De-de converter for Example 1.6.2.

Gate control

R

c

26

POWER ELECTRONICS AND THE ENERGY REVOLUTION •

•

lout

L

I

L

out

+

+

R

R

c

c

FIGURE 1.25

Circuit configurations for switching converter. a) Configuration with left switch on. b) Configuration with right switch on.

Example 1.6.2 The switches of Figure 1.24 operate in alternation. The left switch is on with duty ratio D, while the right switch is on the remainder of the period T. Given that the voltages and inductor current do not change much, use energy analysis to find Vout in terms of Vin· The inductor is exposed to both the input and the output voltages, so it provides a logical place to start energy analysis. Figure 1.25 shows the respective left and right switch-on configurations. Be aware of polarities. The inductor input energy is ~n(left) =

fDT

J0 ~n I L dt = ~n I L DT

~n(right) = s.;;T(~n

- Vout)IL dt

~n(total) =~nIL DT

=~nIL (T- DT)- Vout IL(T- DT)

(1.13)

+ ~n ILT- ~nIL DT- vout IL T + vout IL DT = 0

Since the total input energy over a cycle must be zero, and given nonzero T and Iv it is straightforward to solve for vout to find that V

out

=

vm

_ 1 D

(1.14)

Notice that D cannot be less than 0 (a switch cannot be on less than none of the time), nor can it be greater than 1 (a switch cannot be on more than all of the time). For 0 < D < 1, the output voltage from Example 1.6.2 will be higher than the input. This circuit is a boost de-de converter. Energy analysis based on the capacitor can be used to solve for the currents. The general energy analysis process for de-de converters is outlined in Figure 1.26. It represents a "one port" approach to analysis, in which a given lossless energy storage device is taken as being enclosed in a box. The terminal voltage and input current determine the input power, which is integrated over the appropriate time intervals to compute energy. Over time, the net energy into a lossless storage one port in a periodic system must be zero whatever goes in must be taken back out. This becomes the basis for a solution of the operating voltages and currents. In all cases, the circuits conserve energy. They also conserve charge, but voltages and currents are different; they are not "conserved" in general and differ between input and output. Many experienced electrical engineers are accustomed to thinking about conservation of current and find the double current of equation (1.12) to be surprising. In power electronics, we recognize this current scaling to be a consequence of energy conservation, and it does not violate charge conservation. Energy analysis is useful even when losses need to be considered. The circuit of Figure 1.27 shows a boost de-de converter in which the inductor has series de resistance.

27

ENERGY ANALYSIS OF SWITCHING POWER CONVERTERS

Illustration of energy analysis process. The "one port" outline emphasizes the storage elements. FIGURE 1.26

+

•

1in

I I I Electrical I I circuit or I device I I 1 One port I_--- --- --I

. vm

-

De-de boost converter with series resistance to represent losses in the inductor. FIGURE 1.27

----- ---

•

L

lout

+ Gate control

R

Gate control

c

-

With piecewise circuit analysis, the added resistor means there are exponential relationships that must be computed and connected. Energy analysis offers a more direct result.

Example 1.6.3 Find the output voltage for the lossy boost de-de converter in Figure 1.27 as a function of input voltage, switch duty ratio D, and any necessary circuit parameters, based on energy analysis. The switches act in alternation with period T, and the input and output voltages and inductor current do not change much. In this problem, the inductor energy must be in balance; over a full period, whatever energy goes in must come back out. The left and right switch configurations now include series resistance Rv but otherwise the situation is essentially unchanged. The voltage at the left side of the inductor is now Vin- ILRv and the energy results in the configurations lead to

2 ~n(right) = DT (Yin -IL RL - vout)I L dt ="'in I L(T - DT) - vout I L (T- DT) - I L RL (T - DT) T

J

~n(total) ="'in IL DT +"'in I L T - "'in I L DT- vout I L T +

2 vout I L DT - I L RL T =

(1.15)

