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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
- Veröffentlichungsjahr: 2022
POWER ELECTRONICS A FIRST COURSE Enables students to understand power electronics systems, as one course, in an integrated electric energy systems curriculum Power Electronics A First Course provides instruction on fundamental concepts related to power electronics to undergraduate electrical engineering students, beginning with an introductory chapter and moving on to discussing topics such as switching power-poles, switch-mode dc-dc converters, and feedback controllers. The authors also cover diode rectifiers, power-factor-correction (PFC) circuits, and switch-mode dc power supplies. Later chapters touch on soft-switching in dc-dc power converters, voltage and current requirements imposed by various power applications, dc and low-frequency sinusoidal ac voltages, thyristor converters, and the utility applications of harnessing energy from renewable sources. Power Electronics A First Course is the only textbook that is integrated with hardware experiments and simulation results. The simulation files are available on a website associated with this textbook. The hardware experiments will be available through a University of Minnesota startup at a low cost. In Power Electronics A First Course, readers can expect to find detailed information on: * Availability of various power semiconductor devices that are essential in power electronic systems, plus their switching characteristics and various tradeoffs * Common foundational unit of various converters and their operation, plus fundamental concepts for feedback control, illustrated by means of regulated dc-dc converters * Basic concepts associated with magnetic circuits, to develop an understanding of inductors and transformers needed in power electronics * Problems associated with hard switching, and some of the practical circuits where this problem can be minimized with soft-switching Power Electronics A First Course is an ideal textbook for Junior/Senior-Undergraduate students in Electrical and Computer Engineering (ECE). It is also valuable to students outside of ECE, such as those in more general engineering fields. Basic understanding of electrical engineering concepts and control systems is a prerequisite.
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Power Electronics A First Course
Simulations and Laboratory Implementations
Second Edition
NED MOHAN AND SIDDHARTH RAJU
University of Minnesota, Minneapolis, MN, USA
Copyright © 2023 by John Wiley & Sons Inc.. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data
Names: Mohan, Ned, author. | Raju, Siddharth, author. Title: Power electronics A first course : simulations and laboratory implementations / Ned Mohan and Siddharth Raju, University of Minnesota, Minneapolis, MN. Description: Second edition. | Hoboken, New Jersey : John Wiley & Sons, [2023] |Includes bibliographical references and index. Identifiers: LCCN 2022038114 (print) | LCCN 2022038115 (ebook) | ISBN 9781119818564 (hardback) | ISBN 9781119818571 (pdf) | ISBN 9781119818588 (epub) Subjects: LCSH: Electric power systems. | BISAC: TECHNOLOGY & ENGINEERING / Power Resources / General. Classification: LCC TK1001 .M5985 2023 (print) | LCC TK1001 (ebook) | DDC 621.31--dc23/eng/20221017 LC record available at https://lccn.loc.gov/2022038114 LC ebook record available at https://lccn.loc.gov/2022038115
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To our families
Contents
Cover
Title page
Copyright
Dedication
LIST OF SIMULATION AND HARDWARE IMPLEMENTATION EXAMPLE AND FIGURES
PREFACE
ACKNOWLEDGMENT
ABOUT THE COMPANION WEBSITE
CHAPTER 1 POWER ELECTRONICS: AN ENABLING TECHNOLOGY
1.1 Introduction to Power Electronics
1.2 Applications and the Role of Power Electronics
1.3 Energy and the Environment: Role of Power Electronics in Providing Sustainable Electric Energy
1.4 Need for High Efficiency and High Power Density
1.5 Structure of Power Electronics Interface
1.6 Voltage-Link-Structure
1.7 Recent Advances in Solid-State Devices Based on Wide Bandgap (WBG) Materials
1.8 Use of Simulation and Hardware Prototyping
References
Problems
CHAPTER 2 DESIGN OF SWITCHING POWER-POLES
2.1 Power Transistors and Power Diodes
2.2 Selection of Power Transistors
2.3 Selection of Power Diodes
2.4 Switching Characteristics and Power Losses in Power Poles
2.5 Justifying Switches and Diodes as Ideal
2.6 Design Considerations
2.7 The PWM IC
2.8 Hardware Prototyping
References
Problems
Appendix 2A Diode Reverse Recovery and Power Losses
CHAPTER 3 SWITCH-MODE DC-DC CONVERTERS: SWITCHING ANALYSIS, TOPOLOGY SELECTION, AND DESIGN
3.1 DC-DC Converters
3.2 Switching Power-Pole in DC Steady State
3.3 Simplifying Assumptions
3.4 Common Operating Principles
3.5 Buck Converter Switching Analysis in DC Steady State
3.6 Boost Converter Switching Analysis in DC Steady State
3.7 Buck-Boost Converter Analysis in DC Steady State
3.8 Topology Selection
3.9 Worst-Case Design
3.10 Synchronous-Rectified Buck Converter for Very Low Output Voltages
3.11 Interleaving of Converters
3.12 Regulation of DC-DC Converters by PWM
3.13 Dynamic Average Representation of Converters in CCM
3.14 Bi-Directional Switching Power-Pole
3.15 Discontinuous-Conduction Mode (DCM)
References
Problems
Appendix 3A Average Representation in Discontinuous- Conduction Mode (DCM)
CHAPTER 4 DESIGNING FEEDBACK CONTROLLERS IN SWITCH-MODE DC POWER SUPPLIES
4.1 Introduction and Objectives of Feedback Control
4.2 Review of Linear Control Theory
4.3 Linearization of Various Transfer Function Blocks
4.4 Feedback Controller Design in Voltage-Mode Control
