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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley - IEEE
- Sprache: Englisch
Classic power system dynamics text now with phasor measurement and simulation toolbox
This new edition addresses the needs of dynamic modeling and simulation relevant to power system planning, design, and operation, including a systematic derivation of synchronous machine dynamic models together with speed and voltage control subsystems. Reduced-order modeling based on integral manifolds is used as a firm basis for understanding the derivations and limitations of lower-order dynamic models. Following these developments, multi-machine model interconnected through the transmission network is formulated and simulated using numerical simulation methods. Energy function methods are discussed for direct evaluation of stability. Small-signal analysis is used for determining the electromechanical modes and mode-shapes, and for power system stabilizer design.
Time-synchronized high-sampling-rate phasor measurement units (PMUs) to monitor power system disturbances have been implemented throughout North America and many other countries. In this second edition, new chapters on synchrophasor measurement and using the Power System Toolbox for dynamic simulation have been added. These new materials will reinforce power system dynamic aspects treated more analytically in the earlier chapters.
Key features:
- Systematic derivation of synchronous machine dynamic models and simplification.
- Energy function methods with an emphasis on the potential energy boundary surface and the controlling unstable equilibrium point approaches.
- Phasor computation and synchrophasor data applications.
- Book companion website for instructors featuring solutions and PowerPoint files. Website for students featuring MATLABTM files.
Power System Dynamics and Stability, 2nd Edition, with Synchrophasor Measurement and Power System Toolbox combines theoretical as well as practical information for use as a text for formal instruction or for reference by working engineers.
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Power System Dynamics and Stability
With Synchrophasor Measurement and Power System Toolbox
Second Edition
Peter W. Sauer and M. A. Pai
Department of Electrical and Computer Engineering The University of Illinois at Urbana-Champaign
Joe H. Chow
Department of Electrical, Computer, and Systems Engineering Rensselaer Polytechnic Institute
This edition first published 2018 © 2018 John Wiley & Sons Ltd
Edition HistoryPrentice Hall (1st Edition, 1997), Stipes (1st Edition Revised, 2007)
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.
The right of Peter W. Sauer, M. A. Pai and Joe H. Chow to be identified as the authors of this work has been asserted in accordance with law.
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Library of Congress Cataloging-in-Publication Data
Names: Sauer, Peter W., author. | Pai, M. A., 1931– author. | Chow, J. H. (Joe H.), 1951– author.Title: Power system dynamics and stability : with synchrophasor measurement and power system toolbox / Peter W Sauer, M. A Pai, University of Illinois at Urbana-Champaign, United States, Joe H. Chow, Rensselaer Polytechnic Institute, Troy, New York, United States.Description: Second edition. | Hoboken, NJ, USA : Wiley, [2017] | Includes bibliographical references and index. |Identifiers: LCCN 2017012512 (print) | LCCN 2017014476 (ebook) | ISBN 9781119355793 (pdf) | ISBN 9781119355748 (epub) | ISBN 9781119355779 (cloth)Subjects: LCSH: Electric power system stability. | Electric machinery, Synchronous–Mathematical models. | Electric power systems–Control.Classification: LCC TK1010 (ebook) | LCC TK1010 .S38 2017 (print) | DDC 621.31–dc23LC record available at https://lccn.loc.gov/2017012512
Cover Images: (Background) © troyek/Gettyimages; (Foreground) MATLAB®Cover design by Wiley
To
Sylvia, Nandini, and Doris
CONTENTS
Preface
About the Companion Website
1 Introduction
1.1 Background
1.2 Physical Structures
1.3 Time-Scale Structures
1.4 Political Structures
1.5 The Phenomena of Interest
1.6 New Chapters Added to this Edition
2 Electromagnetic Transients
2.1 The Fastest Transients
2.2 Transmission Line Models
2.3 Solution Methods
2.4 Problems
3 Synchronous Machine Modeling
3.1 Conventions and Notation
3.2 Three-Damper-Winding Model
3.3 Transformations and Scaling
3.4 The Linear Magnetic Circuit
3.5 The Nonlinear Magnetic Circuit
3.6 Single-Machine Steady State
3.7 Operational Impedances and Test Data
3.8 Problems
4 Synchronous Machine Control Models
4.1 Voltage and Speed Control Overview
4.2 Exciter Models
4.3 Voltage Regulator Models
4.4 Turbine Models