0

Given nonzero I L and T, the period, but not the current, can be eliminated. The result simplifies to

V out

= ~n - ILRL

_ D 1

(1.16)

This is equivalent to the result from Example 1.6.2: the input voltage, less the resistor drop, divided by 1 - D determines the output. However, IL is not an independent variable, so the

28

POWER ELECTRONICS AND THE ENERGY REVOLUTION

expression is misleading. We must eliminate IL by relating it to Vout and the load resistance. A second equation is needed for current. A logical strategy is to use an energy balance on the capacitor. The capacitor voltage is Vout' while its input current changes. The energy balance is given by

~n(left) =

v2

fDT

dt =- out DT

Jo vout

R

Vout ~n(right) = fDT vout I L - R T

2

dt = V I (T- DT)- Vout (T- DT) out L R

~n(total) = vout I L T - vout I L DT -

(1.17)

v2

out T = 0 R

For nonzero I L and T, this simplifies to I

_ L-

Vout R(l- D)

(1.18)

When this result is substituted into the voltage expression, the output is V = ~n out 1- D + [RL I R(1- D)]

(1.19)

This expression reduces to the previous result if RL = 0. The ratio RifR is important. If it is small, there is little impact. If it is substantial, the output voltage is reduced considerably. For instance, if Dis 112 and RifR is 1110, the output voltage is 1.43Vin rather than the ideal2Vin- As an exercise, compute the efficiency, the ratio of output power to input power Viniv The loss in the series resistance reduces conversion efficiency. In the boost circuit, the ideal expression Vini(1-D) implies that high voltages are possible, while equation (1.19) has an upper limit. The upper limit can be found by maximizing equation (1.19): take the derivative with respect to D and then solve an equation in which this derivative is set to zero. The constraint 0 < D < 1 is also important. The result of this process shows that the maximum output voltage is produced when

D(max output) = 1 -

(1.20)

and the maximum output voltage is given by

V

outmax

=

~n

2~RL I R

(1.21)

This maximum is quite limiting in practice. For example, if RL is just 1% of the load resistor value, the maximum output is 5Vin- Boost converters are rarely used for high conversion ratios.

ENERGY ANALYSIS OF SWITCHING POWER CONVERTERS

29

Energy analysis based on periodic behavior implies that a power converter has been started up and operated until everything is steady. Under such a condition, energy input and output must match and the analysis conducted in these examples is valid. What about starting up a converter? Take the boost circuit of Figure 1.24, connected initially with the switches off. All currents and voltages are zero. As the switches operate, voltage is imposed on the inductor and its current increases. This will continue, cycle by cycle, building up the output voltage. When Vout matches Vin' the current will still increase when the left switch is on, although not when the right switch is on. The output voltage will be forced to climb higher than Vin- This will continue until the energy injected when the left switch is on is exactly balanced by the energy removed when the right switch is on the energy condition in Example 1.6.2. The time required to reach this condition will depend on the switching period and the values of L, C, and R. The boost converter has an important flaw. What if an unsuspecting user attempts to operate it without connecting a load? Now there is a problem: every time the left switch turns on, some energy is stored in the inductor. When the right switch is on, some of this energy will be delivered to the capacitor. There is no resistive load to remove any energy! Energy continues to pump in, cycle after cycle, but never leaves. The capacitor energy 1/2 CV2 continues to grow and so does the capacitor voltage. The voltage builds higher and higher until energy is removed from the circuit by some other means, and the capacitor will fail destructively when the voltage increases about its design limit. Energy analysis, when considered in advance, can help avoid these unfortunate situations.

1.6.3 Energy Flows and Action in Rectifiers Rectifiers, as ac-to-de conversion circuits, require more complicated energy analysis. The basic principles of configurations, conservation of energy, and piecewise evaluation still apply. But the waveforms are sinusoidal, and the integrals needed for energy computation require more effort. In many cases, direct piecewise analysis is more tractable. To examine the action, let us look first at a simple circuit and then add energy storage.