4.5 Peak-Current Mode Control
4.6 Feedback Controller Design in DCM
References
Problems
Appendix 4A Bode Plots of Transfer Functions with Poles and Zeros
Appendix 4B Transfer Functions in Continuous Conduction Mode (CCM)
Appendix 4C Derivation of Parameters of the Controller Transfer Functions
CHAPTER 5 RECTIFICATION OF UTILITY INPUT USING DIODE RECTIFIERS
5.1 Introduction
5.2 Distortion and Power Factor
5.3 Classifying the “Front-End” of Power Electronic Systems
5.4 Diode-Rectifier Bridge “Front-End”
5.5 Means to Avoid Transient Inrush Currents at Starting
5.6 Front-Ends with Bi-Directional Power Flow
References
Problems
CHAPTER 6 POWER-FACTOR-CORRECTION (PFC) CIRCUITS AND DESIGNING THE FEEDBACK CONTROLLER
6.1 Introduction
6.2 Operating Principle of Single-Phase PFCS
6.3 Control of PFCS
6.4 Designing the Inner Average-Current-Control Loop
6.5 Designing the Outer Voltage-Control Loop
6.6 Example of Single-Phase PFC Systems
6.7 Simulation Results
6.8 Feedforward of the Input Voltage
6.9 Other Control Methods for PFCS
References
Problems
Appendix 6A Proof that
Appendix 6B Proof that
CHAPTER 7 MAGNETIC CIRCUIT CONCEPTS
7.1 Ampere-Turns and Flux
7.2 Inductance
L
7.3 Faraday’s Law: Induced Voltage in a Coil Due to Time-Rate of Change of Flux Linkage
7.4 Leakage and Magnetizing Inductances
7.5 Transformers
Reference
Problems
CHAPTER 8 SWITCH-MODE DC POWER SUPPLIES
8.1 Applications of Switch-Mode DC Power Supplies
8.2 Need for Electrical Isolation
8.3 Classification of Transformer-Isolated DC-DC Converters
8.4 Flyback Converters
8.5 Forward Converters
8.6 Full-Bridge Converters
8.7 Half-Bridge and Push-Pull Converters
8.8 Practical Considerations
References
Problems
CHAPTER 9 DESIGN OF HIGH-FREQUENCY INDUCTORS AND TRANSFORMERS
9.1 Introduction
9.2 Basics of Magnetic Design
9.3 Inductor and Transformer Construction
9.4 Area-Product Method
9.5 Design Example of an Inductor
9.6 Design Example of a Transformer for a Forward Converter
9.7 Thermal Considerations
References
Problems
CHAPTER 10 SOFT-SWITCHING IN DC-DC CONVERTERS AND HALF-BRIDGE RESONANT CONVERTERS
10.1 Introduction
10.2 Hard-Switching in Switching Power poles
10.3 Soft-switching in Switching Power-Poles
10.4 Half-Bridge Resonant Converter
References
Problems
CHAPTER 11 APPLICATIONS OF SWITCH-MODE POWER ELECTRONICS IN MOTOR DRIVES, UNINTERRUPTIBLE POWER SUPPLIES, AND POWER SYSTEMS
11.1 Introduction
11.2 Electric Motor Drives
11.3 Uninterruptible Power Supplies (UPS)
11.4 Utility Applications of Switch-Mode Power Electronics
Reference
Problems
CHAPTER 12 SYNTHESIS OF DC AND LOW-FREQUENCY SINUSOIDAL AC VOLTAGES FOR MOTOR DRIVES, UPS, AND POWER SYSTEMS APPLICATIONS
12.1 Introduction
12.2 Bidirectional Switching Power-Pole as the Building Block
12.3 Converters for DC Motor Drives
12.4 Synthesis of Low-Frequency AC
12.5 Single-Phase Inverters
12.6 Three-Phase Inverters
12.7 Multilevel Inverters
12.8 Converters For Bidirectional Power Flow
12.9 Matrix Converters (Direct Link System)
References
Problems
CHAPTER 13 THYRISTOR CONVERTERS
13.1 Introduction
13.2 Thyristors (SCRs)
13.3 Single-phase, Phase-controlled Thyristor Converters
13.4 Three-Phase, Full-Bridge Thyristor Converters
13.5 Current-Link Systems
Reference
Problems
CHAPTER 14 UTILITY APPLICATIONS OF POWER ELECTRONICS
14.1 Introduction
14.2 Power Semiconductor Devices and Their Capabilities
14.3 Categorizing Power Electronic Systems
14.4 Distributed Generation (DG) Applications
14.5 Power Electronic Loads
14.6 Power Quality Solutions
14.7 Transmission and Distribution (T&D) Applications
References
Problems
Index
End User License Agreement
List of Tables
CHAPTER 03
TABLE 3.1 Topology selection criteria.
TABLE 3.2 V
k
and I
k
.
CHAPTER 05
TABLE 5.1 Harmonic current distortion...
CHAPTER 06
Parameters and operating values.
List of Illustrations
CHAPTER 01
FIGURE 1.1 Power electronics...
FIGURE 1.2 Regulated low-voltage...
FIGURE 1.3 Boost DC-DC converter...
FIGURE 1.4 Block Diagram...
FIGURE 1.5 Power electronics interface...
FIGURE 1.6 Power electronics interface...
FIGURE 1.7 Percentage use of electricity...
FIGURE 1.8 Role of adjustable-speed...
FIGURE 1.9 Power electronics interface...
FIGURE 1.10 Hybrid electric vehicles...
FIGURE 1.11 Photovoltaic systems.
FIGURE 1.12 Wind-electric systems.
FIGURE 1.13 Uninterruptible power...
FIGURE 1.14 Power output capability...
FIGURE 1.15 Block diagram of power...
FIGURE 1.16 Voltage-link structure...
FIGURE 1.17 Current-link structure...
FIGURE 1.18 Matrix converter structure...
FIGURE 1.19 Load-side converter...
FIGURE 1.20 Switching power-pole...
FIGURE 1.21 PWM of the switching...
FIGURE 1.22 Switching power-pole...
FIGURE 1.23 Waveforms in the...
FIGURE 1.24 Transistor and diode...
FIGURE 1.25 Applications of...
FIGURE P1-1 Flowrate profile.
CHAPTER 02
FIGURE 2.1 MOSFET: (a) symbol, (b) I-V...
FIGURE 2.2 IGBT: (a) symbol,...
FIGURE 2.3 Diode: (a) symbol,...
FIGURE 2.4 MOSFET in a switching...
FIGURE 2.5 MOSFET turn-on.
FIGURE 2.6 MOSFET transfer characteristic.
FIGURE 2.7 MOSFET turn-off.
FIGURE 2.8 MOSFET switching losses.
FIGURE 2.9 Gate-driver IC...
FIGURE 2.10 Bootstrap gate-driver...
FIGURE 2.11 Capacitor ESR and ESL.
FIGURE 2.12 Thermal design:...
FIGURE 2.13 Size of magnetic...
FIGURE 2.14 PWM IC waveforms.
FIGURE 2.15 Sciamble power...
FIGURE 2A.1 Diode reverse-recovery...
FIGURE 2A.2 Waveforms with diode...
CHAPTER 03
FIGURE 3.1 Regulated switch-mode...
FIGURE 3.2 Switching power-pole...
FIGURE 3.3 Example 3.1.
FIGURE 3.4 Example 3.2.
FIGURE 3.5 Buck DC-DC converter.
FIGURE 3.6 Example 3.3.
FIGURE 3.7 LTspice model.
FIGURE 3.8 LTspice simulation...
FIGURE 3.9 Workbench model.
