Power Electronics Converters, Applications, and Design (2nd Edition) PDF

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"" H-||~| |.1|=||||. FIIHEH ELEEIHIJNII S Cfllivflrlcrgq Appliflflliilllu, Elli] DI?HigII |""I1II' I'll-I1 Pu“. run: u.,p_u rl ' ' __||_ |:|-r|:|:I||.|;|I '- 1: l||l|l|||.|I|I|I1'tl I'll-:|'rh;I-Ir f'1l]HIIH."L|HflELHHl]1'Fll]EIE|H5 P()\VER ELECTRONICS ABOUT THE AUTHORS Ned Mohan is a professor in the Department of Electrical Engineering at the University of Minnesota, where he holds the Oscar A. Schott Chair in Power Electronics. He has worked on several power electronics projects sponsored by the industry and the electric power utilities, including the Electric Power Research Institute. He has numerous pub- lications and patents in this field. Tore M. Undeland is a Professor in Power Electronics in the Faculty of Electrical Engineering and Computer Science at the Norwegian Institute of Technology. He is also Scientific Advisor to the Norwegian Electric Power Research Institute of Electricity Supply. He has been a visiting scientific worker in the Power Electronics Converter Department of ASEA in Vaasteras, Sweden, and at Siemens in Trondheim, Norway, and a visiting professor in the Department of Electrical Engineering at the University of Minnesota. He has worked on many industrial research and development projects in the power electronics field and has numerous publications. William P. Robbins is a professor in the Department of Electrical Engineering at the University of Mimresota. Prior to joining the University of Minnesota, he was a research engineer at the Boeing Company. He has taught numerous courses in electronics and semiconductor device fabrication. His research interests are in ultrasonics, pest insect detection via ultrasonics, and micromechanical devices, and he has numerous publications in this field. POWER ELECTRONICS Converters, Applications, and Design SECOND EDITION NED MOHAN Department of Electrical Engineering University of Minnesota Minneapolis, Minnesota TORE M. UNDELAND Faculty of Electrical Engineering and Computer Science Norwegian Institute of Technology Trondheim, Norway WILLIAM P. ROBBINS Department of Electrical Engineering University of Minnesota Minneapolis, Minnesota JOHN WILEY & SONS, INC. New York Chichester Brisbane Toronto Singapore Acquisitions Editor Steven M. Elliot Developmental Editor Sean M. Culhane Marketing Manager Susan Elbe Senior Production Editor Savoula Amanatidis Text Designer Lynn Rogan Cover Designer David Levy Marrufacttuing Manager Lori Bulwin Illustration Coordinator Jaime Perea This book was typeset in Times Roman by The Clarinda Company, and printed and bound by Hamilton Printing Company. The cover was printed by NEBC. Recognizing the importance of preserving what has been written, it is a policy of John Wiley & Sons, Inc. to have books of endtuing value published in the United States printed on acid-free paper, and we exert our best efforts to that end. PSpice is a registered trademark of MicroSim Corporation. MATLAB is a registered trademark of The MathWorks, Inc. Copyright © I989, 1995 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Sections I07 and I08 of the I976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. Library of Congress Cataloging in Publication Dara: Mohan, Ned. Power electronics : converters, applications, and design I Ned Mohair, Tore M. Undeland, William P. Robbins.—2nd ed. p. cm. Includes bibliographical references and indexes. ISBN 0-471-58408-8 (cloth) l. Power electronics. 2. Electric current converters. 3. Power semiconductors. I. Undeland, Tore M. LI. Robbins, William P. III. Title. TK788l.l5.M64 1995 621.317-—dc20 94-21158 CIP Printed in the United States of America. I0 9 8 7 6 5 4 3 2 I  To Our Families... Mary, Michael, and Tara Mona, Hilde, and Ame Joarme and Jon i i PREFACE SECOND EDITION The first edition of this book was published in 1989. The basic intent of this edition remains the same; that is, as a cohesive presentation of power electronics fundamentals for applications and design in the power range of 500 kW or less, where a huge market exists and where the demand for power electronics engineers is likely to be. Based on the comments collected over a five-year period, we have made a number of substantial changes to the text. The key features are as follows: ' An introductory chapter has been added to provide a review of basic electrical and magnetic circuit concepts, making it easier to use this book in introductory power electronics courses. s ' A chapter on computer simulation has been added that describes the role of com- puter simulations in power electronics. Examples and problems based on PSpice® and MATLAB® are included. However, we have organized the material in such a way that any other simulation package can be used instead or the simulations can be skipped altogether. ' Unlike the first edition, the diode rectifiers and the phase-controlled thyristor con- verters are covered in a complete and easy-to-follow manner. These two chapters now contain 56 problems. ~ A new chapter on the design of inductors and transformers has been added that describes easy-to-understand concepts for step-by-step design procedures. This material will be extremely useful in introducing the design of magnetics into the curriculum. ' A new chapter on heat sinks has been added. ORGANIZATION OF THE BOOK This book is divided into seven parts. Part 1 presents an introduction to the field of power electronics, an overview of power semiconductor switches, a review of pertinent electric and magnetic circuit concepts, and a generic discussion of the role of computer simula- tions in power electronics. Part 2 discusses the generic converter topologies that are used in most applications. The actual semiconductor devices (transistors, diodes, and so on) are assumed to be ideal, thus allowing us to focus on the converter topologies and their applications. Part 3 discusses switch-mode dc and urrinterruptible power supplies. Power supplies represent one of the major applications of power electronics. vii Vlll PREFACE Part 4 considers motor drives, which constitute another major applications area. Part 5 includes several industrial and commercial applications in one chapter. An- other chapter describes various high-power electric utility applications. The last chapter in this part of the book examines the harmonics and electromagnetic interference concems and remedies for interfacing power electronic systems with the electric utilities. Part 6 discusses the power semiconductor devices used in power electronic converters including diodes, bipolar junction thyristors, metal—oxide—semiconductor (MOS) field effect transistors, thyristors, gate tum-off thyristors, insulated gate bipolar transistors, and MOS-controlled thyristors. Part 7 discusses the practical aspects of power electronic converter design including snubber circuits, drive circuits, circuit layout, and heat sinks. An extensive new chapter on the design of high-frequency inductors and transformers has been added. PSPICE SIMULATIONS FOR TEACHING AND DESIGN As a companion to this book, a large number of computer simulations are available directly from Minnesota Power Electronics Research and Education, P.O. Box 14503, Minneapolis, MN 55414 (Phone/Fax: 612-646-1447) to aid in teaching and in the design of power electronic systems. The simulation package comes complete with a diskette with 76 simulations of power electronic converters and systems using the classroom (evalua- tion) version of PSpice for IBM-PC-compatible computers, a 261-page detailed manual that describes each simulation and a number of associated exercises for home assignments and self-learning, a 5-page instruction set to illustrate PSpice usage using these simula- tions as examples, and two high-density diskettes containing a copy of the classroom (evaluation) version of PSpice. This package (for a cost of $395 plus a postage of $4 within North America and $25 outside) comes with a site license, which allows it to be copied for use at a single site within a company or at an educational institution in regular courses given to students for academic credits. SOLUTIONS MANUAL As with the first edition of this book, a solutions manual with completely worked-out solutions to all the problems is available from the publisher. A ACKNOWLEDGMENTS We wish to thank all the instructors who have allowed us this opportunity to write the second edition of our book by adopting its first edition. Their cormnents have been most useful. We are grateful to Professors Peter Lauritzen of the University of Washington, Thomas Habetler of the Georgia Institute of Technology, Daniel Chen of the Virginia Institute of Technology, Alexander