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Digital Control in Power Electronics.pdf

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    Contents
    1. Introduction: Digital ControlApplication to Power ElectronicCircuits
    1.1 MODERN POWER ELECTRONICS
    2. The Test Case: a Single-PhaseVoltage Source Inverter
    2.1.4 Dead-Times
    2.2.3 Single Update and Double UpdatePWMMode
    3. Digital Current Mode Control
    3.1 REQUIREMENTS OF THE DIGITAL CONTROLLER
    3.1.1 Signal Conditioning and Sampling
    3.1.2 Synchronization Between Sampling and PWM
    3.1.3 Quantization Noise and Arithmetic Noise
    3.2 BASIC DIGITAL CURRENT CONTROL IMPLEMENTATIONS
    3.2.1 The Proportional Integral Controller:Overview
    3.2.2 Simplified Dynamic Model of Delays
    3.2.3 The Proportional Integral Controller: Discretization Strategies
    3.2.4 Effects of the Computation Delay
    3.2.5 Derivation of a Discrete Time Domain Converter Dynamic Model
    3.2.6 Minimization of the Computation Delay
    3.2.7 The Predictive Controller
    3.2.7.1 Derivation of the Predictive Controller
    3.2.7.2 Robustness of the Predictive Controller
    3.2.7.3 Effects of Converter Dead-Times
    3.2.7.4 Comparison with PI Controller
    4. Extension to Three-Phase Inverters
    5. External Control Loops
    5.1 MODELING THE INTERNAL CURRENT LOOP
    5.2 DESIGN OF VOLTAGE CONTROLLERS
    5.2.1 Possible Strategies: Large andNarrow Bandwidth Controllers
    5.3 LARGE BANDWIDTH CONTROLLERS
    5.3.1 PI Controller
    5.3.2 The Predictive Controller
    5.3.2.1 The Multiloop Implementation
    5.3.2.2 The Multivariable Implementation
    5.4 NARROW BANDWIDTH CONTROLLERS
    5.4.1 The Repetitive-Based Voltage Controller
    5.4.2 The DFT Filter Based Voltage Controller
    5.5 OTHER APPLICATIONS OF THE CURRENT CONTROLLED VSI
    6. Conclusions
    P1: IML/FFX Morgan-FM P2: IML/FFX QC: IML/FFX T1: IML MOBK037-Buso.cls October 20, 2006 15:44 Digital Control in Power Electronics i
    Copyright © 2006 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Digital Control in Power Electronics Simone Buso and Paolo Mattavelli www.morganclaypool.com ISBN-10: 1598291122 ISBN-13: 9781598291124 paperback paperback ISBN-10: 1598291130 ISBN-13: 9781598291131 ebook ebook DOI10.2200/S00047ED1V01Y200609PEL002 A lecture in the Morgan & Claypool Synthesis Series LECTURES ON POWER ELECTRONICS #2 Lecture #2 Series Editor: Jerry Hudgins, University of Nebraska-Lincoln Series ISSN: 1930-9525 Series ISSN: 1930-9533 print electronic First Edition 10 9 8 7 6 5 4 3 2 1 Printed in the United States of America
    P1: IML/FFX Morgan-FM P2: IML/FFX QC: IML/FFX T1: IML MOBK037-Buso.cls October 20, 2006 15:44 Digital Control in Power Electronics Simone Buso Department of Information Engineering University of Padova, Italy Paolo Mattavelli Department of Electrical, Mechanical and Management Engineering University of Udine, Italy LECTURES ON POWER ELECTRONICS #2 M&C Morgan & Claypool Publishers iii
    P1: IML/FFX Morgan-FM P2: IML/FFX QC: IML/FFX T1: IML MOBK037-Buso.cls October 20, 2006 15:44 iv ABSTRACT This book presents the reader, whether an electrical engineering student in power electronics or a design engineer, some typical power converter control problems and their basic digital solutions, based on the most widespread digital control techniques. The presentation is focused on different applications of the same power converter topology, the half-bridge voltage source inverter, considered both in its single- and three-phase implementation. This is chosen as the case study because, besides being simple and well known, it allows the discussion of a significant spectrum of the more frequently encountered digital control applications in power electronics, from digital pulse width modulation (DPWM) and space vector modulation (SVM), to inverter output current and voltage control. The book aims to serve two purposes: to give a basic, introductory knowledge of the digital control techniques applied to power converters, and to raise the interest for discrete time control theory, stimulating new developments in its application to switching power converters. KEYWORDS Digital control in power electronics, Discrete time control theory, Half-bridge voltage source converters, Power converters, Power electronics
    P1: IML/FFX Morgan-FM P2: IML/FFX QC: IML/FFX T1: IML MOBK037-Buso.cls October 20, 2006 15:44 v Contents 1. 2. Introduction: Digital Control Application to Power Electronic Circuits . . . . . . . . . . . . 1.1 Modern Power Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Why Digital Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Trends and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 What is in this Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Test Case: a Single-Phase Voltage Source Inverter. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Voltage Source Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Fundamental Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Required Additional Electronics: Driving and Sensing . . . . . . . . . . . . . . . . . 2.1.3 Principle of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Dead-Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Low-Level Control of the Voltage Source Inverter: PWM Modulation . . . . . . . . . 2.2.1 Analog PWM: the Naturally Sampled Implementation . . . . . . . . . . . . . . . . 2.2.2 Digital PWM: the Uniformly Sampled Implementation . . . . . . . . . . . . . . . 2.2.3 Single Update and Double Update PWM Mode . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Minimization of Modulator Delay: a Motivation for Multisampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Analog Control Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Linear Current Control: PI Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Nonlinear Current Control: Hysteresis Control . . . . . . . . . . . . . . . . . . . . . . . 3. Digital Current Mode Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Requirements of the Digital Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Signal Conditioning and Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Synchronization Between Sampling and PWM . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Quantization Noise and Arithmetic Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Basic Digital Current Control Implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The Proportional Integral Controller: Overview. . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Simplified Dynamic Model of Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 The Proportional Integral Controller: Discretization Strategies . . . . . . . . . 3.2.4 Effects of the Computation Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
    P1: IML/FFX Morgan-FM P2: IML/FFX QC: IML/FFX T1: IML MOBK037-Buso.cls October 20, 2006 15:44 vi CONTENTS 3.2.5 Derivation of a Discrete Time Domain Converter Dynamic Model . . . . . 3.2.6 Minimization of the Computation Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.7 The Predictive Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extension to Three-Phase Inverters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The αβ Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Space Vector Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 4.2.1 Space Vector Modulation Based Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 The Rotating Reference Frame Current Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Park’s Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Design of a Rotating Reference Frame PI Current Controller . . . . . . . . . . 4.3.3 A Different Implementation of the Rotating Reference Frame PI Current Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 External Control Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Modeling the Internal Current Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Design of Voltage Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Possible Strategies: Large and Narrow Bandwidth Controllers . . . . . . . . . . 5.3 Large Bandwidth Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 PI Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 The Predictive Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Narrow Bandwidth Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 The Repetitive-Based Voltage Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 The DFT Filter Based Voltage Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Other Applications of the Current Controlled VSI. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 The Controlled Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 The Active Power Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 5. 6. 7.
