Instantaneous Power Theory and Applications to Power Conditioning - Hirofumi Akagi - ebook

Instantaneous Power Theory and Applications to Power Conditioning ebook

Hirofumi Akagi

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This book covers instantaneous power theory as well as the importance of design of shunt, series, and combined shunt-series power active filters and hybrid passive-active power filters * Illustrates pioneering applications of the p-q theory to power conditioning, which highlights distinct differences from conventional theories * Explores p-q-r theory to give a new method of analyzing the different powers in a three-phase circuit * Provides exercises at the end of many chapters that are unique to the second edition

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IEEE Press445 Hoes LanePiscataway, NJ 08854

IEEE Press Editorial BoardTariq Samad, Editor in Chief

 

Giancarlo Fortino

Xiaoou Li

Ray Perez

Dmitry Goldgof

Andreas Molisch

Linda Shafer

Don Heirman

Saeid Nahavandi

Mohammad Shahidehpour

Ekram Hossain

Jeffrey Nanzer

Zidong Wang

SECOND EDITION

INSTANTANEOUS POWER THEORY AND APPLICATIONS TO POWER CONDITIONING

HIROFUMI AKAGI

Professor of Electrical EngineeringTIT—Tokyo Institute of Technology, Japan

EDSON HIROKAZU WATANABE

Professor of Electrical EngineeringUFRJ—Federal University of Rio de Janeiro, Brazil

MAUR:CIO AREDES

Associate Professor of Electrical EngineeringUFRJ—Federal University of Rio de Janeiro, Brazil

Copyright © 2017 by The Institute of Electrical and Electronics Engineers, Inc.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reservedPublished simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data is available.

ISBN: 978-1-118-36210-5

This book is dedicated

to all the scientists and engineers who have participated in the development of Instantaneous Power Theory and Applications to Power Conditioning,

and

to our families Nobuko, Chieko, and Yukiko, Yukiko, Edson Hiroshi, and Beatriz Yumi, Marília, Mariah, and Maynara.

CONTENTS

Preface

Chapter 1:

INTRODUCTION

1.1 Concepts and Evolution of Electric Power Theory

1.2 Applications of the

p-q

theory to Power Electronics Equipment

1.3 Harmonic Voltages in Power Systems

1.4 Identified and Unidentified Harmonic-Producing Loads

1.5 Harmonic Current and Voltage Sources

1.6 Basic Principles of Harmonic Compensation

1.7 Basic Principle of Power Flow Control

References

Chapter 2:

ELECTRIC POWER DEFINITIONS: BACKGROUND

2.1 Power Definitions Under Sinusoidal Conditions

2.2 Voltage and Current Phasors and Complex Impedance

2.3 Complex Power and Power Factor

2.4 Concepts of Power Under Nonsinusoidal Conditions: Conventional Approaches

2.5 Electric Power in Three-Phase Systems

2.6 Summary

2.7 Exercises

References

Chapter 3:

THE INSTANTANEOUS POWER THEORY

3.1 Basis of the

p-q

Theory

3.2 The

p-q

Theory in Three-Phase, Three-Wire Systems

3.3 The

p-q

Theory in Three-Phase, Four-Wire Systems

3.4 Instantaneous

abc

Theory

3.5 Comparisons Between The

p-q

Theory and The

abc

Theory

3.6 The

p-q-r

Theory

3.7 Summary

3.8 Exercises

References

Notes

Chapter 4:

SHUNT ACTIVE FILTERS

4.1 General Description of Shunt Active Filters

4.2 Three-Phase, Three-Wire Shunt Active Filters

4.3 Three-Phase, Four-Wire Shunt Active Filters

4.4 Compensation Methods Based on the

p-q-r

Theory

4.5 Comparisons Between Control Methods Based on the

p-q

Theory and The

p-q-r

Theory

4.6 Shunt Selective Harmonic Compensation

4.7 Summary

4.8 Exercises

References

Chapter 5:

HYBRID AND SERIES ACTIVE FILTERS

5.1 Basic Series Active Filter

5.2 Combined Series Active Filter and Shunt Passive Filter

5.3 Series Active Filter Integrated with a Double-Series Diode Rectifier

5.4 Comparisons Between Hybrid and Pure Active Filters

5.5 Hybrid Active Filters for Medium-Voltage Motor Drives

5.6 Summary

5.7 Exercises

References

Notes

Chapter 6:

COMBINED SERIES AND SHUNT POWER CONDITIONERS

6.1 The Unified Power Flow Controller

6.2 The Unified Power Quality Conditioner

6.3 The Universal Active Power Line Conditioner

6.4 Combined Shunt-Series Filters for AC and DC Sides of Three-Phase Rectifiers

6.5 Summary

6.6. Exercises

References

Index

IEEE Press Series on Power Engineering

EULA

List of Tables

Chapter 1

Table 1.1

Table 1.2

Table 1.3

Table 1.4

Chapter 4

Table 4.1

Table 4.2

Table 4.3

Table 4.4

Table 4.5

Table 4.6

Table 4.7

Table 4.8

Table 4.9

Table 4.10

Chapter 5

Table 5.1

Table 5.2

Table 5.3

Table 5.4

Table 5.5

Table 5.6

Table 5.7

Table 5.8

Table 5.9

Table 5.10

Table 5.11

Table 5.12

Table 5.13

Chapter 6

Table 6.1

Table 6.2

Table 6.3

Table 6.4

Table 6.5

Table 6.6

Table 6.7

Table 6.8

Guide

Cover

Table of Contents

Preface

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Preface

THE CONCEPT OF “instantaneous active and reactive power” was first presented in 1982 in Japan. Since then, many scientists and engineers have made significant contributions to its modifications in three-phase, four-wire circuits, its expansions to more than three-phase circuits, and its applications to power electronics equipment. However, neither a monograph nor book on this subject has been available in the market until 2007. Filling this gap was the main motivation for writing this book. The instantaneous power theory, or simply “the p-q theory,” makes clear the physical meaning of what the instantaneous active and reactive power is in a three-phase circuit. Moreover, it provides a clear insight into how energy flows from a source to a load, or circulates between phases, in a three-phase circuit. At the beginning of writing this book, we decided to try to present the basic concepts of the theory as didactically as possible. For this second edition, we added some exercises at the end of some chapters.

Hence, the book was structured to present in Chapter 1 the problems related to nonlinear loads and harmonics.

Chapter 2 describes the background of electrical power definitions based on conventional theories. Then, Chapter 3 deals with the instantaneous power theory. In this chapter, special attention is paid to the effort to offer abundant materials intended to make the reader understand the theory, particularly for designing controllers for active filters for power conditioning. Part of Chapter 3 is dedicated to presenting alternative sets of instantaneous power definitions. One of the alternatives, called the “modified p-q theory,” expands the original imaginary power definition to an instantaneous imaginary power vector with three components. Another approach, called in this book the “abc theory,” uses the abc-phase voltages and currents directly to define the active and nonactive current components. Comparisons in difference and physical meaning between these theories conclude Chapter 3. In this second edition, a section about the p-q-r power theory is added to give one more possible way to analyze the different powers in a three-phase circuit.

Chapter 4 is exclusively dedicated to shunt active filters with different filter structures, showing clearly whether energy storage elements such as capacitors and inductors are necessary or not, and how much they are theoretically dispensable to the active filters. This consideration of the energy storage elements is one of the strongest points in the instantaneous power theory. A new section is added in this second edition, showing how to use the p-q-r power theory to design active compensators.

Chapter 5 addresses series active filters, including hybrid configurations of active and passive filters. The hybrid configurations may provide an economical solution to harmonic filtering, particularly in medium-voltage, adjustable-speed motor drives. A section on hybrid active filters for medium-voltage motor drives is introduced for this new edition. Practical hybrid active filters have been proposed on the basis of the combination of a simple single-tuned passive filter with an active filter using a three-phase, two-level or three-level PWM converter.

Chapter 6 presents combined series and shunt power conditioners, including the unified power quality conditioner (UPQC), and the unified power flow controller (UPFC) that is a FACTS (flexible ac transmission system) equipment. Finally, it leads to the universal active power line conditioner that integrates the UPQC with the UPFC in terms of functionality. This second edition introduces an especial shunt and series active filter to be connected in the ac side and dc side of a three-phase rectifier, respectively. Ideally, this would result in a rectifier with sinusoidal ac current and voltage and pure dc voltage and current in its output.

Pioneering applications of the p-q theory to power conditioning are illustrated throughout the book, which helps the reader to understand the substantial nature of the instantaneous power theory, along with distinct differences from conventional theories as well as others theories in some cases.

The authors would like to acknowledge the encouragement and support received from many colleagues in various forms. The first author greatly appreciates his former colleagues, Prof. A. Nabae, the late Prof. I. Takahashi, and Mr. Y. Kanazawa at the Nagaoka University of Technology, where the p-q theory was born in 1982 and research on its applications to pure and hybrid active filters was initiated to spur many scientists and engineers to do further research on theory and practice.

The long distance between the homelands of the authors was not a serious problem because research-supporting agencies like CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) and JSPS (the Japan Society for the Promotion of Science) gave financial support for the authors to travel to Brazil or to Japan when a conference was held in one of these countries. Thus, the authors were able to meet and discuss face to face the details of the book, which would not be easily done over the Internet. The support received from the Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) is also acknowledged.