Emanuel of the Worcester Polytechnic Institute, F. P. Dawson of the University of Toronto, and Marian Kazimierczuk of the Wright State University for their helpful suggestions in the second edition manuscript. We express our sincere appreciation to the Wiley editorial staff, including Steven Elliot, Sean Culhane, Lucille Buonocore, and Savoula Arnanatidis, for keeping us on schedule and for many spirited discussions. Ned Mohan Tore M. Undeland William P. Robbins  CONTENTS PART 1 INTRODUCTION 1 Chapter 1 Power Electronic Systems 3 1-1 Introduction 3 1-2 Power Electronics versus Linear Electronics 4 1-3 Scope and Applications 7 1-4 Classification of Power Processors and Converters 9 1-5 About the Text 12 1-6 Interdisciplinary Nature of Power Electronics 13 1-7 Convention of Symbols Used 14 Problems 14 References 15 Chapter 2 Overview of Power Semiconductor Switches 16 2-1 Introduction I 16 2-2 Diodes 16 2-3 Thyristors 18 2-4 Desired Characteristics in Controllable Switches 20 2-5 Bipolar Junction Transistors and Monofithic Darlingtons 24 2-6 Metal—Oxide— Semiconductor Field Effect Transistors 25 2-7 Gate-Turn-Off Thyristors 26 2-8 Insulated Gate Bipolar Transistors 27 2-9 MOS-Controlled Thyristors 29 2-10 Comparison of Controllable Switches 29 2-11 Drive and Snubber Circuits 30 2-12 Justification for Using Idealized Device Characteristics 31 I Summary 32 Problems 32 References 32 Chapter 3 Review of Basic Electrical and Magnetic Circuit Concepts 33 3-1 Introduction - 33 3-2 Electric Circuits 33 3-3 Magnetic Circuits 46 I Summary 57 Problems 58 References 60 ix x CONTENTS Chapter 4 Computer Simulation of Power Electronic Converters and Systems 4-1 Introduction 61 4-2 Challenges in Computer Simulation 62 4-3 Simulation Process 62 4-4 Mechanics of Simulation 64 4-5 Solution Techniques for Time-Domain Analysis 65 4-6 Widely Used, Circuit-Oriented Simulators 69 4-7 Equation Solvers 72 Summary 74 Problems 74 References 75 PART 2 GENERIC POWER ELECTRONIC CIRCUITS Chapter 5 Line-Frequency Diode Rectifiers: Line-Frequency ac —> Uncontrolled dc 5-1 Introduction 79 5-2 Basic Rectifier Concepts.. 80 5-3 Single-Phase Diode Bridge Rectifiers 82 5-4 Voltage-Doubler (Single-Phase) Rectifiers 100 5-5 Effect of Single-Phase Rectifiers on Neutral Currents in Three-Phase, Four-Wire Systems 101 5-6 Three-Phase, Full-Bridge Rectifiers 103 5-7 Comparison of Single-Phase and Three-Phase Rectifiers 112 5-8 Inrush Current and Overvoltages at Tum-On 112 5-9 Concems and Remedies for Line-Current Harmonics and Low Power Factor 1 13 Summary I13 Problems 114 References I16 Appendix II 7 Chapter 6 Line-Frequency Phase-Controlled Rectifiers and Inverters: Line-Frequency ac Controlled dc 6-1 Introduction 121 6-2 Thyristor Circuits and Their Control 122 A 6-3 Single-Phase Converters 126 6-4 Three-Phase Converters 138 6-5 Other Three-Phase Converters 153 Summary I53 Problems I54 References I57 Appendix I58 Chapter 7 dc—dc Switch-Mode Converters 7-1 Introduction I61 7-2 Control of dc—dc Converters 162  CONTENTS Ki 7-3 Step-Down (Buck) Converter 164 7-4 Step-Up (Boost) Converter 172 7-5 Buck-Boost Converter 178 7-6 Cfik dc-dc Converter 184 7-7 Full Bridge dc—dc Converter 188 7-8 dc—dc Converter Comparison 195 Summary 196 Problems I 97 References 199 Chapter 8 Switch-Mode dc—ac Inverters: dc Sinusoidal ac 200 8-1 Introduction 200 8-2 Basic Concepts of Switch-Mode Inverters 202 8-3 Single-Phase Inverters 211 8-4 Three-Phase Inverters 225 8-5 Effect of Blanking Time on Output Voltage in PWM Inverters 236 8-6 Other Inverter Switching Schemes 239 8-7 Rectifier Mode of Operation 243 Summary 244 Problems 246 References 248 Chapter 9 Resonant Converters: Zero-Voltage and/or Zero-Current Switchings 249 9-1 Introduction 249 9-2 Classification of Resonant Converters 252 9-3 Basic Resonant Circuit Concepts 253 9-4 Load-Resonant Converters 258 9-5 Resonant-Switch Converters 273 9-6 Zero-Voltage-Switching, Clamped-Voltage Topologies 280 9-7 Resonant-dc-Link Inverters with Zero-Voltage Switchings 287 9-8 High-Frequency-Link Integral-Half-Cycle Converters 289 Summary 291 Problems 291 References 295 PART 3 POWER SUPPLY APPLICATIONS 299 Chapter 10 Switching dc Power Supplies 301 10-1 Introduction 301 10-2 Linear Power Supplies 301 10-3 Overview of Switching Power Supplies 302 10-4 dc-dc Converters with Electrical Isolation 304 10-5 Control of Switch-Mode dc Power Supplies 322 10-6 Power Supply Protection 341 10-7 Electrical Isolation in the Feedback Loop 344 10-8 Designing to Meet the Power Supply Specifications 346 Summary 349 XII CONTENTS Problems 349 References 351 Chapter 11 Power Conditioners and Uninterruptible Power Supplies 11-1 Introduction 354 11-2 Power Line Disturbances 354 ll-3 Power Conditioners 357 11-4 Uninterruptible Power Supplies (UPSs) 358 Summary 363 Problems 363 References 364 PART 4 MOTOR DRIVE APPLICATIONS Chapter 12 Introduction to Motor Drives 12-1 Introduction 367 12-2 Criteria for Selecting Drive Components 368 Summary 375 Problems 376 References 3 76 Chapter 13 dc Motor Drives 13-1 Introduction 377 13-2 Equivalent Circuit of dc Motors 377 13-3 Pennanent-Magnet dc Motors 380 13-4 dc Motors with a Separately Excited Field Winding 381 13-5 Effect of Armature Current Waveform 382 13-6 dc Servo Drives 383 13-7 Adjustable-Speed dc Drives 391 Summary 396 Problems 396 References 398 Chapter 14 Induction Motor Drives 14-1 Introduction 399 14-2 Basic Principles of Induction Motor Operation 400 14-3 Induction Motor Characteristics at Rated (Line) Frequency and Rated Voltage 405 I4-4 Speed Control by Varying Stator Frequency and Voltage 406 I4-5 Impact of Nonsinusoidal Excitation on Induction Motors 415 I4-6 Variable-Frequency Converter Classifications 418 14-7 Variable-Frequency PWM-VSI Drives 419 I4-8 Variable-Frequency Square-Wave VSI Drives 425 14-9 Variable-Frequency CSI Drives 426 14-10 Comparison of Variable-Frequency Drives 427  CONTENTS xiii 14-ll Line-Frequency Variable-Voltage Drives 428 14-I2 Reduced Voltage Starting (“Soft Start”) of Induction Motors 430 14-13 Speed Control by Static Slip Power Recovery 431 Summary 432 Problems 433 References 434 Chapter 15 Synchronous Motor Drives 435 15-1 Introduction 435 15-2 Basic Principles of Synchronous Motor Operation 435 15-3 Synchronous Servomotor Drives with Sinusoidal Waveforms 439 15-4 Synchronous Servomotor Drives with Trapezoidal Waveforms 440 15-5 Load-Commutated Inverter Drives 442 15-6 Cycloconverters 445 Summary 445 Problems 446 References 447 PART 5 OTHER APPLICATIONS 449 Chapter 16 Residential and Industrial Applications 451 16-1 Introduction 451 16-2 Residential Applications 451 16-3 Industrial Applications 455 Summary 459 Problems 459 References 459 Chapter 17 Electric Utility Applications 460 17-1 Introduction 460 17-2 High-voltage dc Transmission 460 17-3 Static var Compensators 471 17-4 Intercomrection of Renewable Energy Sources and Energy Storage Systems to the Utility Grid 475 17-5 Active Filters 480 Summary 480 Problems 481 References 482 Chapter 18 Optimizing the Utility Interface with Power Electronic Systems 483 18-1 Introduction 483 18-2 Generation of Current Harmonics 484 18-3 Current Harmonics and Power Factor 485 18-4 Harmonic Standards and Recormnended Practices 485 18-5 Need for Improved Utility Interface 487 XIV CONTENTS 18-6 Improved Single-Phase Utility Interface 488 18-7 Improved Three-Phase Utility Interface 498 18-8 Electromagnetic Interference 500 Summary 502 Problems 503 References 503 PART 6 SEMICONDUCTOR DEVICES Chapter 19 Basic Semiconductor Physics 19-1 Introduction 507 19-2 Conduction Processes in Semiconductors 507 19-3 pn Junctions 513 19-4 Charge Control Description of pn-Junction Operation 19-5 Avalanche Breakdown 520 Summary 522 Problems 522 References 523 Chapter 20 Power Diodes 20-1 Introduction 524 20-2 Basic Structure and I-V Characteristics 524 20-3 Breakdown Voltage Considerations 526 20-4 On-State Losses 531 20-5 Switching Characteristics 535 20-6 Schottky Diodes 539 Summary 543 Problems 543 References 545 Chapter 21 Bipolar Junction Transistors 21-1 Introduction 546 21-2 Vertical Power Transistor Structures 546 21-3 I-V Characteristics 548 21-4 Physics of BJT Operation 550 21-5 Switching Characteristics 556 21-6 Breakdown Voltages 562 21-7 Second Breakdown 563 21-8 On-State Losses 565 21-9 Safe Operating Areas 567 Summary 568 Problems 569 References 570 Chapter 22 Power MOSFETs 22-1 Introduction 571 22-2 Basic Structure 571  CONTENTS xv 22-3 I-V Characteristics 574 22-4 Physics of Device Operation 576 22-5 Switching Characteristics 581 22-6 Operating Limitations and Safe Operating Areas 587 Summary 593 Problems 594 References 595 Chapter 23 Thyristors 596 23-1 Introduction 596 23-2 Basic Structure 596 23-3 1- V Characteristics 597 23-4 Physics of Device Operation 599 