Modern Power Systems Analysis

Transcription

1 Modern Power Systems Analysis

2 Xi-Fan Wang l Yonghua Song l Malcolm Irving Modern Power Systems Analysis 123

3 Xi-Fan Wang Xi an Jiaotong University Xi an People s Republic of China Yonghua Song The University of Liverpool Liverpool United Kingdom Malcolm Irving Brunel University Middlesex United Kingdom ISBN e-isbn Library of Congress Control Number: # 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper springer.com

4 Preface The power industry, a capital and technology intensive industry, is a basic national infrastructure. Its security, reliability, and economy have enormous and far-reaching effects on a national economy. An electrical power system is a typical large-scale system. Questions such as how to reflect accurately the characteristics of modern electrical power systems, how to analyze effectively their operating features, and how to improve further the operating performance are always at the forefront of electrical power systems research. Electrical power system analysis is used as the basic and fundamental measure to study planning and operating problems. In the last century, electrical power researchers have undertaken a great deal of investigation and development in this area, have made great progress in theoretical analysis and numerical calculation, and have written excellent monographs and textbooks. Over the last 20 years, the changes in electrical power systems and other relevant technologies have had a profound influence on the techniques and methodologies of electrical power system analysis. First, the development of digital computer technology has significantly improved the performance of hardware and software. Now, we can easily deal with load flow issues with over ten thousand nodes. Optimal load flow and static security analysis, which were once considered hard problems, have attained online practical applications. Second, the applications of HVDC and AC flexible transmission technologies (FACTS) have added new control measures to electrical power systems, and have increased power transmission capacity, enhanced control capability, and improved operating characteristics. However, these technologies bring new challenges into the area of electrical power system analysis. We must build corresponding mathematical models for these new devices and develop algorithms for static and dynamic analysis of electrical power systems including these devices. In addition, the rapid development of communication technology has enabled online monitoring of electrical power systems. Therefore, the demand for online software for electrical power system analysis becomes more and more pressing. Furthermore, worldwide power industry restructuring and deregulation has separated the former vertically integrated system into various parts, and the once v

5 vi Preface unified problem of power system dispatching is now conducted via complicated bilateral contracts and spot markets. New issues such as transmission ancillary service and transmission congestion have emerged. In recent years, several power blackouts have taken place worldwide, especially the 8.13 blackout on the eastern grid of USA and Canada and the blackouts that occurred successively in other countries have attracted a great deal of attention. All of these aspects require new theories, models, and algorithms for electrical power system analysis. It is within such an environment that this book has been developed. The book is written as a textbook for senior students and postgraduates as well as a reference book for power system researchers. We acknowledge the support from various research funding organizations, their colleagues, and students, especially, the special funds for Major State Basic Research Projects of China Research on Power System Reliability under Deregulated Environment of Power Market (2004CB217905). We express our special gratitude to Professor Wan-Liang Fang and Professor Zheng-Chun Du for providing the original materials of Chaps. 5 and 6, and 7 and 8, respectively. We also express our sincere gratitude to the following colleagues for their contributions to various chapters of the book: Professor Zhao-Hong Bie for Chaps. 1 and 3; Professor Xiu-Li Wang for Chaps. 2 and 4; Dr. Ze-Chun Hu for Chap. 3; Dr. Xiao-Ying Ding for Chap. 4; Dr. Lin Duan for Chaps. 5 and 6; Professor De-Chiang Gang for Chap. 7; and Professor Hai-Feng Wang for Chaps. 6 and 8. Xi an, China Liverpool, UK London, UK Xi-Fan Wang Yonghuna Song Malcolm Irving

6 Contents 1 Mathematical Model and Solution of Electric Network Introduction Basic Concepts Node Equation and Loop Equation Equivalent Circuit of Transformer and Phase Shift Transformer Nodal Admittance Matrix Basic Concept of Nodal Admittance Matrix Formulation and Modification of Nodal Admittance Matrix Solution to Electric Network Equations Gauss Elimination Method Triangular Decomposition and Factor Table Sparse Techniques Sparse Vector Method Optimal Ordering Schemes of Electric Network Nodes Nodal Impedance Matrix Basic Concept of Nodal Impedance Matrix Forming Nodal Impedance Matrix Using Admittance Matrix Forming Nodal Impedance Matrix by Branch Addition Method Load Flow Analysis Introduction Formulation of Load Flow Problem Classification of Node Types Node Power Equations Load Flow Solution by Newton Method Basic Concept of Newton Method Correction Equations vii