Example 1.6.4 Consider the circuit shown in Figure 1.28.1t contains an ac source, a switch, and a resistive load. It is a simple but complete power electronic system. A control action has been assigned to the switch: it is turned on whenever v s > 0 and turned off otherwise. Find the output instantaneous, average, and RMS voltage values. The input and output voltage waveforms are shown in Figure 1.29, following from direct piecewise analysis: the current and output voltage must be zero when the switch is off and must match vs when the switch is on. The input voltage has a time average of zero and an RMS value equal to Vpea/~2. The output has a nonzero average value that can be computed directly as 1 ( vout (t)) = f n Vpeak sin 0 dO+ 2n Jo = ___. vp_ea_k - 0 3183 1C

-

.

f

2

n

n0

dO (1.22)

vpeak

and an RMS value equal to Vpea/2. (Confirm this RMS value as an exercise.) The output has nonzero de voltage content, so the circuit acts as a rectifier. The circuit in Example 1.6.4 is a half-wave rectifier with a resistive load. The diode places restrictions on the current direction, while an ideal switch would not. An ideal switch

30

POWER ELECTRONICS AND THE ENERGY REVOLUTION

+ R

FIGURE 1.28

A simple power electronic system.

FIGURE 1.29

Source voltage and output voltage waveforms for Figure 1.28. (a)

•

I

+

L

R

0-L-R circuit (b)

(c) •

I

+

L

•

I

R

Diode on FIGURE 1.30

+

L

R

Diode off

Series D-L-R circuit and the two configurations.

allows control over whether it is on or off, whereas a diode's operation is constrained by circuit variables. Consider a second half-wave circuit, now with a series L-R load, shown in Figure 1.30.

Example 1.6.5 A series D-L-R circuit has ac voltage-source input. This circuit operates much differently than the half-wave rectifier with resistive load. Start with direct piecewise analysis. A diode will be on if forward biased and off if reverse biased. In this circuit, an off diode will give i = 0. Whenever the diode is on, the circuit is the ac source with R-L load (Figure 1.30b). Let the ac voltage be V0 cos(mt). From Kirchhoff's Voltage Law, V0 cos(mt) = L di + Ri dt

(1.23)

ENERGY ANALYSIS OF SWITCHING POWER CONVERTERS

31

Let us assume that the diode is initially off (this assumption is arbitrary, and we will check it as the example is solved). If the diode is off, i = 0, and the voltage across the diode is vd = vac· The diode will become forward biased when vac becomes positive. Therefore, the diode will turn on when the input voltage makes a zero crossing in the positive direction. This allows us to establish initial conditions for the circuit: i(t0 ) = 0, t0 = -n/(2m). The differential equation can be solved in the conventional way2 to give

i(t) = V0

-t mL _R_2_+_m_2_L_2 exp r

+ 2mr

R cos( mt) + mL sin( mt) 2 2 2 2 2 2 R +mL R +mL

(1.24)

where r is the time constant L/R, but eventually the diode will turn off. When will this happen? One first guess might be that the diode turns off when the voltage becomes negative, but this is not correct. We notice from the solution that the current is not zero when the voltage becomes negative at time t = n/(2m). (Check this!) If the diode somehow turns off, the inductor current must drop to zero instantly. The derivative of current in the inductor, dildt, would become negative infinite. What happens instead is that the falling current and associated negative inductor voltage maintain forward bias on the diode. The diode will turn off only when the current reaches zero. The moment when the current reaches zero does not have a closed-form solution from equation (1.24). For radian frequency m = 120 n rad/s and time constant r = LIR = 0.01 s, the diode turns off at time t = 8.39 ms. The voltage and current waveforms are shown in Figure 1.31. Energy analysis is possible but does not offer much help. When the diode is on, the inductor input energy is

Win( on) =

f

toff

ton

•

(1.25)

[V0 cos( mt) - vout (t)]z(t) dt

When it is off, the energy input is zero. Since the current is the output voltage divided by R, and since the net input energy over a cycle must be zero, energy analysis requires ~n(on) =

ftoff

J

ton

[V0 cos(mt)vout(t)-

2

V0 u/t)]

IR dt = 0

(1.26)

It is difficult to solve this for voult), although the expression is valid.