    P1: IML/FFX MOBK037-01 P2: IML/FFX MOBK037-Buso.cls QC: IML/FFX T1: IML October 20, 2006 15:36 1 C H A P T E R 1 Introduction: Digital Control Application to Power Electronic Circuits Power electronics and discrete time system theory have been closely related to each other from the very beginning. This statement may seem surprising at first, but, if one thinks of switch mode power supplies as variable structure periodic systems, whose state is determined by logic signals, the connection becomes immediately clearer. A proof of this may also be found in the first, fundamental technical papers dealing with the analysis and modeling of pulse width modulated power supplies or peak current mode controlled dc–dc converters: they often provide a mathematical representation of both the switching converters and the related control circuits, resembling or identical to that of sampled data dynamic systems. This fundamental contiguousness of the two apparently far areas of engineering is probably the strongest, more basic motivation for the considerable amount of research that, over the years, has been dedicated to the application of digital control to power electronic circuits. From the original, basic idea of implementing current or voltage controllers for switching converters using digital signal processors or microcontrollers, which represents the foundation of all current industrial applications, the research focus has moved to more sophisticated approaches, where the design of custom integrated digital controllers is no longer presented like an academic curiosity, but is rather perceived like a sound, viable solution for the next generation of high- performance power supplies. If we consider the acceleration in the scientific production related to these topics in the more recent years, we can easily anticipate, for a not too far ahead future, the creation of energy processing circuits, where power devices and control logic can be built on the same semiconductor die. From this standpoint, the distance we see today between the tools and the design methodology of power electronics engineers and those of analog and/or digital integrated circuit designers can be expected to significantly reduce in the next few years.
    P1: IML/FFX MOBK037-01 P2: IML/FFX MOBK037-Buso.cls QC: IML/FFX T1: IML October 20, 2006 15:36 2 DIGITAL CONTROL IN POWER ELECTRONICS We have to admit that, in this complex scenario, the purpose of this book is very sim- ple. We just would like to introduce the reader to basic control problems in power electronic circuits and to illustrate the more classical, widely applied digital solutions to those problems. We hope this will serve two purposes: first, to give a basic, introductory knowledge of the digital control techniques applied to power converters, and second, to raise the interest for dis- crete time control theory, hopefully stimulating new developments in its application to power converters. MODERN POWER ELECTRONICS 1.1 Classical power electronics may be considered, under several points of view, a mature discipline. The technology and engineering of discrete component based switch mode power supplies are nowadays fully developed industry application areas, where one does not expect to see any outstanding innovation, at least in the near future. Symmetrically, at the present time, the research fields concerning power converter topologies and the related conventional, analog control strategies seem to have been thoroughly explored. On the other hand, we can identify some very promising research fields where the future of power electronics is likely to be found. For example, a considerable opportunity for innovation can be expected in the field of large bandgap semiconductor devices, in particular if we consider the semiconductor technologies based on silicon carbide, SiC, gallium arsenide, GaAs, and gallium nitride, GaN. These could, in the near future, prove to be practically usable not only for ultra-high-frequency amplification of radio signals, but also for power conversion, opening the door to high-frequency (multi-MHz) and/or high-temperature power converter circuits and, consequently, to a very significant leap in the achievable power densities. The rush for higher and higher power densities motivates research also in other directions. Among these, we would like to mention three that, in our vision, are going to play a very significant role. The first is the integration in a single device of magnetic and capacitive passive components, which may allow the implementation of minimum volume, quasi monolithic, converters. The second is related to the analysis and mitigation of electromagnetic interference (EMI), which is likely to become fundamental for the design of compact, high frequency, converters, where critical autosusceptibility problems can be expected. The third one is the development of technologies and design tools allowing the integration of control circuits and power devices on the same semiconductor chip, according to the so-called smart power concept. These research areas represent good examples of what, in our vision, can be considered modern power electronics. From this standpoint, the application of digital control techniques to switch mode power supplies can play a very significant role. Indeed, the integration of complex control func- tions, such as those that are likely to be required by the next generation power supplies,
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