FIGURE 3.10 Workbench hardware results:...
FIGURE 3.11 Boost DC-DC converter.
FIGURE 3.12 Boost converter:...
FIGURE 3.13 Example 3.5.
FIGURE 3.14 Boost converter:...
FIGURE 3.15 LTspice model.
FIGURE 3.16 LTspice simulation results.
FIGURE 3.17 Workbench model.
FIGURE 3.18 Workbench hardware...
FIGURE 3.19 Buck-boost DC-DC converter.
FIGURE 3.20 Buck-boost...
FIGURE 3.21 Example 3.7.
FIGURE 3.22 Buck-boost...
FIGURE 3.23 LTspice model.
FIGURE 3.24 LTspice simulation results...
FIGURE 3.25 Workbench model.
FIGURE 3.26 Workbench hardware...
FIGURE 3.27 SEPIC converter.
FIGURE 3.28 Ćuk converter.
FIGURE 3.29 Buck converter...
FIGURE 3.30 LTspice model.
FIGURE 3.31 LTspice simulation results.
FIGURE 3.32 Workbench model.
FIGURE 3.33 Workbench hardware...
FIGURE 3.34 Switch-node voltage:...
FIGURE 3.35 Interleaving of converters.
FIGURE 3.36 Regulation of output by PWM.
FIGURE 3.37 Average dynamic model...
FIGURE 3.38 Average dynamic...
FIGURE 3.39 Bi-directional power...
FIGURE 3.40 Average dynamic model...
FIGURE 3.41 Inductor current...
FIGURE 3.42 Buck converter in DCM.
FIGURE 3.43 LTspice simulation results.
FIGURE 3.44 Workbench...
FIGURE 3.45 Non-ideal buck...
FIGURE 3.46 Boost converter in DCM.
FIGURE 3.47 LTspice simulation results.
FIGURE 3.48 Workbench hardware:...
FIGURE 3.49 Buck-boost converter in DCM.
FIGURE 3.50 LTspice simulation results.
FIGURE 3.51 Workbench hardware:...
FIGURE 3.52 Average representation...
CHAPTER 04
FIGURE 4.1 Regulated DC power supply.
FIGURE 4.2 Feedback control.
FIGURE 4.3 Small-signal control...
FIGURE 4.4 DEFINITIONS OF...
FIGURE 4.5 PWM waveforms.
FIGURE 4.6 Linearizing...
FIGURE 4.7 Linearizing single-switch...
FIGURE 4.8 Small-signal equivalent...
FIGURE 4.9 LTspice circuit model...
FIGURE 4.10 The gain and the phase...
FIGURE 4.11 Bode plot of
FIGURE 4.12 Controller implementation of
FIGURE 4.13 Workbench script...
FIGURE 4.14 LTspice model.
FIGURE 4.15 LTspice simulation results.
FIGURE 4.16 Workbench model.
FIGURE 4.17 Controller subsystem.
FIGURE 4.18 Output voltage waveform.
FIGURE 4.19 Workbench model.
FIGURE 4.20 Workbench hardware...
FIGURE 4.21 Peak current mode control.
FIGURE 4.22 Peak-current-mode...
FIGURE 4.23 LTspice circuit...
FIGURE 4.24 Bode plot...
FIGURE 4.25 Controller...
FIGURE 4.26 LTspice model.
FIGURE 4.27 LTspice simulation results.
FIGURE 4.28 Workbench model.
FIGURE 4.29A Controller subsystem.
FIGURE 4.29B Controller subsystem.
FIGURE 4.30 Output voltage waveform.
FIGURE 4.31 Workbench model.
FIGURE 4.32A Workbench hardware...
FIGURE 4.32B Workbench hardware...
FIGURE 4.33 LTspice circuit for...
FIGURE 4.34 The gain and phase...
FIGURE 4A.1 Gain and phase plots...
FIGURE 4A.2 Gain and phase plots...
FIGURE 4A.3 Gain and phase plots...
FIGURE 4A.4 Gain and phase plots...
FIGURE 4B.1 Equivalent...
FIGURE 4B.2 Equivalent...
FIGURE 4B.4A Equivalent...
FIGURE 4B.4B Equivalent...
FIGURE 4B.4C Equivalent...
FIGURE 4C.1 Controller...
FIGURE 4C.2 Controller implementation...
CHAPTER 05
FIGURE 5.1 Block diagram of power...
FIGURE 5.2 Voltage and current...
FIGURE 5.3 Current drawn by power...
FIGURE 5.4 Example 5.1.
FIGURE 5.5 Relation between...
FIGURE 5.6 (a) Utility supply;...
FIGURE 5.7 Front-end of power...
FIGURE 5.8 Full-bridge diode...
FIGURE 5.9 Full-bridge diode...
FIGURE 5.10 Full-bridge diode...
FIGURE 5.11 Waveforms for the...
FIGURE 5.12 Single-phase diode-bridge...
FIGURE 5.13 LTspice model.
FIGURE 5.14 LTspice simulation results.
FIGURE 5.15 Three-phase diode bridge rectifier.
FIGURE 5.16 Waveforms in a...
FIGURE 5.17 Effect...
FIGURE 5.18 LTspice model.
FIGURE 5.19 LTspice simulation results.
FIGURE 5.20 Means to avoid inrush current.
CHAPTER 06
FIGURE 6.1 PFC circuit and waveforms.
FIGURE 6.2 Average model in CCM (Average model in CCM (
FIGURE 6.3 Current division in the output stage.
FIGURE 6.4 PFC control loops.
FIGURE 6.5 PFC current loop.
FIGURE 6.6 Voltage control loop.
FIGURE 6.7 Op-amp circuit to...
FIGURE 6.8 LTspice simulation...
FIGURE 6.9 Simulation...
FIGURE 6.10 Feedforward...
CHAPTER 07
FIGURE 7.1 Magnetic structure...
FIGURE 7.2 Coil inductance.
FIGURE 7.3 Voltage polarity...
FIGURE 7.4 (a) Magnetic and...
FIGURE 7.5 (a) Circuit...
FIGURE 7.6 Transformer...
FIGURE 7.7 Equivalent circuits...
CHAPTER 08
FIGURE 8.1 Block diagram...
FIGURE 8.2 Buck-boost...
FIGURE 8.3 Flyback converter waveforms.
FIGURE 8.4 LTspice model.
FIGURE 8.5 LTspice simulation results.
FIGURE 8.6 Workbench model.
FIGURE 8.7 Workbench hardware...
FIGURE 8.8 Practical flyback...
FIGURE 8.9 RCD snubber.