Finally, our special thanks go to the following former graduate students and visiting scientists who worked with the authors: S. Ogasawara, K. Fujita, T. Tanaka, S. Atoh, F. Z. Peng, Y. Tsukamoto, H. Fujita, S. Ikeda, T. Yamasaki, H. Kim, K. Wada, P. Jintakosonwit, S. Srianthumrong, Y. Tamai, R. Inzunza, R. Kondo, K. Isozaki, P. G. Barbosa, A. Santisteban, and G. Casaravilla, who are now working in industry or academia. They patiently helped to develop many good ideas, to design and build experimental systems, and to obtain experimental results. Without their enthusiastic support, the authors could not have published this book. The authors would like to thank Maynara Aredes and Laís Crispino for their help in the revision of the text for this second edition.

HIROFUMI AKAGI

EDSON HIROKAZU WATANABE

MAURíCIO AREDES

Tokyo/Rio de Janeiro

CHAPTER 1INTRODUCTION

THE INSTANTANEOUS ACTIVE AND REACTIVE POWER theory, or the so-called “p-q theory,” was introduced by Akagi, Kanazawa, and Nabae in 1983. Since then, it has been extended by the authors of this book, as well as other research scientists. This book deals with the theory in a complete form for the first time, including comparisons with other sets of instantaneous power definitions. The usefulness of the p-q theory is confirmed in the following chapters dealing with applications in controllers of compensators that are generically classified here as active power line conditioners.

The term “power conditioning” used in this book has much broader meaning than the term “harmonic filtering.” In other words, the power conditioning is not confined to harmonic filtering, but contains harmonic damping, harmonic isolation, harmonic termination, reactive-power control for power factor correction, power flow control, and voltage regulation, load balancing, voltage-flicker reduction, and/or their combinations. Active power line conditioners are based on leading edge power electronics technology that includes power conversion circuits, power semiconductor devices, analog/digital signal processing, voltage/current sensors, and control theory.

Concepts and evolution of electric power theory are briefly described later. Then, the need for a consistent set of power definitions is emphasized to deal with electric systems under nonsinusoidal conditions. Problems with harmonic pollution in alternating current systems (ac systems) are classified, including a list of the principal harmonic-producing loads. Basic principles of harmonic compensation are introduced. Finally, this chapter describes the fundaments of power flow control. All these topics are the subjects of scope and will be discussed deeply in the following chapters of the book.

1.1 Concepts and Evolution of Electric Power Theory

One of main points in the development of alternating current (ac) transmission and distribution power systems at the end of the nineteenth century was based on sinusoidal voltage at constant-frequency generation. Sinusoidal voltage with constant frequency has made easier the design of transformers and transmission lines, including very long distance lines. If the voltage were not sinusoidal, complications would appear in the design of transformers, machines, and transmission lines. These complications would not allow, certainly, such a development as the generalized “electrification of the human society.” Today, there are very few communities in the world without ac power systems with “constant” voltage and frequency.

With the emergence of sinusoidal voltage sources, the electric power network could be made more efficient if the load current were in phase with the source voltage. Therefore, the concept of reactive power was defined to represent the quantity of electric power due to the load current that is not in phase with the source voltage. The average of this reactive power during one period of the line frequency is zero. In other words, this power does not contribute to energy transfer from the source to the load. At the same time, the concepts of apparent power and power factor were created. Apparent power gives the idea of how much power can be delivered or consumed if the voltage and current are sinusoidal and perfectly in phase. The power factor gives a relation between the average power actually delivered or consumed in a circuit and the apparent power at the same point. Naturally, the higher the power factor, the better the circuit utilization. As a consequence, the power factor is more efficient not only electrically but also economically. Therefore, electric power utilities have specified lower limits for the power factor. Loads operated at low power factor pay an extra charge for not using the circuit efficiently.

For a long time, one of the main concerns related to electric equipment was power factor correction, which could be done by using capacitor banks or, in some cases, reactors. For all situations, the load acted as a linear circuit drawing a sinusoidal current from a sinusoidal voltage source. Hence, the conventional power theory based on active-, reactive-, and apparent-power definitions was sufficient for design and analysis of power systems. Nevertheless, some papers were published in the 1920s, showing that the conventional concept of reactive and apparent power loses its usefulness in nonsinusoidal cases [1,2]. Then, two important approaches to power definitions under nonsinusoidal conditions were introduced by Budeanu [3,4] in 1927 and Fryze [5] in 1932. Fryze defined power in the time domain, whereas Budeanu did it in the frequency domain. At that time, nonlinear loads were negligible, and little attention was paid to this matter for a long time.