23-5 Switching Characteristics 603 23-6 Methods of Improving dz’/dt and dv/dt Ratings 608 Summary 610 Problems 61 I References 612 Chapter 24 Gate Turn-Off Thyristors 613 24-1 Introduction 613 24-2 Basic Structure and I-V Characteristics 613 24-3 Physics of Turn-Off Operation 614 24-4 GTO Switching Characteristics 616 24-5 Overcurrent Protection of GTOs 623 Summary 624 Problems 624 References 625 Chapter 25 Insulated Gate Bipolar Transistors 626 25-1 Intr'oduction 626 25-2 Basic Structure 626 25-3 I-V Characteristics 628 25-4 Physics of Device Operation 629 25-5 Latchup in IGBTs 631 25-6 Switching Characteristics 634 25-7 Device Limits and SOAs 637 Summary 639 Problems 639 References 640 Chapter 26 Emerging Devices and Circuits 641 26-1 Int1'oduction 641 26-2 Power Junction Field Effect Transistors 641 26-3 Field-Controlled Thyristor 646 26-4 JFET-Based Devices versus Other Power Devices 26-5 MOS-Controlled Thyristors 649 xvi CONTENTS 26-6 Power Integrated Circuits 656 26-7 New Semiconductor Materials for Power Devices 661 Summary 664 Problems 665 References 666 PART 7 PRACTICAL CONVERTER DESIGN CONSIDERATIONS Chapter 27 Snubber Circuits 27-1 Function and Types of Snubber Circuits 669 27-2 Diode Snubbers 670 27-3 Snuber Circuits for Thyristors 678 27-4 Need for Snubbers with Transistors 680 27-5 Tum-Off Snubber 682 27-6 Overvoltage Snubber 686 27-7 Tum-On Snubber 688 27-8 Snubbers for Bridge Circuit Configurations 691 27-9 GTO Snubber Considerations 692 Summary 693 Problems 694 References 695 Chapter 28 Gate and Base Drive Circuits 28-1 Preliminary Design Considerations 696 28-2 dc-Coupled Drive Circuits 697 28-3 Electrically Isolated Drive Circuits 703 28-4 Cascode-Connected Drive Circuits 710 28-5 Thyristor Drive Circuits 712 28-6 Power Device Protection in Drive Circuits 717 28-7 Circuit Layout Considerations 722 Summary 728 Problems 729 References 729 Chapter 29 Component Temperature Control and Heat Sinks 29-1 Control of Semiconductor Device Temperatrues 730 29-2 Heat Transfer by Conduction 731 29-3 Heat Sinks 737 29-4 Heat Transfer by Radiation and Convection 739 Summary 742 Problems 743 References 743 Chapter 30 Design of Magnetic Components 30-1 Magnetic Materials and Cores 744 30-2 Copper Windings 752  CONTENTS xvii 30-3 Thermal Considerations 754 30-4 Analysis of a Specific Inductor Design 756 30-5 Inductor Design Procedures 760 30-6 Analysis of a Specific Transformer Design 767 30-7 Eddy Currents 771 30-8 Transformer Leakage Inductance 779 30-9 Transformer Design Procedure 780 30-10 Comparison of Transformer and Inductor Sizes 789 Summary 789 Problems 790 References 792 Index 793 PART 1 INTRODUCTION CHAPTER 1 PO\VER ELECTRONIC SYSTEMS 1- INTRODUCTION In broad terms, the task of power electronics is to process and control the flow of electric energy by supplying voltages and currents in a form that is optimally suited for user loads. Figure 1-1 shows a power electronic system in a block diagram form. The power input to this power processor is usually (but not always) from the electric utility at a line frequency of 60 or 50 Hz, single phase or three phases. The phase angle between the input voltage and the current depends on the topology and the control of the power processor. The processed output (voltage, current, frequency, and the number of phases) is as desired by the load. If the power processor’s output can be regarded as a voltage source, the output current and the phase angle relationship between the output voltage and the current depend on the load characteristic. Normally, a feedback controller compares the output of the power processor unit with a desired (or a reference) value, and the error between the two is minimized by the controller. The power flow through such systems may be reversible, thus interchanging the roles of the input and the output. = p In recent years, the field of power electronics has experienced a large growth due to confluence of several factors. The controller in the block diagram of Fig. 1-1 consists of linear integrated circuits and/or digital signal processors. Revolutionary advances in mi- croelectronics methods have led to the development of such controllers. Moreover, these advances in semiconductor fabrication technology have made it possible to significantly improve the vo1tage- and current-handling capabilities and the switching speeds of power semiconductor devices, which make up the power processor unit of Fig. 1-1. At the same time, the market for power electronics has significantly expanded. Electric utilities in the United States expect that by the year 2000 over 50% of the electrical load may be supplied through power electronic systems such as in Fig. 1-1. This growth in market may even be Power rnput Power Power output _,.. processor _,.. UT it - to ' Saga Measurements Figure 1-1 Block diagram of a power Controller - Reference electronic system. 3 4 CHAPTER 1 POWER ELECTRONIC SYSTEMS higher in other parts of the world where the cost of energy is significantly higher than that in the United States. Various applications of power electronics are considered in Sec- tion 1-3. 1- POWER ELECTRONICS VERSUS LINEAR ELECTRONICS In any power conversion process such as that shown by the block diagram in Fig. 1-1, a small power loss and hence a high energy efficiency is important because of two reasons: the cost of the wasted energy and the difficulty in removing the heat generated due to dissipated energy. Other important considerations are reduction in size, weight, and cost. The above objectives in most systems cannot be met by linear electronics where the semiconductor devices are operated in their linear (active) region and a line-frequency transformer is used for electrical isolation. As an example, consider the direct current (dc) power supply of Fig. 1-2a to provide a regulated output voltage V, to a load. The utility input may be typically at 120 or 240 V and the output voltage may be, for example, 5 V. The output is required to be electrically isolated from the utility input. In the linear power supply, a line-frequency transformer is used to provide electrical isolation and for step- ping down the line voltage. The rectifier converts the altemating current (ac) output of the transformer low-voltage winding into dc. The filter capacitor reduces the ripple in the dc voltage vd. Figure 1-2b shows the vd waveform, which depends on the utility voltage magnitude (normally in a 1 10% range around its nominal value). The transformer tums o@,~C1-0 I Line-freq uency T + transformer __ “d Controller V0 Rload Ut|l|ty supply V0, ref Rectifier Filter-capacitor (0) ii _ V0 OI - - -... (b) Figure 1-2 Linear dc power supply.  1-2 POWER ELECTRONICS VERSUS LINEAR ELECTRONICS 5 ratio must be chosen such that the minimum of the input voltage vd is greater than the desired output V0. For the range of the input voltage waveforms shown in Fig. 1-2b, the transistor is controlled to absorb the voltage difference between vd and V0, thus providing a regulated output. The transistor operates in its active region as an adjustable resistor, resulting in a low energy efficiency. The line-frequency transformer is relatively large and heavy. In power electronics, the above voltage regulation and the electrical isolation are achieved, for example, by means of a circuit shown in Fig. 1-3a. In this system, the utility input is rectified into a dc voltage vd, without a line-frequency transformer. By operating the transistor as a switch (in a switch mode, either fully on or fully off) at some high switching frequency f,, for example at 300 kl-Iz, the dc voltage vd is converted into an ac voltage at the switching frequency. This allows a high-frequency transformer to be used for stepping down the voltage and for providing the electrical isolation. In order to simplify this circuit for analysis, we will begin with the dc voltage vd as the dc input and omit the transformer, resulting in an equivalent circuit shown in Frg. 1-3b. Suffice it to Power processor |i 1 I I I I IT b || A Rload Utility supply I L _ _ , 5 _ I _ _ ______ __ ‘ High-frequency Rectifier Low-pass I transformer filter Rectifier capacitor F"‘°." W 1 j cOI‘! t1'0 || Bl’ V“ ' Va, ref (a) Power processor i it. ——+- 1‘ + A I Va Rload I 1 0 l 1' I 1, Controller ' Va, ref (b) Figure 1-3 Switch-mode dc power supply. CHAPTER 1 POWER ELECTRONIC SYSTEMS say at this stage (this circuit is fully discussed in Chapters 7 and 10) that the transistor- diode combination can be represented by a hypothetical two-position switch shown in Fig. 1-4a (provided iL(t) > 0). The switch is in position a during the interval ton when the transistor is on and in position b when the transistor is off during toff. As a consequence, vo, equals Vd and zero during ton and toff, respectively, as shown in Fig. 1-4b. Let us define vo:'(t) = Vol‘ + vr|'pple(t) where V0, is the average (dc) value of vo,-, and the instantaneous ripple voltage vfipp1e(t), which has a zero average value, is shown in Fig. 1-4c. The L- C elements form a low-pass filter that reduces the ripple in the output voltage and passes the average of the input voltage, so that V0 = Vol’ where V0 is the average output voltage. From the repetitive waveforms in Fig. 1-4b, it is easy to see that n=i1 T’ ton %m=Ew (m) L L + + vd b voi C vo Rload 0 (0) voi V011‘ C 0 ' "-"- ** *""*e~ t t C ii ton ’i"'tofij T8 =—- rs (5) vripplem 0—* -----L— e e 1-g (c) tmw 0. 