FIGURE 8.10 RCD snubber waveforms
FIGURE 8.11 LTspice model.
FIGURE 8.12 LTspice simulation results.
FIGURE 8.13 Workbench hardware...
FIGURE 8.14 LTspice simulation results.
FIGURE 8.15 Workbench hardware...
FIGURE 8.16 Buck and forward converters.
FIGURE 8.17 Forward converter operation.
FIGURE 8.18 Forward Converter Core Flux.
FIGURE 8.19 Waveforms in...
FIGURE 8.20 LTspice model.
FIGURE 8.21 LTspice simulation results.
FIGURE 8.22 Workbench model.
FIGURE 8.23 Workbench hardware...
FIGURE 8.24 Two-switch forward converter.
FIGURE 8.25 Full-bridge converter.
FIGURE 8.26 Full-bridge converter waveforms.
FIGURE 8.27 PWM IC and control...
FIGURE 8.28 Full-bridge: sub-circuits.
FIGURE 8.29 Full-bridge converter waveforms.
FIGURE 8.30 Waveforms of the...
FIGURE 8.31 LTspice model.
FIGURE 8.32 LTspice simulation results.
FIGURE 8.33 Workbench model.
FIGURE 8.34 Workbench hardware...
FIGURE 8.35 Half-bridge...
CHAPTER 09
FIGURE 9.1 Cross-sections.
FIGURE 9.2 Waveforms in...
FIGURE 9.3 Inductor current waveforms.
FIGURE 9.4 Pot core mounted...
CHAPTER 10
FIGURE 10.1 Hard switching...
FIGURE 10.2 ZVS in a MOSFET.
FIGURE 10.3 Synchronous-rectified...
FIGURE 10.4 Synchronous-rectified...
FIGURE 10.5 Transition in...
FIGURE 10.6 Phase-shift modulated...
FIGURE 10.7 Half-bridge resonant...
FIGURE 10.8 Converter output waveforms.
CHAPTER 11
FIGURE 11.1 Block diagram...
FIGURE 11.2 Exploded view...
FIGURE 11.3 DC motor equivalent circuit.
FIGURE 11.4 (a) Torque-speed characteristics...
FIGURE 11.5 Two-pole PMAC machine.
FIGURE 11.6 Block diagram...
FIGURE 11.7 Equivalent circuit...
FIGURE 11.8 Torque-speed...
FIGURE 11.9 (a) Three-phase stator...
FIGURE 11.10 Induction machine...
FIGURE 11.11 Induction motor...
FIGURE 11.12 Induction motor...
FIGURE 11.13 Induction motor...
FIGURE 11.14 Block diagram of UPS.
FIGURE 11.15 Interaction of the...
FIGURE 11.16 Per-phase equivalent...
CHAPTER 12
FIGURE 12.1 Voltage-link system.
FIGURE 12.2 Converters for...
FIGURE 12.3 Bidirectional power...
FIGURE 12.4 Bidirectional...
FIGURE 12.5 Switching-cycle-averaged...
FIGURE 12.6 Waveforms for PWM...
FIGURE 12.7 Switching power-pole...
FIGURE 12.8 Harmonics in the output...
FIGURE 12.9 Converter for DC motor drive.
FIGURE 12.10 Switching-cycle-averaged...
FIGURE 12.11 Gain of the converter for DC drives.
FIGURE 12.12 Switching voltage waveforms...
FIGURE 12.13 Currents defined in the...
FIGURE 12.14 Superposition of DC and...
FIGURE 12.15 Switching current waveforms...
FIGURE 12.16 Waveforms of a switching...
FIGURE 12.17 Single-phase...
FIGURE 12.18 Switching-cycle-averaged...
FIGURE 12.19 OUTPUT VOLTAGE AND CURRENT.
FIGURE 12.20 Waveforms in the UPS of...
FIGURE 12.21 LTspice model.
FIGURE 12.22 LTspice simulation results.
FIGURE 12.23 Workbench model.
FIGURE 12.24 Workbench hardware...
FIGURE 12.25 Three-phase converter.
FIGURE 12.26 Switching-cycle-averaged...
FIGURE 12.27 Switching-cycle-averaged...
FIGURE 12.28 Switching waveforms in...
FIGURE 12.29 LTspice model.
FIGURE 12.30 LTspice simulation results.
FIGURE 12.31 Workbench model.
FIGURE 12.32 Workbench hardware...
FIGURE 12.33 Inverter with a three-phase output.
FIGURE 12.34 Basic voltage vectors...
FIGURE 12.35 Voltage vector in sector 1.
FIGURE 12.36 Waveforms in sector 1...
FIGURE 12.37 Limit on amplitude...
FIGURE 12.38 LTspice model.
FIGURE 12.39 LTspice simulation results.
FIGURE 12.40 Workbench model.
FIGURE 12.41 Workbench hardware results:...
FIGURE 12.42 Square-wave (six-step) waveforms.
FIGURE 12.43 Three-level inverters.
FIGURE 12.44 Voltage-link structure...
FIGURE 12.45 Matrix converter.
CHAPTER 13
FIGURE 13.1 Thyristors.
FIGURE 13.2 A simple thyristor...
FIGURE 13.3 Thyristor circuit with...
FIGURE 13.4 Full-bridge, single-phase...
FIGURE 13.5 Single-phase thyristor...
FIGURE 13.6 Effect of the delay angle...
FIGURE 13.7 Single-phase thyristor...
FIGURE 13.8 Effect of...
FIGURE 13.9 Three-phase full-bridge...
FIGURE 13.10 Waveforms with...
FIGURE 13.11 Waveforms in the inverter mode.
FIGURE 13.12 Commutation of...
FIGURE 13.13 Waveforms with...
FIGURE 13.14 Block diagram of current-link systems.
CHAPTER 14
FIGURE 14.1 Power semiconductor devices.
FIGURE 14.2 Back-to-back thyristors...
FIGURE 14.3 Power electronics...
FIGURE 14.4 Block diagram...
FIGURE 14.5 Block diagram...
FIGURE 14.6 Wind-resource...
FIGURE 14.7A Induction generator directly...
FIGURE 14.7B Doubly-fed, wound-rotor...
FIGURE 14.7C Power electronics...
FIGURE 14.8 Photovoltaic systems.
FIGURE 14.9 A rooftop PV system...
FIGURE 14.10 Fuel cell V-I relationship...
FIGURE 14.11 Flywheel storage system.
FIGURE 14.12 Adjustable-speed drive.
FIGURE 14.13 Dual-feeders.
FIGURE 14.14 Uninterruptible power supplies.
FIGURE 14.15 Dynamic voltage restorers.