4.5 Speed Governor Models
4.6 Problems
5 Single-Machine Dynamic Models
5.1 Terminal Constraints
5.2 The Multi-Time-Scale Model
5.3 Elimination of Stator/Network Transients
5.4 The Two-Axis Model
5.5 The One-Axis (Flux-Decay) Model
5.6 The Classical Model
5.7 Damping Torques
5.8 Single-Machine Infinite-Bus System
5.9 Synchronous Machine Saturation
5.10 Problems
6 Multimachine Dynamic Models
6.1 The Synchronously Rotating Reference Frame
6.2 Network and R-L Load Constraints
6.3 Elimination of Stator/Network Transients
6.4 Multimachine Two-Axis Model
6.5 Multimachine Flux–Decay Model
6.6 Multimachine Classical Model
6.7 Multimachine Damping Torques
6.8 Multimachine Models with Saturation
6.9 Frequency During Transients
6.10 Angle References and an Infinite Bus
6.11 Automatic Generation Control (AGC)
7 Multimachine Simulation
7.1 Differential-Algebraic Model
7.2 Stator Algebraic Equations
7.3 Network Equations
7.4 Industry Model
7.5 Simplification of the Two-Axis Model
7.6 Initial Conditions (Full Model)
7.7 Numerical Solution: Power-Balance Form
7.8 Numerical Solution: Current-Balance Form
7.9 Reduced-Order Multimachine Models
7.10 Initial Conditions
7.11 Conclusion
7.12 Problems
Notes
8 Small-Signal Stability
8.1 Background
8.2 Basic Linearization Technique
8.3 Participation Factors
8.4 Studies on Parametric Effects
8.5 Electromechanical Oscillatory Modes
8.6 Power System Stabilizers
8.7 Conclusion
8.8 Problems
9 Energy Function Methods
9.1 Background
9.2 Physical and Mathematical Aspects of the Problem
9.3 Lyapunov’s Method
9.4 Modeling Issues
9.5 Energy Function Formulation
9.6 Potential Energy Boundary Surface (PEBS)
9.7 The Boundary Controlling u.e.p (BCU) Method
9.8 Structure-Preserving Energy Functions
9.9 Conclusion
9.10 Problems
10 Synchronized Phasor Measurement
10.1 Background
10.2 Phasor Computation
10.3 Phasor Data Communication
10.4 Power System Frequency Response
10.5 Power System Disturbance Propagation
10.6 Power System Disturbance Signatures
10.7 Phasor State Estimation
10.8 Modal Analyses of Oscillations
10.9 Energy Function Analysis
10.10 Control Design Using PMU Data
10.11 Conclusions and Remarks
10.12 Problems
Notes
11 Power System Toolbox
11.1 Background
11.2 Power Flow Computation
11.3 Dynamic Simulation
11.4 Linear Analysis
11.5 Conclusions and Remarks
11.6 Problems
Notes
A Integral Manifolds for Model Reduction
A.1 Manifolds and Integral Manifolds
A.2 Integral Manifolds for Linear Systems
A.3 Integral Manifolds for Nonlinear Systems
Bibliography
Index
EULA
List of Tables
Chapter 7
Table 7.1
Table 7.2
Table 7.3
Chapter 8
Table 8.1
Table 8.2
Table 8.3
Table 8.4
Table 8.5
Table 8.6
Table 8.7
Table 8.8
Table 8.9
Table 8.10
Table 8.11
Chapter 10
Table 10.1
Table 10.2
Table 10.3
Table 10.4
Table 10.5
Table 10.6
Chapter 11
Table 11.1
Table 11.2
Table 11.3
Guide
Cover
Table of Contents
Preface
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Preface
The need for power system dynamic analysis has grown significantly in recent years. This is due largely to the desire to utilize transmission networks for more flexible interchange transactions. While dynamics and stability have been studied for years in a long-term planning and design environment, there is a recognized need to perform this analysis in a weekly or even daily operation environment. This book is devoted to dynamic modeling and simulation as it relates to such a need, combining theoretical as well as practical information for use as a text for formal instruction or for reference by working engineers.
The investigation of power system dynamics has taken on a new urgency since the August 14, 2003 US Northeast Blackout, resulting in power disruption to 40 million people, some for up to a week. This event led to the installation of large number of time-synchronized high-sampling-rate phasor measurement units (PMUs) in the US, China, and many other countries, to monitor power system dynamic response to disturbances in real time. In this second edition, a new chapter on synchrophasor measurement has been added, showing several traces of actual PMU data. It is envisioned that the materials will reinforce the power system dynamic aspects treated more analytically in the earlier chapters.
As a text for formal instruction, this book assumes a background in electromechanics, machines, and power system analysis. As such, the text would normally be used in a graduate course in electrical engineering. It has been designed for use in a one-semester (15-week), 3-hour course. The notation follows that of most traditional machine and power system analysis books and attempts to follow the industry standards so that a transition to more detail and practical application is easy.