FIGURE 1.31

D-L-R circuit.

Current and voltageinahalf-wave Input voltage t---+-----1'--------+---t-----+--+--

Output

2 Many

of the equations in this book can be analyzed using symbolic tools such as Mathematic a.

Time

32

POWER ELECTRONICS AND THE ENERGY REVOLUTION

Input voltage

FIGURE 1.32 Input and output voltage waveforms for Example 1.6.6 circuit.

~+----r----~--~--~----+--Time

Output voltage

~~----~~~--~--~~--~-Time

We have considered the diode in two simple example circuits so far. Although the device acts as a switch, we do not have any control over its behavior. Let us consider a different way to operate the switch in the first example circuit. Example 1.6.6 Consider again the circuit of Figure 1.28. Instead, turn the switch on whenever Vac > Vpea,/2 and tum it off one-half cycle later. The input and output voltage waveforms are shown in Figure 1.32. The input has ( v) = 0 and VRMS = Vpea,/~2. The switch turns on as the input waveform crosses the line Vpea,/2, at an angle of 30°. The output average value is given by

J3

1 J7n/6 . ( V ou/t)) = Vpeak Sln (}d(} = Vpeak = 0.2757 Vpeak 2n ~6 2n

(1.27)

which is 87% of the de value in equation (1.22). The RMS value is still Vpea,/2, but the timing change has adjusted the rectifier output. In the Example 1.6.6 circuit, a diode cannot support the requested operation. The circuit still performs rectification, but a different device will be needed to permit the necessary control. Rectifier operation can be adjusted by manipulating switch timing or the load properties if the devices allow. The de output depends on when the switch turns on or off. However, in each case the output is not a clean de waveform. We need filtering to recover the de value. A low-pass filter could work in principle, but it must be lossless to meet the requirements. Filters are one way in which energy storage elements are applied in power electronics. So far, the circuits of the examples have few components. A commercial solar inverter that incorporates a boost circuit and bridge inverter is shown in Figure 1.33. The circuit also allows interfacing to a 48 V battery set. The boost portion can supply up to 3000 W at 400 V de. There are extra components for control functions, but that portion of the power electronics is essentially the same as that in Figure 1.24. Another commercial circuit [32] is shown in Figure 1.34. Although it is more complicated than the preceding examples, its power electronic heart is the polarity reversal circuit.

1.7 POWER ELECTRONICS APPLICATIONS: A UNIVERSAL ENERGY ENABLER 1.7.1 Solar Energy Architectures Power electronics continues to grow in importance for energy processing. Renewable energy resource applications illustrate many of the important aspects. For solar power, PV

0

FIGURE 1.33

/

Inverter with boost converter front-end for 3000 W solar array and battery interface.

¥'\r

.------- - FEEDBACK

,~

~~>(

230V

l.O,uF 22 I - Ql uFN 84 1 • IIlil+------.>-1\'v ~v A v- -

T2 ~so,u:-

120V

>>-

> 56k
--

Tl

>

I

2.5k

•

. . . . - - - - - - o+ SV 15A

L..

>--

>.-5 X 2200J.1F

UZ8715'

>-

160nH

1N6391. (COMMERCIAL)

>--

=~

=~

=~

==

=~

>-~ ~~~~~_.~~+---~------~

--< (2) 1N4944-r

/\-


'---1

COMP 1------,

Nl

e ---1TH. ADJ. SOURCE

510

v iN-

>

47,uF

820

68 (

2.7k SES5402

UZ8715