FIGURE 14.16 HVDC voltage-link...
FIGURE 14.17 Block diagram HVDC...
FIGURE 14.18 Power flow on a...
FIGURE 14.19 Shunt-connected...
FIGURE 14.20 Thyristor-controlled...
FIGURE 14.21 Unified power...
FIGURE 14.1 Power semiconductor devices.
FIGURE 14.2 Back-to-back thyristors...
FIGURE 14.3 Power electronics...
FIGURE 14.4 Block diagram...
FIGURE 14.5 Block diagram...
FIGURE 14.6 Wind-resource...
FIGURE 14.7A Induction generator...
FIGURE 14.7B Doubly-fed, wound-rotor...
FIGURE 14.7C Power electronics...
FIGURE 14.8 Photovoltaic systems.
FIGURE 14.9 A rooftop PV system....
FIGURE 14.10 Fuel cell V-I relationship...
FIGURE 14.11 Flywheel storage system.
FIGURE 14.12 Adjustable-speed drive.
FIGURE 14.13 Dual-feeders.
FIGURE 14.14 Uninterruptible power supplies.
FIGURE 14.15 Dynamic voltage restorers.
FIGURE 14.16 HVDC voltage-link...
FIGURE 14.17 Block diagram HVDC...
FIGURE 14.18 Power flow on a transmission line.
FIGURE 14.19 Shunt-connected devices...
FIGURE 14.20 Thyristor-controlled...
FIGURE 14.21 Unified power flow...
Guide
Cover
Title page
Copyright
Dedication
Table of Contents
List of Simulation and Hardware Implementation Example and Figures
Preface
Acknowledgment
About the Companion Website
Begin Reading
Index
End User License Agreement
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LIST OF SIMULATION AND HARDWARE IMPLEMENTATION EXAMPLE AND FIGURES
Experiment
Simulation
Hardware
Lab kit
N/A
Figure 2.15
Buck converter - CCM
Example 3.4
Figures 3.7 and 3.8
Example 3.4
Figures 3.9 and 3.10
Boost converter - CCM
Example 3.6
Figures 3.15 and 3.16
Example 3.6
Figures 3.17 and 3.18
Buck-Boost converter - CCM
Example 3.8
Figures 3.23 and 3.24
Example 3.8
Figures 3.25 and 3.26
Synchronous-rectified Buck converter
Example 3.9
Figures 3.30 and 3.31
Example 3.9
Figures 3.32 through 3.34
Buck converter - DCM
Example 3.10
Figures 3.43
Example 3.10
Figures 3.44
Boost converter - DCM
Example 3.12
Figures 3.47
Example 3.12
Figures 3.48
Buck-Boost converter - DCM
Example 3.13
Figures 3.50
Example 3.13
Figures 3.51
Buck converter frequency response
Example 4.2
Figures 4.9 and 4.10
N/A
Buck converter - Voltage mode control
Example 4.4
Figures 4.13 through 4.18
Example 4.4
Figures 4.19 and 4.20
Buck-Boost converter – Peak-current-mode control
Example 4.6
Figures 4.23 through 4.27
Example 4.6
Figures 4.28 and 4.29
Single-phase diode-bridge rectifier
Example 5.2
Figures 5.13 and 5.14
N/A
Three-phase diode-bridge rectifier
Example 5.3
Figures 5.18 and 5.19
N/A
Control of Power-Factor-Correction circuit
Figures 6.8
and
6.9
N/A
Flyback converter – CCM without snubber
Example 8.2
Figures 8.4 and 8.5
Example 8.2
Figures 8.6 and 8.7
Flyback converter – CCM with snubber
Example 8.5
Figures 8.11 and 8.12
Example 8.5
Figure 8.13
Flyback converter – DCM without snubber
Example 8.6
Figure 8.14
Example 8.6
Figures 8.15
Forward converter
Example 8.8
Figures 8.20 and 8.21
Example 8.8
Figures 8.22 and 8.23
PWM Full-Bridge converter
Example 8.10
Figures 8.31 and 8.32
Example 8.10
Figures 8.33 and 8.34
Single-phase Inverter
Example 12.5
Figures 12.21 and 12.22
Example 12.5
Figures 12.23 and 12.24
Three-phase Inverter – Sine PWM
Example 12.7
Figures 12.29 and 12.30
Example 12.7
Figures 12.31 and 12.32
Three-phase Inverter – SVPWM
Example 12.9
Figures 12.38 and 12.39
Example 12.9
Figures 12.40 and 12.41
PREFACE
Role of Power Electronics in Providing Sustainable Electric Energy
As discussed in the introductory chapter of this textbook, power electronics is an enabling technology for powering information technology and making factory automation feasible. In addition, power electronics has a crucial role to play in providing sustainable electric energy. Most scientists now believe that carbon-based fuels for energy production contribute to climate change, which is a serious threat facing human civilization. In the United States, the Department of Energy reports that approximately 40% of all the energy consumed is first converted into electricity. Potentially, use of electric and plug-in hybrid cars, high-speed rails, and so on, may increase this to even 60%. Therefore, it is essential that we generate electricity from renewable sources such as wind and solar, which at present represent only slightly over 4%, build the next-generation smarter and robust grid to utilize renewable resources often in remote locations, and use electricity in more energy-efficient ways. Undoubtedly, using electricity efficiently and generating it from renewable sources are the twin pillars of sustainability, and as described in this textbook, power electronic systems are a key to them both!
This textbook focuses on power electronic systems as one of the topics in an integrated electric energy systems curriculum consisting of power electronics, power systems, and electric machines and drives. This textbook follows a top-down systems-level approach to power electronics to highlight interrelationships between these subfields within this curriculum, and is intended to cover both the fundamentals and practical design in a single-semester course.
This textbook follows a building-block approach to power electronics that allows an in-depth discussion of several important topics that are left out in a conventional course, for example, designing feedback control, power-factor-correction circuits, soft-switching, and space-vector PWM, which is a PWM technique, far superior to sine-PWM, to name a few. Topics in this book are carefully sequenced to maintain continuity and student interest throughout the course.
In a fast-paced course with proper student background, this book can be covered from front-to-back in one semester. However, the material is arranged in such a way that an instructor, to accommodate the students’ background, can either omit an entire topic or cover it quickly to provide just an overview using the accompanying slides, without interrupting the flow.