The text is divided into two parts. Chapters 1 to 6 give an introduction to electromagnetic transient analysis and a systematic derivation of synchronous machine dynamic models together with speed and voltage control subsystems. They include a rigorous explanation of model origins, development, and simplification. Particular emphasis is given to the concept of reduced-order modeling using integral manifolds as a firm basis for understanding the derivations and limitations of lower-order dynamic models. An appendix on integral manifolds gives a mathematical introduction to this technique of model reduction.
In the second part, Chapters 6 to 9 utilize these dynamic models for simulation and stability analysis. Particular care is given to the calculation of initial conditions and the alternative computational methods for simulation. Small-signal stability analysis is presented in a sequential manner, concluding with the design of power system stabilizers. Transient stability analysis is formulated using energy function methods with an emphasis on the essentials of the potential energy boundary surface and the controlling unstable equilibrium point approaches. The new Chapter 10 describes synchrophasor technology and PMU data applications. In addition, a new Chapter 11 describes the Power System Toolbox, a MATLABTM-based free software. This simulation tool can be used for many examples throughout the book. Thus this chapter can be used as a reference as well as a primer on building a practical power system simulator. The Power System Toolbox, the PMU Simulator, and data and MATLABTM code for selected examples and problems can be downloaded from the website https://ecse.rpi.edu/∼chowj/.
The book does not claim to be a complete collection of all models and simulation techniques, but seeks to provide a basic understanding of power system dynamics. While many more detailed and accurate models exist in the literature, a major goal of this book is to explain how individual component models are interfaced for a system study. Our objective is to provide a firm theoretical foundation for power system dynamic analysis to serve as a starting point for deeper exploration of complex phenomena and applications in electric power engineering.
We have so many people to acknowledge for their assistance in our careers and lives that we will limit our list to six people who have had a direct impact on the University of Illinois power program and the preparation of this book: Stan Helm, for his devotion to the power area of electrical engineering for over 60 years; George Swenson, for his leadership in strengthening the power area in the department; Mac VanValkenburg, for his fatherly wisdom and guidance; David Grainger, for his financial support of the power program; Petar Kokotovic, for his inspiration and energetic discussions; and Karen Chitwood, for preparing the manuscript. We have also benefited from our interactions with many power system experts from General Electric Company, including William Price, Richard Schulz, Einar Larsen, Dale Swann, and Thomas Younkins. The opportunity to work with Jay Murphy (Macrodyne) and Jim Ingleson (NYISO) on PMUs has greatly helped us. A special thank is due to Dr. Daniel Dotta (State University of Campinas (UNICAMP), Brazil) for writing the first part of Chapter 10.
Throughout our many years of collaboration at the University of Illinois and Rensselaer Polytechnic Institute, we have strived to maintain a healthy balance between education and research. We thank the University administration and the funding support of the National Science Foundation, the Department of Energy, and the Grainger Foundation for making this possible.
Peter W. Sauer and M. A. Pai Urbana, IllinoisJoe H. Chow Troy, New York
About the Companion Website
This book is accompanied by a companion website:
www.wiley.com/go/sauer/powersystemdynamics
The website hosts a variety of supplementary resources for students and instructors.
For Instructors:
PowerPoint files of the illustrations presented within this text
MATLAB codes and data for Examples and Problems
Solutions to Problems at the end of each chapter
Example Folders
Sample lecture slides
For Students:
Example Folders
Data for Problems
1Introduction
1.1 Background
The modern power grid has become more complex with the addition of many devices both in terms of transmission and generating sources. But the central generating systems station concept supported by a highly interconnected system remains the major part of power delivery network. The techniques for analysis and operation of the grid have been influenced both by advanced computational techniques and GPS-based communication such as synchronized phasor measurements for monitoring and control purposes.
Compared to other disciplines within electrical engineering, the analytical techniques of power systems were often based on experience and heuristic assumptions. The impact of control, system theory, and in recent years, communication and signal processing techniques has been significant. It is necessary to develop a sound theoretical basis for the area of power system dynamics, stability, and control. The purpose of this book is to achieve these objectives.
The subject of power system dynamics, stability, and control is an extremely broad topic with a long history and volumes of published literature. There are many ways to divide and categorize this subject for both education and research. While a substantial amount of information about the dynamic behavior of power systems can be gained through experience, working with and testing individual pieces of equipment, the complex problems and operating practices of large interconnected systems can be better understood if this experience is coupled with a mathematical model. There are several main divisions in the study of power system dynamics and stability [1].