11 1 2 -r__ 3 1 4 A._.-_J6 5 4- r 7 8 A ":.tq°"‘= 9 (d) Figure 1-4 Equivalent circuit, waveforms, and frequency spectrum of the supply in Fig. 1-3.  1-3 SCOPE AND APPLICATIONS 7 As the input voltage vd changes with time, Eq. l-3 shows that it is possible to regulate V0 at its desired value by controlling the ratio ton/Ts, which is called the duty ratio D of the transistor switch. Usually, T, (=1/1,) is kept constant and rm, is adjusted. There are several characteristics worth noting. Since the transistor operates as a switch, fully on or fully off, the power loss is minimized. Of cotu'se, there is an energy loss each time the transistor switches from one state to the other state through its active region (discussed in Chapter 2). Therefore, the power loss due to switchings is linearly proportional to the switching frequency. This switching power loss is usually much lower than the power loss in linear regulated power supplies. At high switching frequencies, the transformer and the filter components are very small in weight and size compared with line-frequency components. To elaborate on the role of high switching frequencies, the harmonic content in the waveform of v,,,- is obtained by means of Fourier analysis (see Problem l-3 and its further discussion in Chapter 3) and plotted in Fig. 1-4d. It shows that vo, consists of an average (dc) value and of harmonic components that are at a multiple of the switching frequency f,. If the switching frequency is high, these ac components can be easily eliminated by a small filter to yield the desired dc voltage. The selection of the switching frequency is dictated by the compromise between the switching power dissipation in the transistor, which increases with the switching frequency, and the cost of the transformer and filter, which decreases with the switching frequency. As transistors with higher switching speeds become avail- able, the switching freq_l1§l1Ci¢§._ can be increased and the transformer and filter size reduced for the same switchi_.ng..po3ve_r dissipation. An important observation in the switch-mode circuit described above is that both the input and the output are dc, as in the linear regulated supply. The high switching fre- quencies are used to synthesize the output waveform, which in this example is dc. In many applications, the output is a low-frequency sine wave. 1-3 SCOPE AND APPLICATIONS The expanded market demand for power electronics has been due to several factors discussed below (see references 1-3). 1. Switch-mode (dc) power supplies and uninterruptible power supplies. Advances in microelectronics fabrication technology have led to the development of com- puters, communication equipment, and consumer electronics, all of which require regulated dc power supplies and often uninterruptible power supplies. 2. Energy conservation. Increasing energy costs and the concem for the environ- ment have combined to make energy conservation a priority. One such application of power electronics is in operating fluorescent _]___a_[[1P§____a_l high_,_f1'_e_quencies(e.g., above 20 kHz) for higher efficiency. Another opportunity for large energy con- servation (see Problem 1-7) is in rngtor-d1j,ven punfrpand cgmpr_e_s_s_9r systems_. In a conventional pump system shown in Fig. 1-5a, the pump operates at essen- tially a constant speed, and the pump flow rate is controlled by adjusting the position of the throttling valve. This procedure results in significant power loss across the valve at reduced flow rates where the power drawn from the utility remains essentially the same as at the full flow rate. This power loss is eliminated in the system of Fig. 1-5b, where an adjustable-speed motor drive adjusts the pump speed to a level appropriate to deliver the desired flow rate. As will be discussed in Chapter 14 (in combination with Chapter 8), motor speeds can be adjusted very efficiently using power electronics. Load-proportional, capacity- 8 cnxrren 1 rowan ELECTRONIC svsrarus Output Output Throttling /7 /7 valve q DC 4. Adjustable- I‘ Line.§ Line Sgied.§ input A 1-- input We /, ~t--- I t I t Pump npu Pump npu (a) (b) Figure 1-5 Energy conservation: (a) conventional drive, (b) adjustable-speed drive. modulated heat pumps and air conditioners are examples of applying power elec- tronics to achieve energy conservation. Process control and factory automation. There is a growing demand for the enhanced performance offered by adjustable-speed-driven pumps and compres- sors in process control. Robots in automated factories are powered by electric servo (adjustable-speed and position) drives. It should be noted that the availabil- ity of process computers is a significant factor in making process control and factory automation feasible. Transportation. In many countries, electric trains have been in widespread use for a long time. Now, there is also a possibility of using electric vehicles in large TABLE 1-1 Power Electronic Applications (a) Residential (d) Transportation Refrigeration and freezers Traction control of electric vehicles Space heating Battery chargers for electric vehicles Air conditioning Electric locomotives Cooking Street cars, trolley buses Lighting Subways Electronics (personal computers, Automotive electronics including engine other entertainment equipment) controls (b) Commercial (e) Utility systems Heating, ventilating, and air High-voltage dc transmission (HVDC) conditioning Static var compensation (SVC) Central refrigeration Supplemental energy sources (wind, Lighting photovoltaic), fuel cells Computers and office equipment Energy storage systems Uninterruptible power supplies Induced-draft fans and boiler (UPSs) feedwater pumps Elevators (f) Aerospace (c) Industrial Space shuttle power supply systems Pumps Satellite power systems Compressors Aircraft power systems Blowers and fans (g) Telecommunications Machine tools (robots) Battery chargers Arc fumaces, induction fumaces Power supplies (dc and UPS) Lighting Industrial lasers Induction heating Welding 7* _ ll-In-m~|___ ' 1-nqni 7' ' '___1u—  1-4 CLASSIFICATION OF POWER PROCESSORS AND CONVERTERS 9 metropolitan areas to reduce smog and pollution. Electric vehicles would also require battery chargers that utilize power electronics. 5. Electra-technical applications. These include equipment for welding, electroplat- ing, and induction heating. 6. Utility-related applications. One such application is in transmission of power over high-voltage dc (HVDC) lines. At the sending end of the transmission line, line-frequency voltages and currents are converted into dc. This dc is converted back into the line-frequency ac at the receiving end of the line. Power electronics is also beginning to play a significant role as electric utilities attempt to utilize the existing transmission network to a higher capacity. Potentially, a large appli- cation is in the interconnection of photovoltaic and wind-electric systems to the utility grid. Table 1-1 lists various applications that cover a wide power range from a few tens of watts to several hundreds of megawatts. As power semiconductor devices improve in perfor- mance and decline in cost, more systems will undoubtedly use power electronics. CLASSIFICATION OF POWER PROCESSORS AND CONVERTERS 1-4-1 POWER PROCESSORS For a systematic study of power electronics, it is useful to categorize the power proces- sors, shown in the block diagram of Fig. 1-1, in terms of their input and output form or frequency. In most power electronic systems, the input is from the electric utility source. Depending on the application, the output to the load may have any of the following forms: 1. dc (a) regulated (constant) magnitude (b) adjustable magnitude 2. ac (a) constant frequency, adjustable magnitude (b) adjustable frequency and adjustable magnitude The utility and the ac load, independent of each other, may be single phase or three phase. The power flow is generally from the utility input to the output load. There are exceptions, however. For example, in a photovoltaic system interfaced with the utility grid, the plow flow is from the photovoltaics (a dc input source) to the ac utility (as the output load). In some systems the direction of power flow is reversible, depending on the operating conditions. 