ACKNOWLEDGMENT
The authors are greatly indebted to two grants to the University of Minnesota from the Office of Naval Research (ONR): N00014-15-1-2391 “Web-Enabled, Instructor-Taught Online Courses,” and N00014-19-1-2018 “Developing WBG-Based, Extremely Low-Cost Laboratories for Power Electronics, Motor Drives, and Power System Protection and Relays for National Dissemination.” These grants allowed the development of the Workbench simulation platform, which is available free-of-cost for educational purposes. These grants also allowed the development of a low-cost hardware laboratory, available from Sciamble (https://sciamble.com) - a University of Minnesota startup.
The authors would like to sincerely thank Dr. Madhukar Rao Airineni and Dr. Saurabh Tewari for their assistance in developing the LTspice example files and reviewing the material.
ABOUT THE COMPANION WEBSITE
This book is accompanied by companion website:
www.wiley.com/go/mohan/powerelectronics2e
This website includes
Solution
Slides
Simulation
CUSP website is a link to another site
Lab manual is a link to another site
1 POWER ELECTRONICS: AN ENABLING TECHNOLOGY
Power electronic systems are essential for energy sustainability, which can be defined as meeting our present needs without compromising the ability of future generations to meet their needs. Using renewable energy for generating electricity and increasing the efficiency of transmitting and consuming it are the twin pillars of sustainability. Some of the applications of power electronics in doing so are as mentioned below:
Harnessing renewable energy such as wind energy and solar energy using photovoltaics .
Storage of electricity in batteries and flywheels to offset the variability in the electricity generated by renewables.
Increasing the efficiency of transmitting electricity.
Increasing efficiency in consuming the electricity in motor-driven systems and lighting, for example.
This introductory chapter highlights all the points mentioned above, which are discussed in further detail in the context of describing the fundamentals of power electronics in the subsequent chapters.
1.1 INTRODUCTION TO POWER ELECTRONICS
Power electronics is an enabling technology, providing the needed interface between an electrical source and an electrical load, as depicted in Figure 1.1 [1]. The electrical source and the electrical load can, and often do, differ in frequency, voltage amplitudes, and the number of phases. The power electronics interface facilitates the transfer of power from the source to the load by converting voltages and currents from one form to another, in which it is possible for the source and load to reverse roles. The controller shown in Figure 1.1 allows management of the power transfer process in which the conversion of voltages and currents should be achieved with as high energy efficiency and high power density as possible. Adjustable-speed electric drives, for example in wind turbines, represent an important application of power electronics.
FIGURE 1.1 Power electronics interface between the source and load.
1.2 APPLICATIONS AND THE ROLE OF POWER ELECTRONICS
Power electronics and drives encompass a wide array of applications. A few important applications and their role are described below.
1.2.1 Powering the Information Technology
Most of the consumer electronics equipment such as personal computers (PCs) and entertainment systems supplied from the utility need very low DC voltages internally. They, therefore, require power electronics in the form of switch-mode DC power supplies for converting the input line voltage into a regulated low DC voltage, as shown in Figure 1.2a. Figure 1.2b shows the distributed architecture typically used in computers in which the incoming AC voltage from the utility is converted into DC voltage, for example, at 24 V. This semi-regulated voltage is distributed within the computer where onboard power supplies in logic-level printed circuit boards convert this 24 V DC input voltage to a lower voltage, for example, 5 V DC, which is very tightly regulated. Very large-scale integration and higher logic circuitry speed require operating voltages much lower than 5 V; hence 3.3 V, 1 V, and eventually, 0.5 V levels would be needed.
FIGURE 1.2 Regulated low-voltage DC power supplies.
Many devices such as cell phones operate from low battery voltages with one or two battery cells as inputs. However, the electronic circuitry within them requires higher voltages, thus necessitating a circuit to boost input DC to a higher DC voltage as shown in the block diagram of Figure 1.3.
FIGURE 1.3 Boost DC-DC converter needed in cell-operated equipment.
1.2.2 Robotics and Flexible Production
Robotics and flexible production are now essential to industrial competitiveness in a global economy. These applications require adjustable-speed drives for precise speed and position control. Figure 1.4 shows the block diagram of adjustable-speed drives in which the AC input from a 1-phase or a 3-phase utility source is at the line frequency of 50 or 60 Hz . The role of the power electronics interface, as a power-processing unit, is to provide the required voltage to the motor. In the case of a DC motor, DC voltage is supplied with an adjustable magnitude that controls the motor speed. In the case of an AC motor, the power electronics interface provides sinusoidal AC voltages with adjustable amplitude and frequency to control the motor speed. In certain cases, the power electronics interface may be required to allow bidirectional power flow through it, between the utility and the motor load.
FIGURE 1.4 Block diagram of adjustable-speed drives.
Induction heating and electric welding, shown in Figures 1.5 and 1.6, respectively, by their block diagrams, are other important industrial applications of power electronics for flexible production.
FIGURE 1.5 Power electronics interface required for induction heating.
FIGURE 1.6 Power electronics interface required for electric welding.
1.3 ENERGY AND THE ENVIRONMENT: ROLE OF POWER ELECTRONICS IN PROVIDING SUSTAINABLE ELECTRIC ENERGY
As mentioned in the preface of this textbook, power electronics is an enabling technology in providing sustainable electric energy. Most scientists now believe that carbon-based fuels for energy production contribute to climate change, which is threatening human civilization. In the United States, the Department of Energy reports that approximately 40% of all the energy consumed is first converted into electricity. Potentially, the use of electric and plug-in hybrid cars, high-speed rails, and so on, may increase this to even 60%. Therefore, it is essential that we generate electricity from renewable sources such as wind and solar, which, at present, represent only slightly over 4%, build the next-generation smarter grid to utilize renewable resources often in remote locations, and use electricity in more energy-efficient ways. Undoubtedly, using electricity efficiently and generating it from renewable sources are the twin pillars of sustainability, and power electronic systems discussed in this textbook are a key to them both!
1.3.1 Energy Conservation
It’s an old adage: a penny saved is a penny earned. Not only does energy conservation lead to financial savings, but it also helps the environment. The pie chart in Figure 1.7 shows the percentages of electricity usage in the United States for various applications. The potential for energy conservation in these applications are discussed below.
FIGURE 1.7 Percentage use of electricity in various sectors in the US.
1.3.1.1 Electric-Motor Driven Systems
Figure 1.7 shows that electric motors, including their applications in heating, ventilating, and air conditioning (HVAC), are responsible for consuming one-half to two-thirds of all the electricity generated. Traditionally, motor-driven systems run at a nearly constant speed, and their output, for example, the flow rate in a pump, is controlled by wasting a portion of the input energy across a throttling valve. This waste is eliminated by an adjustable-speed electric drive, as shown in Figure 1.8, by efficiently controlling the motor speed, hence the pump speed, by means of power electronics [2].