Since power electronics was introduced in the late 1960s, nonlinear loads that consume nonsinusoidal current have increased significantly. In some cases, they represent a very high percentage of the total loads. Today, it is common to find a house without linear loads such as conventional incandescent lamps. In most cases, these lamps have been replaced by electronically controlled fluorescent lamps. In industrial applications, an induction motor that can be considered as a linear load in a steady state is now equipped with a rectifier and inverter for the purpose of achieving adjustable speed control. The induction motor together with its drive is no longer a linear load. Unfortunately, the previous power definitions under nonsinusoidal currents were dubious, thus leading to misinterpretations in some cases. Chapter 2 presents a review of some theories dealing with nonsinusoidal conditions.

As pointed out earlier, the problems related to nonlinear loads have significantly increased with the proliferation of power electronics equipment. The modern equipment behaves as a nonlinear load drawing a significant amount of harmonic current from the power network. Hence, power systems in some cases have to be analyzed under nonsinusoidal conditions. This makes it imperative to establish a consistent set of power definitions that are also valid during transients and under nonsinusoidal conditions.

The power theories presented by Budeanu [3,4] and Fryze [5] had basic concerns related to the calculation of average power or root-mean-square values (rms values) of voltage and current. The development of power electronics technology has brought new boundary conditions to the power theories. Exactly speaking, the new conditions have not emerged from the research of power electronics engineers. They have resulted from the proliferation of power converters using power semiconductor devices such as diodes, thyristors, insulated-gate bipolar transistors (IGBTs), gate-turn-off thyristors, and so on. Although these power converters have a quick response in controlling their voltages or currents, they may draw reactive power as well as harmonic current from power networks. This has made it clear that conventional power theories based on average or rms values of voltages and currents are not applicable to the analysis and design of power converters and power networks. This problem has become more serious and clear during comprehensive analysis and design of active filters intended for reactive-power compensation as well as harmonic compensation.

From the end of the 1960s to the beginning of the 1970s, Erlicki and Emanuel-Eigeles [6], Sasaki and Machida [7], and Fukao et al. [8] published their pioneer papers presenting what can be considered as a basic principle of controlled reactive-power compensation. For instance, Erlicki and Emanuel-Eigeles [6] presented some basic ideas like “compensation of distortive power is unknown to date….” They also determined that “a non-linear resistor behaves like a reactive-power generator while having no energy-storing elements” and presented the very first approach to active power-factor control. Fukao et al. [8] stated that “by connecting a non-active-power source in parallel with the load, and by controlling it in such a way as to supply reactive power to the load, the power network will only supply active power to the load. Therefore, ideal power transmission would be possible.”

Gyugyi and Pelly [9] presented the idea that reactive power could be compensated by a naturally commutated cycloconverter without energy storage elements. This idea was explained from a physical point of view. However, no specific mathematical proof was presented. In 1976, Harashima et al. [10] presented, probably for the first time, the term “instantaneous reactive power” for a single-phase circuit. That same year, Gyugyi and Strycula [11] used the term “active ac power filters” for the first time. A few years later, in 1981, Takahashi et al. published two papers [12,13] giving a hint of the emergence of the instantaneous power theory or “p-q theory.” In fact, the formulation they reached can be considered a subset of the p-q theory that forms the main scope of this book. However, the physical meaning of the variables introduced to the subset was not explained by them.

The p-q theory in its first version was published in the Japanese language in 1982 [14] in a local conference, and later in Transactions of the Institute of Electrical Engineers of Japan [15]. With a minor time lag, a paper was published in English in an international conference in 1983 [16], showing the possibility of compensating for instantaneous reactive power without energy storage elements. Then, a more complete paper including experimental verifications was published in the IEEE Transactions on Industry Applications in 1984 [17].

The p-q theory defines a set of instantaneous powers in the time domain. Since no restrictions are imposed on voltage or current behaviors, it is applicable to three-phase systems with or without neutral conductors, as well as to generic voltage and current waveforms. Thus, it is valid for steady and transient states. Contrary to other traditional power theories treating a three-phase system as three single-phase circuits, the p-q theory deals with all the three phases at the same time, as a unity system. Therefore, this theory always considers three-phase systems together, not as a superposition or sum of three single-phase circuits. It was defined by using the αβ0 transformation, also known as the Clarke transformation [18], which consists of a real matrix that transforms three-phase voltages and currents into the αβ0-stationary reference frames. As will be seen in this book, the p-q theory provides a very efficient and flexible basis for designing control strategies and implementing them in the form of controllers for power conditioners based on power electronics devices.

There are other approaches to power definitions in the time domain. Chapter 3 is dedicated to the time-domain analysis of power in three-phase circuits, and it is especially dedicated to the p-q Theory.

1.2 Applications of the p-q theory to Power Electronics Equipment

The proliferation of nonlinear loads has spurred interest in research on new power theories, thus leading to the p-q