F. P. deMello classified dynamic processes into three categories:
Electrical machine and system dynamics
System governing and generation control
Prime-mover energy supply dynamics and control
In the same reference, C. Concordia and R. P. Schulz classify dynamic studies according to four concepts:
The time of the system condition: past, present, or future
The time range of the study: microsecond through hourly response
The nature of the system under study: new station, new line, etc.
The technical scope of the study: fault analysis, load shedding, sub-synchronous resonance, etc.
All of these classifications share a common thread: They emphasize that the system is not in steady state and that many models for various components must be used in varying degrees of detail to allow efficient and practical analysis. The first six chapters of this book are thus devoted to the subject of modeling. The next the next three chapters discuss the use of the interconnected models for common dynamic studies. Finally we discuss the use of synchro phasor measurements for monitoring the system in real time. It forms the foundation for modern control techniques optimization and security analysis of the grid.
1.2 Physical Structures
The major components of a power system can be represented in a block-diagram format, as shown in Figure 1.1. While this block-diagram representation does not show all of the complex dynamic interaction between components and their controls, it serves to broadly describe the dynamic structures involved. Historically, there has been a major division into the mechanical and electrical subsystems as shown. This division is not absolute, however, since the electrical side clearly contains components with mechanical dynamics (tap-changing-under-load (TCUL) transformers, motor loads, etc.) and the mechanical side clearly contains components with electrical dynamics (auxiliary motor drives, process controls, etc.). Furthermore, both sides are coupled through the monitoring and control functions of the energy control center. The energy control center gets information about the states of the system, that is, voltages and phase angles at various buses, through the phasor measurement units (PMUs) positioned all over the network.
Figure 1.1 System dynamic structure.
1.3 Time-Scale Structures
Perhaps the most important classification of dynamic phenomena is their natural time range of response. A typical classification is shown in Figure 1.2. A similar concept is presented in [6]. This time-range classification is important because of its impact on component modeling. It should be intuitively obvious that it is not necessary to solve the complex transmission line wave equations to investigate the impact of a change in boiler control set points. This confirms a statement made earlier that “the system is not in steady state.” Evidently, depending on the nature of the dynamic disturbance, portions of the power system can be considered in “quasi-steady state.” This rather ambiguous term will be explained fully in the context of time-scale modeling [2].
Figure 1.2 Time ranges of dynamic phenomena.
1.4 Political Structures
The dynamic structure and time-range classifications of dynamic phenomena illustrate the potential complexity of even small or moderate-sized problems. The problems of power system dynamics and stability are compounded immensely by the current size of interconnected systems. A general system structure is shown in Figure 1.3. While this structure is not necessarily common to interconnected systems throughout the world, it represents a typical North American system and serves to illustrate the concept of a “large-scale system.” If we speculate about the possible size of a single interconnected system containing 8 regional reliability organizations, 4 pools per regional reliability organization, 6 companies per pool, and 10 generators per company, the total possible number of generating stations can exceed 2000. The bulk power transmission network (138–765 kV) then typically consists of over 10,000 buses. Indeed, the current demand in the 8 regional reliability organizations within the North American Electric Reliability Corporation (NERC) exceeds 500,000 MW [3]. At an average 250 MW per generator, this roughly confirms the estimate of over 2000 generators in the interconnected North American grid.
Figure 1.3 System organizational structure.
Dynamic studies are routinely performed on systems ranging in size from the smallest company to the largest regional reliability organization. These are made at both the planning/design and operating stages. These studies provide information about local capabilities as well as regional power interchange capabilities. In view of the potential size, dynamic studies must be capable of sufficiently accurate representation without prohibitive computational cost. The nature of system engineering problems inherent in such a complex task was emphasized in two benchmark reports by the Department of Energy (DOE) and the Electric Power Research Institute (EPRI) [4, 5]. These reports resulted in a meeting of international leaders to identify directions for the future of this technology. These reports set the stage for a whole new era of power system planning and operation. The volume of follow-on research and industry application has been tremendous. Perhaps the most significant impact of these reports was the stimulation of new ideas that grew into student interest and eventual manpower.
1.5 The Phenomena of Interest
The dynamic performance of power systems is important to both the system organizations, from an economic viewpoint, and society in general, from a reliability viewpoint. The analysis of power system dynamics and stability is increasing daily in terms of number and frequency of studies, as well as in complexity and size. Dynamic phenomena have been discussed according to basic function, time-scale properties, and problem size. These three fundamental concepts are very closely related and represent the essence of the challenges of effective simulation of power system dynamics. When properly performed, modeling and simulation capture the phenomena of interest at minimal cost. The first step in this process is understanding the phenomena of interest. Only with a solid physical and mathematical understanding can the modeling and simulation properly reflect the critical system behavior. This means that the origin of mathematical models must be understood, and their purpose must be well defined. Once this is accomplished, the minimal cost is achieved by model reduction and simplification without significant loss in accuracy.