FIGURE 1.8 Role of adjustable-speed drives in pump-driven systems.
One out of three new homes in the United States now uses an electric heat pump, in which an adjustable-speed drive can reduce energy consumption by as much as 30% [3] by eliminating on-off cycling of the compressor and running the heat pump at a speed that matches the thermal load of the building. The same is true for air conditioners.
A Department of Energy report [4] estimates that operating all these motor-driven systems more efficiently in the United States could annually save electricity equivalent to the annual electricity usage by the entire state of New York!
1.3.1.2 Lighting Using LEDs
As shown in the pie chart in Figure 1.7, approximately one-fifth of the electricity produced is used for lighting. LEDs (light-emitting diodes) can improve this efficiency by more than a factor of six. They offer a longer lifetime and have become equally affordable as incandescent lamps. They require a power-electronic interface, as shown in Figure 1.9, to convert the line-frequency to supply DC current to the LEDs.
FIGURE 1.9 Power electronics interface required for LED.
1.3.1.3 Transportation
Electric drives offer huge potential for energy conservation in transportation. While efforts to introduce commercially viable electric vehicles (EVs) continue with progress in battery [5] and fuel cell technologies [6] being reported, hybrid electric vehicles (HEVs) are sure to make a huge impact [7]. According to the US Environmental Protection Agency, the estimated gas mileage of the hybrid-electrical vehicle shown in Figure 1.10 in combined city and highway driving is 48 miles per gallon [8]. This is in comparison to the gas mileage of 22.1 miles per gallon for an average passenger car in the United States [9]. Since automobiles are estimated to account for about 20% of the emission of all CO2 [10], which is a greenhouse gas, doubling the gas mileage of automobiles would have an enormous positive impact.
FIGURE 1.10 Hybrid electric vehicles with much higher gas mileage.
Conventional automobiles need power electronics for various applications [11]. EVs and HEVs, of course, need power electronics in the form of adjustable-speed electric drives. Add to automobiles other transportation systems, such as light rail, fly-by-wire planes, all-electric ships, and drive-by-wire automobiles, and the conclusion is clear: transportation represents a major application area of power electronics.
1.3.2 Renewable Energy
Clean and renewable energy can be derived from the sun and the wind. In photovoltaic systems, solar cells produce DC, with an I-V characteristic shown in Figure 1.11a that requires a power electronics interface to transfer power to the utility system, as shown in Figure 1.11b.
FIGURE 1.11 Photovoltaic systems.
Wind is the fastest-growing energy resource with enormous potential [12]. Figure 1.12 shows the need for power electronics in wind-electric systems to interface variable-frequency AC to the line-frequency AC voltages of the utility grid.
FIGURE 1.12 Wind-electric systems.
1.3.3 Utility Applications of Power Electronics
Applications of power electronics and electric drives in power systems are growing rapidly. In distributed generation, power electronics is needed to interface nonconventional energy sources such as wind, photovoltaic, and fuel cells to the utility grid. The use of power electronics allows control over the flow of power on transmission lines, an attribute that is especially significant in a deregulated utility environment. Also, the security and the efficiency aspects of power systems operation necessitate increased use of power electronics in utility applications.
Uninterruptible power supplies (UPS) are used for critical loads that must not be interrupted during power outages. The power electronics interface for UPS, shown in Figure 1.13, has line-frequency voltages at both ends, although the number of phases may be different, and a means for energy storage is usually provided by batteries, which supply power to the load during the utility outage.
FIGURE 1.13 Uninterruptible power supply (UPS) system.
1.3.4 Strategic Space and Defense Applications
Power electronics is essential for space exploration and for interplanetary travel. Defense has always been an important application, but it has become critical in the post-September 11th world. Power electronics will play a huge role in tanks, ships, and planes in which replacement of hydraulic drives by electric drives can offer significant cost, weight, and reliability advantages.
1.4 NEED FOR HIGH EFFICIENCY AND HIGH POWER DENSITY
Power electronic systems must be energy-efficient and reliable, have a high power density, thus reducing their size and weight, and be low cost to make the overall system economically feasible. High energy efficiency is important for several reasons: it lowers operating costs by avoiding the cost of wasted energy, contributes less to global warming, and reduces the need for cooling (by heat sinks, discussed later in this book), therefore increasing power density.
We can easily show the relationship in a power electronic system between the energy efficiency, η, and the power density. The energy efficiency of a system in Figure 1.14a is defined in Equation 1.1 in terms of the output power Po and the power loss Ploss within the system as:
FIGURE 1.14 Power output capability as a function of efficiency
Equation 1.1 can be rewritten for the output power in terms of the efficiency and the power loss as:
Using Equation 1.2, the output power rating is plotted in Figure 1.14b, as a function of efficiency, for two values of Ploss.
In power electronics equipment, the cooling system is designed to transfer dissipated power, as heat, without allowing the internal temperatures to exceed certain limits. Therefore, for an equipment package designed to handle certain power loss dissipation, the plots in Figure 1.14b based on Equation 1.2 show that increasing the conversion efficiency from 84% to 94%, for example, increases the power output capability, same as the power rating, of that equipment by a factor of three. This could mean an increase in the power density, which is the power rating divided by the volume of the package, by approximately the same factor. This is further illustrated by Example 1.1 on the following page.
Example 1.1
A power electronics package is designed to handle 200 W of power dissipation. Compare the two values of the output power capability if the conversion efficiency is increased from 89% to 94%.
Solution In this example, . Using Equation 1.2, at , , and at , .
This example shows the importance of high energy conversion efficiency, where the power output capability and the power density (in watts per unit volume) of this package are nearly doubled by increasing the efficiency from 89% to 94%.
1.5 STRUCTURE OF POWER ELECTRONICS INTERFACE
By reviewing the role of power electronics in various applications discussed earlier, we can summarize that a power electronics interface is needed to efficiently control the transfer of power between DC-DC, DC-AC, and AC-AC systems. In general, the power is supplied by the utility, and hence, as depicted by the block diagram of Figure 1.15, the line-frequency AC is at one end. At the other end, one of the following is synthesized: adjustable magnitude DC, sinusoidal AC of adjustable frequency and amplitude, or high-frequency AC as in induction heating or systems using high-frequency transformers as an intermediate stage. Applications that do not require utility interconnection can be considered as the subset of the block diagram shown in Figure 1.15.
FIGURE 1.15 Block diagram of power electronic interface.
1.5.1 Voltage-Link Structure
To provide the needed functionality to the interface in Figure 1.15, the transistors and diodes, which can block voltage only of one polarity, have led to a commonly used voltage-link-structure, shown in Figure 1.16.