1-4-2 POWER CONVERTERS The power processors of Fig. 1-1 usually consist of more than one power conversion stage (as shown in Fig. 1-6) where the operation of these stages is decoupled on an instanta- neous basis by means of energy storage elements such as capacitors and inductors. Therefore, the instantaneous power input does not have to equal the instantaneous power output. We will refer to each power conversion stage as a converter. Thus, a converter is a basic module (building block) of power electronic systems. It utilizes power semicon- 10 CHAPTER 1 rowan ELECTRONIC SYSTEMS Power processor I C F ‘P it I ” P Tl Input —-—* 1,-—— Output Converter 1 Energy Converter 2 ‘ storage element Q _ — _7 _ mi _ _ _ Figure 1-6 Power processor block diagram. ductor devices controlled by signal electronics (integrated circuits) and possibly energy storage elements such as inductors and capacitors. Based on the fomr (frequency) on the two sides, converters can be divided into the following broad categories: ac to dc dc to ac dc to dc :"“P’!‘-'1-‘ ac to ac We will use converter as a generic temi to refer to a single power conversion stage that may perform any of the functions listed above. To be more specific, in ac-to-dc and dc-to-ac conversion, rectifier refers to a converter when the average power flow is from the ac to the dc side. Inverter refers to the converter when the average power flow is from the dc to the ac side. In fact, the power flow through the converter may be reversible. In that case, as shown in Fig. 1-7, we refer to that converter in terms of its rectifier and inverter modes of operation. As an example, consider that the power processor of Fig. 1-6 represents the block diagram of an adjustable-speed ac motor drive (described in Chapter 14). As shown in Fig. 1-8, it consists of two converters: converter 1 operating as a rectifier that converts line-frequency ac into dc and converter 2 operating as an inverter that converts dc into adjustable-magnitude, adjustable-frequency ac. The flow of power in the nomral (domi- nant) mode of operation is from the utility input sotuce to the output motor load. During regenerative braking, the power flow reverses direction (from the motor to the utility), in which case converter 2 operates as a rectifier and converter 1 operates as an inverter. As mentioned earlier, an energy storage capacitor in the dc link between the two converters decouples the operation of the two converters on an instantaneous basis. Further insight can be gained by classifying converters according to how the devices within the converter are switched. There are three possibilities: 1. Line frequency (naturally commutated) converters, where the utility line voltages present at one side of the converter facilitate the tum-off of the power semicon- P -"—'>' Rectifier mode Inverter mode -4--—-— _ P Figure 1-7 ac-to-dc converters.  1-4 CLASSIFICATION OF POWER PROCESSORS AND CONVERTERS I1 Power processor BC BC Utility Q i i Figure 1-8 Block diagram of an ac motor drive. ductor devices. Similarly, the devices are turned on, phase locked to the line- voltage waveform. Therefore, the devices switch on and off at the line frequency of 50 or 60 Hz. 2. Switching (forced-commutated) converters, where the controllable switches in the converter are turned on and off at frequencies that are high compared to the line frequency. In spite of the high switching frequency internal to the converter, the converter output may be either dc or at a frequency comparable to the line frequency. As a side note in a switching converter, if the input appears as a voltage source, then the output must appear as a current source, or vice versa. 3. Resonant and quasi-resonant converters, where the controllable switches turn on and/or tum off at zero voltage and/or zero current. 1-4-3 MATRIX CONVERTER AS A POWER PROCESSOR In the above two sections, we discussed that most practical power processors utilize more than one converter whose instantaneous operation is decoupled by an energy storage element (an inductor or a capacitor). Theoretically, it is possible to replace the multiple conversion stages and the intermediate energy storage element by a single power con- ver,sion.stagecalledthe~matrix.conve_rt_er. Such a converter uses a matrix of semiconductor bidirectional switches. with a switch connected between each input ‘terniifial to each output terminal, as shown in Fig. 1-9a for an arbitrary number of input and output phases. With this general arrangement of switches, the power flow through the converter can reverse. Because of the absence of any energy storage element, the instantaneous power input must be equal to the power output, assuming idealized zero-loss switches. However, the phase angle between the voltages and ciurents at the input can be controlled and does not have to be the same as at the output (i.e., the reactive power input does not have to equal the reactive power output). Also, the form and the frequency at the two sides are independent, for example, the input may be three-phase ac and the output dc, or both may be dc, or both may be ac. However, there are certain requirements on the switches and restrictions on the converter operation: If the inputs appear as voltage sourcesas shown in Fig_. 1-9a. then the outputs must appear as current sources or vice versa. If both sides, for example, were to appear as voltage sources, the switching actions will inevitably connect voltage sources of unequal magnitude directly across each other; an unacceptable condition. The switch- ing functions in operating such a converter must ensure that the switches do not short- circuit the voltage sources and do not open-circuit the current sources. Otherwise, the converter will be destroyed. I2 CHAPTER 1 POWER ELECTRONIC SYSTEMS Power processor Utility source Iii @ Inputs L or Kg e P" "P _,_ TV°|taB9 Outputs (ct) “KI! G (b) source Figure 1-9 (a) Matrix converter. (b) Voltage source. Through a voltage source, the current can change instantaneously, whereas the volt- age across a current source can change instantaneously. If the input in Fig. l-9a is a utility source, it is not an ideal voltage source due to its intemal impedance corresponding to the transmission and distribution lines, transformers, etc., which are at the back of the utility outlet. To make it appear like a voltage source will require that we connect a small capacitance in parallel with it, as shown in Fig. l-9b to overcome the effect of the intemal impedance. The switches in a matrix converter must be bidirectional, that is, they must be able to block voltages of either polarity and be able to conduct current in either direction. Such switches are not available and must be realized by a combination of the available unidi- rectional switches and diodes discussed in Chapter 2. There are also limits on the ratio of the magnitudes of the input and the output quantities. In spite of numerous laboratory prototypes reported in research publications, the matrix converters so far have failed to show any significant advantage over conventional converters and hence have not found applications in practice. Therefore, we will not discuss them any further in this book. 1- ABOUT THE TEXT The purpose of this book is to facilitate the study of practical and emerging power electronic converters made feasible by the new generation of power semiconductor de- vices. This book is divided into seven parts. Part l of the book, which includes Chapter 1-4, presents an introduction, a brief review of basic concepts and devices, and computer simulations of power electronic systems. An overview of power semiconductor devices (discussed in detail in later parts of the book) and the justification for assuming them as ideal switches are presented in  1-6 INTERDISCIPLINARY NATURE OF POWER ELECTRONICS 13 Chapter 2. The basic electrical and magnetic concepts relevant to the discussion of power electronics are reviewed in Chapter 3. In Chapter 4, we briefly describe the role of computer simulations in the analysis and design of power electronic systems. Some of the simulation software packages suited for this purpose are also presented. Part 2 (Chapters 5-9) describes power electronic converters in a generic marmer. This way, the basic converter topologies used in more than one application can be described once, rather than repeating them each time a new application is encountered. This generic discussion is based on the assumption that the actual power semiconductor switches can be treated as ideal switches. Chapter 5 describes line-frequency diode rec- tifiers for ac-to-dc conversion. The ac-to-dc