1.6 New Chapters Added to this Edition
Two new chapters have been added in this edition of the book to reaffirm learning from the existing chapters. For generations, most power students had to take “faith” in the generator swing equations and excitation system control to determine power system dynamics. However, with high-sampling-rate digital recording of power system signals using the phasor measurement technology and the ability to precisely time tag the measurements over wide geographical areas using a timing signal from the Global Positioning System (GPS), the propagation of a disturbance can be observed as it travels through a power grid. This observation can be used to corroborate the dynamic models of power systems. Synchrophasor measurement is covered in Chapter 10.
Chapter 11 on the Power System Toolbox (PST) is a timely addition to this edition, as the first edition was published before PST was developed. Although limited in the availability of exciter and governor models, the PST program structure is in many aspects similar to those of several commercial power system simulation tools. In addition to a description on the fundamentals of power system computer simulation, Chapter 11 also provides useful pointers for the proper use of such simulation programs. An ambitious reader may even try to incorporate additional models into PST.
The Power System Toolbox, the PMU Simulator, and the data and MATLABTM code for selected examples and problems can be downloaded from the website https://ecse.rpi.edu/~chowj/.
3Synchronous Machine Modeling
3.1 Conventions and Notation
There is probably more literature on synchronous machines than on any other device in electrical engineering. Unfortunately, this vast amount of material often makes the subject complex and confusing. In addition, most of the work on reduced-order modeling is based primarily on physical intuition, practical experience, and years of experimentation. The evolution of dynamic analysis has caused some problems in notation as it relates to common symbols that eventually require data from manufacturers. This text uses the conventions and notations of [20], which essentially follows those of many publications on synchronous machines [21–27]. When the notation differs significantly from these and other conventions, notes are given to clarify any possible misunderstanding. The topics of time constants and machine inductances are examples of such notations. While some documents define time constants and inductances in terms of physical experiments, this text uses fixed expressions in terms of model parameters. Since there can be a considerable difference in numerical values, it is important to always verify the meaning of symbols when obtaining data. This is most effectively done by comparing the model in which a parameter appears with the test or calculation that was performed to produce the data. In many cases, the parameter values are provided from design data based on the same expressions given in this text. In some cases, the parameter values are provided from standard tests that may not precisely relate to the expressions given in this text. In this case, there is normally a procedure to convert the values into consistent data [20].
The original Park’s transformation is used together with the “xad” per-unit system [28, 29]. This results in a reciprocal transformed per-unit model where 1.0 per-unit excitation results in rated open-circuit voltage for a linear magnetic system. Even with this standard choice, there is enough freedom in scaling to produce various model structures that appear different [30]. These issues are discussed further in later sections.
In this chapter, the machine transformation and scaling were separated from the topic of the magnetic circuit representation. This is done so that it is clear which equations and parameters are independent of the magnetic circuit representation.
3.2 Three-Damper-Winding Model
This section presents the basic dynamic equations for a balanced, symmetrical, three-phase synchronous machine with a field winding and three damper windings on the rotor. The simplified schematic of Figure 3.1 shows the coil orientation, assumed polarities, and rotor position reference. The stator windings have axes 120 electrical degrees apart and are assumed to have an equivalent sinusoidal distribution [20]. While a two-pole machine is shown, all equations will be written for a P-pole machine with expressed in electrical radians per second. The circles with dots and x’s indicate the windings. Current flow is assumed to be into the “x” and out of the “dot.” The voltage polarity of the coils is assumed to be plus to minus from the “x” to the “dots.”
Figure 3.1 Synchronous machine schematic.
This notation uses “motor” current notation for all the windings at this point. The transformed stator currents will be changed to “generator” current notation at the point of per-unit scaling. The fundamental Kirchhoff’s, Faraday’s and Newton’s laws give
where λ is flux linkage, r is winding resistance, J is the inertia constant, P is the number of magnetic poles per phase, Tm is the mechanical torque applied to the shaft, − Te is the torque of electrical origin, and Tfw is a friction windage torque. A major modeling challenge is to obtain the relationship between flux linkage and current. These relationships will be presented in later sections.
3.3 Transformations and Scaling
The sinusoidal steady state of balanced symmetrical machines can be transformed to produce constant states. The general form of the transformation that accomplishes this is Park’s transformation [20],
where
and
with the inverse