FIGURE 1.16 Voltage-link structure of power electronics interface.
This structure consists of two separate converters, one on the utility side and the other on the load side. The DC ports of these two converters are connected to each other with a parallel capacitor forming a DC-link, across which the voltage polarity does not reverse, thus allowing unipolar voltage-blocking transistors to be used within these converters.
In the structure of Figure 1.16, the capacitor in parallel with the two converters forms a DC voltage-link. Hence, it is called a voltage-link (or a voltage-source) structure. This structure is used in a very large power range, from a few tens of watts to several megawatts, even extending to hundreds of megawatts in utility applications. Therefore, we will mainly focus on this voltage-link structure in this book.
1.5.2 Current-Link Structure
At extremely high power levels, usually in utility-related applications, which we will discuss in the last two chapters in this book, it may be advantageous to use a current-link (also called current-source) structure, where, as shown in Figure 1.17, an inductor in series between the two converters acts as a current-link. These converters generally consist of thyristors, and the current in them, as discussed in Chapter 14, is “commutated” from one AC phase to another by means of the AC line voltages.
FIGURE 1.17 Current-link structure of power electronics interface.
1.5.3 Matrix Converters (Direct-Link Structure) [13]
Lately, in certain applications, a matrix converter structure, as shown in Figure 1.18 is being reevaluated, where theoretically, there is no energy storage element between the input and the output sides. Therefore, we can consider it to be a direct-link structure where input ports are connected to output ports by switches that can carry currents in both directions when on and block voltages of either polarity when off. A detailed discussion of matrix converters and their controls can be found in [13].
FIGURE 1.18 Matrix converter structure of power electronics interface. [13] / U.S department of energy / public domain.
1.6 VOLTAGE-LINK-STRUCTURE
In the voltage-link structure shown in Figure 1.16 and repeated in Figure 1.19, the role of the utility-side converter is to convert line-frequency utility voltages to an unregulated DC voltage. This can be done by a diode-rectifier circuit such as that discussed in basic electronics courses and also discussed in Chapter 5 of this textbook. However, the power quality concerns often lead to a different structure, discussed in Chapter 6. At present, we will focus our attention on the load-side converter in the voltage-link structure, where a DC voltage is applied as the input on one end, as shown in Figure 1.19.
FIGURE 1.19 Load-side converter in a voltage-source structure.
Applications dictate the functionality needed of the load-side converter. Based on the desired output of the converter, we can group these functionalities as follows:
Group 1
Adjustable DC or a low-frequency sinusoidal AC output in
– DC and AC motor drives
– uninterruptible power supplies
– regulated DC power supplies without electrical isolation
– utility-related applications
Group 2
High-frequency AC in
– systems using high-frequency transformers as an intermediate stage
– induction heating
– regulated DC power supplies where the DC output voltage needs to be electrically isolated from the input, and the load-side converter internally produces high-frequency AC, which is passed through a high-frequency transformer and then rectified into DC.
We will discuss converters used in applications belonging to both groups. However, we will begin with converters for group-1 applications where the load-side voltages are DC or low-frequency AC.
1.6.1 Switch-Mode Conversion: Switching Power-Pole as the Building Block
Achieving high energy efficiency for applications belonging to either group mentioned above requires switch-mode conversion, where in contrast to linear power electronics, transistors (and diodes) are operated as switches, either on or off.
This switch-mode conversion can be explained by its basic building block, a switching power-pole A, as shown in Figure 1.20a. It effectively consists of a bi-positional switch, which forms a two-port: (1) a voltage-port across a capacitor with a voltage Vin that cannot change instantaneously, and (2) a current-port due to the series inductor through which the current cannot change instantaneously. For now, we will assume the switch is ideal with two positions: up or down, dictated by a switching signal qA, which takes on two values: 1 and 0, respectively. The practical aspects of implementing this bi-positional switch are what we will consider in the next chapter.
FIGURE 1.20 Switching power-pole as the building block in converters.
The bi-positional switch “chops” the input DC voltage Vin into a train of high-frequency voltage pulses, shown by vA waveform in Figure 1.20b, by switching up or down at a high repetition rate, called the switching frequency fs. Controlling the pulse width within a switching cycle allows control over the switching-cycle-averaged value of the pulsed output, and this pulse-width modulation forms the basis of synthesizing adjustable DC and low-frequency sinusoidal AC outputs, as described in the next section. High-frequency pulses are clearly needed in applications such as compact fluorescent lamps and induction heating and internally in DC power supplies where electrical isolation is achieved by means of a high-frequency transformer. A switch-mode converter consists of one or more such switching power-poles.
1.6.2 Pulse-Width Modulation (PWM) of the Switching Power-Pole (Constant fs)
For the applications in group 1, the objective of the switching power-pole redrawn in Figure 1.21a is to synthesize the output voltage such that its switching-cycle average is of the desired value: DC or AC that varies sinusoidally at a low frequency, compared to fs. Switching at a constant switching frequency fs produces a train of voltage pulses in Figure 1.21b that repeat with a constant switching time period Ts, equal to 1/fs.
FIGURE 1.21 PWM of the switching power-pole.
Within each switching cycle with the time period Ts (= 1/fs) in Figure 1.21b, the switching-cycle-averaged value of the waveform is controlled by the pulse width Tup (during which the switch is in the up position and vA equals Vin), as a ratio of Ts:
where , which is the average of the qA waveform as shown in Figure 1.21b, is defined as the duty ratio of the switching power pole A, and the switching-cycle-averaged voltage is indicated by a “–” on top (the overbar symbol). The switching-cycle-averaged voltage and the switch duty ratio are expressed by lowercase letters since they may vary as functions of time. The control over the switching-cycle-averaged value of the output voltage is achieved by adjusting or modulating the pulse width, which later on will be referred to as pulse-width-modulation (PWM). This switching power-pole and the control of its output by PWM set the stage for switch-mode conversion with high energy efficiency.
We should note that and dA in the above discussion are discrete quantities, and their values, calculated over a k-th switching cycle, for example, can be expressed as and dA,k. However, in practical applications, the pulse-width Tup changes very slowly over many switching cycles, and hence we can consider them analog quantities as ðtÞ and dAðtÞ that are continuous functions of time. For simplicity, we may not show their time dependence explicitly.
1.6.3 Switching Power-Pole in a Buck DC-DC Converter: An Example
As an example, we will consider the switching power-pole in a buck converter to step down the input DC voltage Vin, as shown in Figure 1.22a, where a capacitor is placed in parallel with the load to form a low-pass L-C filter with the inductor, to provide a smooth voltage to the load.
FIGURE 1.22