conversion using line-cominutated (naturally cominutated) thyristor converters operating in the rectifier and the inverter mode is dis- cussed in Chapter 6. Switching converters for dc to dc, and dc to sinusoidal ac using controlled switches are described in Chapters 7 and 8, respectively. The discussion of resonant converters in a generic manner is presented in Chapter 9. We decided to discuss ac-to-ac converters in the application-based chapters due to their application-specific nature. The matrix converters, which in principle can be ac-to-ac converters, were briefly described in Section 1-4-3. The static transfer switches are discussed in conjunction with the uninterruptible power supplies in Section ll-4-4. Con- verters where only the voltage magnitude needs to be controlled without airy change in ac frequency are described in Section 14-12 for speed control of induction motors and in Section 17-3 for static var compensators (thyristor-controlled inductors and thyristor- switched capacitors). Cycloconverters for very large synchronous-motor drives are dis- cussed in Section 15-6. High-frequency-link integral-half-cycle converters are discussed in Section 9-8. Integral-half-cycle controllers supplied by line-frequency voltages for heating-type applications are discussed in Section 16-3-3. Part 3 (Chapters 10 and ll) deals with power supplies: switching dc power supplies (Chapter 10) and uninterruptible ac power supplies (Chapter 11). Part 4 describes motor drive applications in Chapters 12-15. Other applications of power electronics are covered in Part 5, which includes resi- dential and industrial applications (Chapter 16), electric utility applications (Chapter 17), and the utility interface of power electronic systems (Chapter 18). Part 6 (Chapters 19-26) contains a qualitative description of the physical operating principles of semiconductor devices used as switches. Finally, Part 7 (Chapters 27-30) presents the practical design considerations of power electronic systems, including pro- tection aiid gate-drive circuits, thermal management, and the design of magnetic compo- nents. The reader is also urged to read the overview of the textbook presented in the Preface. INTERDISCIPLINARY NATURE OF POWER ELECTRONICS The discussion in this introductory chapter shows that the study of power electronics encompasses many fields within electrical engineering, as illustrated by Fig. 1-10. These include power systems, solid-state electronics, electrical machines, aiialog/digital control and signal processing, electromagnetic field calculations, and so on. Combining the knowledge of these diverse fields makes the study of power electronics challenging as well as interesting. There are many potential advances in all these fields that will improve the prospects for applying power electronics to new applications. I4 CHAPTER 1 POWER ELECTRONIC SYSTEMS _ Systems and Solid-state control theory physics W Signal processing Simulation and P°*°' mmpuiing electronics - E Electric j machines _ Pgwer Electrorriagnetics systems Figure 1-10 Interdisciplinary nature of power electronics. 1-7 CONVENTION OF SYMBOLS USED In this textbook, for instantaneous values of variables such as voltage, current, and power that are functions of time, the symbols used are lowercase letters v, i, and p, respectively. We may or may not explicitly show that they are functions of time, for example, using v rather than v(t). The uppercase symbols V and I refer to their values computed from their instantaneous waveforms. They generally refer to air average value in dc quantities and a root-mean-square (rms) value in ac quantities. If there is a possibility of confusion, the subscript avg or rms is added explicitly. The peak values are always indicated by the symbol “" " on top of the uppercase letters. The average power is always indicated by P. PROBLEMS 1- In the power processor of Fig. 1-1, the energy efficiency is 95%. The output to the three-phase load is as follows: 200 V line-to-lirie (rrns) sinusoidal voltages at 52 Hz and per-phase current of 10 A at a power factor of 0.8 (lagging). The input to the power processor is a single-phase utility voltage of 230 V at 60 Hz. The input power is drawn at a unity power factor. Calculate the input current and the input power. l-2 Consider a linear regulated dc power supply (Fig. 1-2a). The instantaneous input voltage corre- sponds to the lowest waveform in Fig. 1-2b, where Vd_m,,, = 20 V and Vd_,,,,,, = 30 V. Approximate this waveform by a triangular wave consisting of two linear segments between the above two values. Let V0 = 15 V and assume that the output load is constant. Calculate the energy efficiency in this part of the power supply due to losses in the transistor. 1- Consider a switch-mode dc power supply represented by the circuit in Fig. 1-4a. The input dc voltage Vd = 20 V and the switch duty ratio D = 0.75. Calculate the Fourier components of v0,- using the description of Foiuier analysis in Chapter 3. 1-4 In Problem 1-3, the switching frequency f, = 300 kHz and the resistive load draws 240 W. The filter components corresponding to Fig. 1-4a are L = 1.3 p.H and C = 50 p.F. Calculate the attenuation in decibels of the ripple voltage in v,,,- at various harmonic frequencies. (Hint: To calculate the load resistance, assume the output voltage to be a constant dc without any ripple.) 1- In Problem 1-4, assume the output voltage to be a pure dc V0 = 15 V. Calculate and draw the voltage and current associated with the filter inductor L, and the current through C. Using the capacitor current obtained above, estimate the peak-to-peak ripple in the voltage across C, which was initially assumed to be zero. (Hint: Note that under steady-state conditions, the average value of the cturent through C is zero.)  REFERENCES 15 1-6 Considering only the switching frequency component in v,,,- in Problems 1-3 and 1-4, calculate the peak-to-peak ripple in the output voltage across C. Compare the result with that obtained in Problem 1-5. 1-7 Reference 4 refers to a U.S. Department of Energy report that estimated that over 100 billion kWh/year can be saved in the United States by various energy conservation techniques applied to the pump-driven systems. Calculate (a) how many 1000-MW generating plants running constantly supply this wasted energy, which could be saved, and (b) the savings in dollars if the cost of electricity is 0.1 $/kWh. REFERENCES 1. B. K. Bose, “Power Electroiiics-A Technology Review,” Proceedings of the IEEE, Vol. 80, No. 8, August 1992, pp. 1303-1334. 2. E. Ohno, “The Semiconductor Evolution in Japan—A Foiu' Decade Long Maturity Thriving to an Indispensable Social Standing,” Proceedings of the International Power Electronics Conference (Tokyo), 1990, Vol. 1, pp. 1-10. 3. M. Nishiliara, “Power Electronics Diversity,” Proceedings of the International Power Elec- tronics Conference (Tokyo), l990, Vol. 1, pp. 21-28. 4. N. Mohan and R. J. Ferraro, “Techniques for Energy Conservation in AC Motor Driven Systems,” Electric Power Research Institute Final Report EM-2037, Project 1201-1213, Sep- tember 1981. 5. N. G. Hingorani, “Flexible ac Transmission," IEEE Spectrum, April 1993, pp. 40-45. 6. N. Mohan, “Power Electronic Circuits: An Overview,” IEEE/IECON Conference Proceed- ings, 1988, Vol. 3, pp. 522-527. CHAPTER 2 OVERVIEW OF POWER SEMICONDUCTOR SWITCHES 2-1 INTRODUCTION The increased power capabilities, ease of control, and reduced costs of modern power serriiconductor devices compared to those of just a few years ago have made converters affordable in a large number of applications and have opened up a host of new converter topologies for power electronic applications. In order to clearly understand the feasibility of these new topologies and applications, it is essential that the characteristics of available power devices be put in perspective. To do this, a brief summary of the terminal char- acteristics and the voltage, current, and switching speed capabilities of currently available power devices are presented in this chapter. If the power semiconductor devices can be considered as ideal switches, the analysis of converter topologies becomes much easier. This approach has the advantage that the details of device operation will not obscure the basic operation of the circuit. Therefore, the important converter characteristics can be more clearly understood. The surmnary of device characteristics will enable us to determine how much the device characteristics can be idealized. , Presently available power semiconductor devices can be classified into three groups according to their degree of controllability: j 1. Diodes. On and off states controlled by the power circuit. 2. Thyristors. Latched on by a control signal but must be tumed off by the power circuit. 