7 viii Contents Solution Process of Newton Method Solution of Correction Equations Fast Decoupled Method Introduction to Fast Decoupled Method Correction Equations of Fast Decoupled method Flowchart of Fast Decoupled Method Static Security Analysis and Compensation Method Survey of Static Security Analysis Compensation Method DC Load Flow Method Model of DC Load Flow Outage Analysis by DC Load Flow Method N-1 Checking and Contingency Ranking Method Stochastic Security Analysis of Electrical Power Systems Introduction Basic Concepts of Probability Theory Probability of Stochastic Events Random Variables and its Distribution Numeral Character of Random Variable Convolution of Random Variables Several Usual Random Variable Distributions Markov Process Probabilistic Model of Power Systems Probabilistic Model of Load Probabilistic Model of Power System Components Outage Table of Power System Components Monte Carlo Simulation Method Fundamental Theory of Monte Carlo Simulation Method Sampling of System Operation State State Evaluation Model Indices of Reliability Evaluation Flowchart of Composite System Adequacy Evaluation Markov Chain Monte Carlo (MCMC) Simulation Method Probabilistic Load Flow Analysis Cumulants of Random Distribution Linearization of Load Flow Equation Computing Process of Probabilistic Load Flow Probabilistic Network-Flow Analysis Introduction Network-Flow Model Lower Boundary Points of Feasible Flow Solutions Reliability of Transmission System

8 Contents ix 4 Power Flow Analysis in Market Environment Introduction Transmission Owner Independent Operator Power Exchange Ancillary Service Scheduling Coordinator Optimal Power Flow General Formulation of OPF Problem Approaches to OPF Interior Point Method (IPM) for OPF Problem Application of Optimal Power Flow in Electricity Market Survey Congestion Management Method Based On OPF Power Flow Tracing Current Decomposition Axioms Mathematical Model of Loss Allocation Usage Sharing Problem of Transmission Facilities Methodology of Graph Theory Available Transfer Capability of Transmission System Introduction To Available Transfer Capability Application of Monte Carlo Simulation in ATC Calculation ATC Calculation with Sensitivity Analysis Method HVDC and FACTS Introduction HVDC Basic Principles and Mathematical Models HVDC Basic Principles Converter Basic Equations Neglecting Lc Converter Basic Equations Considering Lc Converter Equivalent Circuits Multiple Bridge Operation Converter Control Power Flow Calculation of AC/DC Interconnected Systems Converter Basic Equations in per Unit System Power Flow Equations Jacobian Matrix of Power Flow Equations Integrated Iteration formula of AC/DC Interconnected Systems Alternating Iteration for AC/DC Interconnected Systems HVDC Dynamic Mathematical Models Basic Principles and Mathematical Models of FACTS Basic Principle and Mathematical Model of SVC Basic Principle and Mathematical Model of STATCOM

9 x Contents Basic Principle and Mathematical Model of TCSC Basic Principle and Mathematical Model of SSSC Basic Principle and Mathematical Model of TCPST Basic Principle and Mathematical Model of UPFC Mathematical Model of Synchronous Generator and Load Introduction Mathematical Model of Synchronous Generator Basic Mathematical Equations of Synchronous Generator Mathematical Equations of Synchronous Generator Using Machine Parameters Simplified Mathematical Model of Synchronous Generator Steady-State Equations and Phasor Diagram Mathematical Equations Considering Effect of Saturation Rotor Motion Equation of Synchronous Generator Mathematical Model of Generator Excitation Systems Mathematical Model of Exciter Voltage Measurement and Load Compensation Unit Limiters Mathematical Model of Power System Stabilizer Mathematical Model of Excitation Systems Mathematical Model of Prime Mover and Governing System Mathematical Model of Hydro-Turbine and Governing System Mathematical Model of Steam Turbine and Governing System Mathematical Model of Load Static Load Model Dynamic Load Model Power System Transient Stability Analysis Introduction Numerical Methods for Transient Stability Analysis Numerical Methods for Ordinary Differential Equations Numerical Methods for Differential-Algebraic Equations General Procedure for Transient Stability Analysis Network Mathematical Model for Transient Stability Analysis The Relationship Between Network and Dynamic Devices Modeling Network Switching and Faults

10 Contents xi 7.4 Transient Stability Analysis with Simplified Model Computing Initial Values Solving Network Equations with Direct Method Solving Differential Equations by Modified Euler Method Numerical Integration Methods for Transient Stability Analysis under Classical Model Transient Stability Analysis with FACTS Devices Initial Values and Difference Equations of Generators Initial Values and Difference Equations of FACTS and HVDC Forming Network Equations Simultaneous Solution of Difference and Network Equations Small-Signal Stability Analysis of Power Systems Introduction Linearized Equations of Power System Dynamic Components Linearized Equation of Synchronous Generator Linearized Equation of Load Linearized Equation of FACTS Components Linearized Equation of HVDC Transmission System Steps in Small-Signal Stability Analysis Network Equation Linearized Differential Equations of Whole Power System Program Package for Small-Signal Stability Analysis Eigenvalue Problem in Small-Signal Stability Analysis Characteristics of State Matrix Given by Its Eigensolution Modal Analysis of Linear Systems Computation of Eigenvalues Eigensolution of Sparse Matrix Application of Eigenvalue Sensitivity Analysis Oscillation Analysis of Power Systems References Index