3. Controllable switches. Turned on and off by control signals. The controllable switch category includes several device types including bipolar junction transistors (BJTs), metal-oxide-serniconductor field effect transistors (MOSFETs), gate tum off (GTO) thyristors, and insulated gate bipolar transistors (IGBTs). There have been major advances in recent years in this category of devices. 2-2 DIODES Figures 2-la and 2-lb show the circuit symbol for the diode and its steady-state i-v characteristic. When the diode is forward biased, it begins to conduct with only a small 16  2-2 DIODES 17 A. I-D 1 -‘ ,4 K I/rated I O-'—"l>li'° ".0 viii + up - U V (I) 0 l-—~ Rovorsej F (=11 blocking region 1, (bl (cl Figure 2-1 Diode: (a) symbol, (b) i-v characteristics, (c) idealized characteristics. forward voltage across it, which is on the order of l V. When the diode is reverse biased, only a negligibly small leakage current flows through the device until the reverse break- down voltage is reached. In normal operation, the reverse-bias voltage should not reach the breakdown rating. In view of the very small leakage currents in the blocking (reverse-bias) state and the small voltage in the conducting (forward-bias) state as compared to the operating voltage and currents of the circuit in which the diode is used, the i-v characteristics for the diode can be idealized, as shown in Fig. 2-lc. This idealized characteristic can be used for analyzing the converter topology but should not be used for the actual design, when, for example, heat sink requirements for the device are being estimated. At turn-on, the diode can be considered an ideal switch because it tums on rapidly compared to the transients in the power circuit. However, at tum-off, the diode current reverses for a reverse-recovery time tm as is indicated in Fig. 2-2, before falling to zero. This reverse-recovery (negative) current is required to sweep out the excess carriers in the diode and allow it to b1ock_a negative polarity voltage. The reverse-recovery current can lead to overvoltages in inductive circuits. In most circuits, this reverse current does not affect the converter input/output characteristic and so the diode can also be considered as ideal during the tum-off transient. Depending on the application requirements, various types of diodes are available: l. Schottky diodes. These diodes are used where a low forward voltage drop (typ- ically 0.3 V) is needed in very low output voltage circuits. These diodes are limited in their blocking voltage capabilities to 50-100 V. 2. Fast-recovery diodes. These are designed to be used in high-frequency circuits in combination with controllable switches where a small reverse-recovery time is needed. At power levels of several hundred volts and several hundred ainperes, such diodes have tr, ratings of less than a few microseconds. 3. Line-frequency diodes. The on-state voltage of these diodes is designed to be as low as possible and as a consequence have larger tn, which are acceptable for "0 tn. —>' “*\ '-Inn Figure 2-2 Diode tum-off. 13 CHAPTER 2 OVERVIEW OF POWER SEMICONDUCTOR SWITCHES line-frequency applications. These diodes are available with blocking voltage ratings of several kilovolts and current ratings of several kiloamperes. Moreover, they can be connected in series and parallel to satisfy any voltage and current requirement. 2-3 THYRISTORS The circuit symbol for the thyristor and its i-v characteristic are shown in Figs. 2-3a and 2-3b. The main current flows from the anode (A) to the cathode (K). In its off-state, the thyristor can block a forward polarity voltage and not conduct, as is shown in Fig. 2-3b by the off-state portion of the i-v characteristic. The thyristor can be triggered into the on state by applying a pulse of positive, gate current for a short duration provided that the device is in_ its forward-blocking state. The resulting i-v relationship is shown by the on-state portion of the characteristics shown in Fig. 2-3b. The forward voltage drop in the on state is only a few volts (typically 1-3 V depending on the device blocking voltage rating). Once the device begins to conduct, it is latched on and the gate current can be removed. The thyristor cannot be tumed off by the gate, and the thyristor conducts as a diode. Only when the anode current tries to go negative, under the influence of the circuit in which the thyristor is connected, does the thyristor tum off and the current go to zero. This allows the gate to regain control in order to tum the device on at some controllable time after it has again entered the forward-blocking state. in A 0ri—state A i _ Ofi-to-on ‘A + l il iG pulse is UAK Reverse | Reverse bl ocking—-i - X applied Ott- G ___'_ _ breakdown region g. :5tate I-G 0 / UAK K Reverse Fmward breakdown breakdow“ (Q) vonage voltage (b) in 0n—state we-to-on U 0 K AK Reverse Forward blocking blocking (cl Figure 2-3 Thyristor: (tr) symbol, (b) i-v characteristics, (0) idealized characteristics.  2-3 THYRISTORS 19 In reverse bias at voltages below the reverse breakdown voltage, only a negligibly small leakage current flows in the thyristor, as is shown in Fig. 2-3b. Usually the thyristor voltage ratings for forward- and reverse-blocking voltages are the same. The thyristor current ratings are specified in terms of maximum rms and average currents that it is capable of conducting. Using the same arguments as for diodes, the thyristor can be represented by the idealized characteristics shown in Fig. 2-3c in analyzing converter topologies. In an application such as the simple circuit shown in Fig. 2-4a, control can be exercised over the instant of current conduction during the positive half cycle of source voltage. When the thyristor current tries to reverse itself when the source voltage goes negative, the idealized thyristor would have its current become zero immediately after r = I/zT, as is shown in the waveform in Fig. 2-4b. However, as specified in the thyristor data sheets and illustrated by the waveforms in Fig. 2-4c, the thyristor current reverses itself before becoming___zero._ The important pa- rameter is not the time it takes for the current to become zero from its negative value, but rather the tum-off time interval rq defined in Fig. 2-4c from the zero crossover of the current to the zero crossover of the voltage across the thyristor. During re a reverse voltage must be maintained across the thyristor, and only after this time is the device capable of blocking a forward voltagewithout going into IIIS on state. If a forward voltage is applied to the thyristor before this interval has passed, the device may prematurely tum on, and damage to the device and/or circuit could result. Thyristor data sheets specify tq with a specified reverse voltage applied during this interval as well as a specified rate of rise of voltage beyond this interval. This interval tq is sometimes called the circuit-commutated recovery time of the thyristor. Depending on the application requirements, various types of thyristors are available. In addition to voltage and current ratings, tum-off time tq, and the forward voltage drop,.v_, R.". [A + Q _.. F F if 5,, * -"- t Q P, v UAR Q %‘ // T I iG'_—' \ / fa) \\--I’ ,A re»; \\ tn O “'-'1 t 1‘ "Ax i I 1 Q s- -- -—> t -$11-j i"—‘q—"'i (cl Figure 2-4 Thyristor: (a) circuit, (b) waveforms, (c) turn-off time interval tq. 20 CHAPTER 2 ovt-tavu-*.w or POWER SEMICONDUCTOR SWITCHES other characteristics that must be considered include the rate of rise of the current (di/dt) at turn-on and the rate of rise of voltage (dv/dt) at tum-off. 1. Phase-control thyristors. Sometimes termed converter thyristors, these are used primarily for rectifying line-frequency voltages and currents in applications such as phase-controlled rectifiers for dc and ac motor drives and in high-voltage dc power transmission. The main device requirements are large voltage and t;l.u:tcni- handling capabilities and a,]_ow on-state voltage drop. This type of thyristor has been produced in wafer diameters of up to 10 cm, where the average current is about 4000 A with blocking voltages of 5-7 kV. On-state voltages range from 1.5 V for 1000-V devices to 3.0 V for the 5-7-kV devices. 2. Inverter-grade thyristors. These are designed to have small tum-off times tq in addition to low on-state voltages, although on-state voltages are larger in devices with shorter values of tq. These devices are available with ratings up to 2500 V and 1500 A. Their tum-off times are usually in the range of a few microseconds to 100 p.s depending on their blocking voltage ratings and on-state voltage drops. 3. Light-activated thyristors. These can be triggered on by a pulse of light guided by optical fibers to a special sensitive region of the thyristor. The light-activated triggering on the thyristor uses the ability of light of appropriate wavelengths to generate excess electron-hole pairs in the silicon. The primary use of these thyristors are in high-voltage applications such as high-voltage dc transmission where many thyristors are connected in series to make up a converter valve. The differing high potentials that each device sees with respect to ground poses sig- nificant difficulties in providing triggering pulses. Light-activated thyristors have been reported with ratings of 4 kV and 3 kA, on-state voltages of about 2 V, and light trigger power requirements of 5 mW. Other variations of these thyristors are gate-assisted tum-off thyristors (GATl"s), asymmetrical silicon-controlled rectifiers (ASCRs), and reverse-conducting thyristors (RCTs). These are utilized based on the application. 2.. DESIRED CHARACTERISTICS IN CONTROLLABLE SWITCHES As mentioned in the introduction, several types of semiconductor power devices including BITs, MOSFETs, GTOs, and IGBTs can be turned on and off by control signals applied to the control terminal of the device. These devices we term controllable switches and are represented in a generic manner by the circuit symbol shown in Fig. 2-5. No current flows when the switch is off, and when it is on, current can flow in the direction of the arrow only. The ideal controllable switch has the following characteristics: 1. Block arbitrarily large forward and reverse voltages with zero current flow when off. 2. Conduct arbitrarily large currents with zero voltage drop when on. rial + "T l— Figure 2-5 Generic controllable switch.  2-4 DESIRED CHARACTERISTICS IN CONTROLLABLE SWITCHES 21 3. Switch from on to off or vice versa instantaneously when triggered. 4. Vanishingly small power required from control source to trigger the switch. Real devices, as we intuitively expect, do not have these ideal characteristics and hence will dissipate power when they are used in the numerous applications already mentioned. If they dissipate too much power,- the devices can fail and, in doing so, not only will destroy themselves but also may damage the other system components. Power dissipation in semiconductor power devices is fairly generic in nature; that is, the same basic factors goveming power dissipation apply to all devices in the same manner. The converter designer must understand what these factors are and how to minimize the power dissipation in the devices. In order to consider power dissipation in a semiconductor device, a controllable switch is connected in the simple circuit shown in Fig. 2-6a. This circuit models a very commonly encountered situation in power electronics; the current flowing through a new-._ 1,, V. d ‘T1 + vr Switch (a ) control signal On 0 - - tr - -0 |t Q" Off 1...,, - _. l U15 if i A l V4 l Yd 1, *. Von 1._ t I :1? 3'? _.+ -atom r T. §r"°r3 III ttfi --Jli PT“) (_i-'—'¢> tcwn), tctom. In order to tum the switch off, a negative control signal is applied to the control terminal of the switch. During the tum-off transition period of the generic switch, the voltage build-up consists of a tum-off delay time tdwm and a voltage rise time t,,,. Oncc the voltage reaches its final value of Vd (see Fig. 2-60), the diode can become forward biased and begin to conduct current. The current in the switch falls to zero with a current fall time tf, as the current Io commutates from the switch to the diode. Large values of switch voltage and switch current occur simultaneously during the crossover interval tcwm, where Hoff) = Irv + {ft 0'4) The energy dissipated in the switch during this tum-off transition can be written, using Fig. 2-6c, as l'V¢-(Off) : 1/2l/(110 Q-(off)  2-4 DFISIRI-ID CHARACTERISTICS IN (IO.\l'|'ROLLABI.l*I SWITCI-ll~1S 23 where any energy dissipation during the tum-off delay interval tdwm is ignored since it is small compared to Wmm. The instantaneous power dissipation p-I-(t) = v-I-i-T plotted in Fig. 2-6c makes it clear that a large instantaneous power dissipation occurs in the switch during the turn-on and turn-off intervals. There are f, such tum-on and turn-off transitions per second. Hence the average switching power loss PS in the switch due to these transitions can be approximated from Eqs. 2-2 and 2-5 as P5: I/2VdIafs(tc(on)+tc(off)) This is an important result because it shows that the switching power loss in a semicon- ductor switch varies linearly with the switching frequency and the switching times. Therefore, if devices with short switching times are available, it is possible to operate at high switching frequencies in order to reduce filtering requirements and at the same time keep the switching power loss in the device from being excessive. The other major contribution to the power loss in the switch is the average power dissipated during the on-state PO“, which varies in proportion to the on-state voltage. From Eq. 2-3, P0,, is given by _"o_n Pon " V0nI0Ts which shows that the on-stage voltage in a switch should be as small as possible. The leakage current during the off state (switch open) of controllable switches is negligibly small, and therefore the power loss during the off state can be neglected in practice. Therefore, the total average power dissipation PT in a switch equals the sum of P, and Pom. Form the considerations discussed in the preceding paragraphs, the following char- acteristics in a controllable switch are desirable: l. Small leakage current in the off state. V Q _ 2. Small on-state voltage V0,, to minimize on-state power losses. , 3. Short turn-on and turn-off times. This will permit the device to be used at high switching frequencies. 4. Large forward- and reverse-voltage-blocking capability. This will minimize the need for series connection of several devices, which complicates the control and protection of the switches. Moreover, most of the device types have a minimum on-state voltage regardless of their blocking voltage rating. A series connection of several such devices would lead to a higher total on-state voltage and hence higher conduction losses. In most (but not all) converter circuits, a diode is placed across the controllable switch to allow the current to flow in the reverse direction. In those circuits, controllable switches are not required to have any significant re- verse-voltage-blocking capability. 5. High on-state current rating. In high-current applications, this would minimize the need to connect several devices in parallel, thereby avoiding the problem of current sharing. 6. Positive temperature coefficient of on-state resistance. This ensures that paralleled devices will share the total current equally. 7. Small control power required to switch the device. This will simplify the control circuit design. 8. Capability to withstand rated voltage and rated current simultaneously while switching. This will eliminate the need for external protection (snubber) circuits across the device. 24 (IIIAPTF.R 2 OVERVll~‘.W OF POWER SEMICOi\Zl)LI(ITOR SWIT(lIIF.S 9. Large dv/dt and di/dt ratings. This will minimize the need for external circuits otherwise needed to limit dv/dt and di/dt in the device so that it is not damaged. We should note that the clamped-inductive-switching circuit of Fig. 2-6a results in higher switching power loss and puts higher stresses on the switch in comparison to the resistive-switching circuit shown in Problem 2-2 (Fig. P2-2). We now will briefly consider the steady-state i-v characteristics and switching times of the commonly used semiconductor power devices that can be used as controllable switches. As mentioned previously, these devices include BJTs, MOSFETs, GTOs, and IGBTs. The details of the physical operation of these devices, their detailed switching characteristics, commonly used drive circuits, and needed snubber circuits are discussed in Chapters 19-28. 2- BIPOLAR JUNCTION TRANSISTORS ANI) MONOLITHIC DARLINGTONS C The circuit symbol for an NPN BJT is shown in Fig. 2-7a, and its steady-state i-v characteristics are shown in Fig. 2-7b. As shown in the i-v characteristics, a sufficiently large base current (dependent on the collector current) results in the device being fully on. This requires that the control circuit provide a base current that is sufficiently large so that lg Ia > T (2-8) FE where hm; is the dc current gain of the device. The on-state voltage VG,-(53,, of the power transistors is usually in the l-2-V range, so that the conduction power loss in the BJT is quite small. The idealized i-v character- istics of the BJT operating as a switch are shown in Fig. 2-7c. Bipolar junction transistors are current-controlled devices, and base current must be supplied continuously to keep them in the on state. The dc cur