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Summary
Summary
A guide for software development of the dynamic security assessment and control of power systems, Structure Preserving Energy Functions in Power Systems: Theory and Applications takes an approach that is more general than previous works on Transient Energy Functions defined using Reduced Network Models. A comprehensive presentation of theory and applications, this book:
Describes the analytics of monitoring and predicting dynamic security and emergency control through the illustration of theory and applications of energy functions defined on structure preserving models Covers different facets of dynamic analysis of large bulk power systems such as system stability evaluation, dynamic security assessment, and control, among others Supports illustration of SPEFs using examples and case studies, including descriptions of applications in real-time monitoring, adaptive protection, and emergency control Presents a novel network analogy based on accurate generator models that enables an accurate, yet simplified approach to computing total energy as the aggregate of energy in individual componentsThe book presents analytical tools for online detection of loss of synchronism and suggests adaptive system protection. It covers the design of effective linear damping controllers using FACTS, for damping small oscillations during normal operation to prevent transition to emergency states, and emergency control based on FACTS, to improve first swing stability and also provide rapid damping of nonlinear oscillations that threaten system security during major disturbances. The author includes detection and control algorithms derived from theoretical considerations and illustrated through several examples and case studies on text systems.
Author Notes
Prof. K.R. Padiyar is with Indian Institute of Science, Bangalore since 1987, where he is presently an Emeritus Professor in the department of Electrical Engineering. Previously he was with Indian Institute of Technology, Kanpur from 1976 to 1987 where he became a Professor in 1980. He obtained B.E. degree from Poona University in 1962, M.E. degree form Indian Institute of Science in 1964 and PhD degree from University of Waterloo, Canada in 1972.
Prof. Padiyar is an internationally recognized expert in the areas of HVDC and FACTS, Power System Stability and Control. He has authored over 200 papers and five books including "HVDC Power Transmission Systems", "Power System Dynamics", "Analysis of Subsynchronous Resonance in Power Systems "and recently, "FACTS Controllers in Power Transmission and Distribution". He is a Fellow of Indian National Academy of Engineering and Life Senior Member of IEEE. He was awarded the Dept. of Power Prize twice by Institution of Engineers (India). He is the recipient of 1999 Prof. Rustom Choksi Award for Excellence in Research for Science/Engineering. He was ABB Chair Professor during 2001-03.
He has published several papers on the subject of power system stability, Structure Preserving Energy Functions(SPEF) and their applications. Some of these are listed below.
Table of Contents
Preface | p. xiii |
Acknowledgments | p. xvii |
Author | p. xix |
Abbreviations and Acronyms | p. xxi |
1 Introduction | p. 1 |
1.1 General | p. 1 |
1.2 Power System Stability | p. 2 |
1.3 Power System Security | p. 3 |
1.4 Monitoring and Enhancing System Security | p. 6 |
1.5 Emergency Control and System Protection | p. 7 |
1.6 Application of Energy Functions | p. 8 |
1.7 Scope of This Book | p. 14 |
2 Review of Direct Methods for Transient Stability Evaluations for Systems with Simplified Models | p. 17 |
2.1 Introduction | p. 17 |
2.2 System Model | p. 18 |
2.2.1 Synchronous Generators | p. 18 |
2.2.2 Network Equations | p. 21 |
2.2.3 Load Model | p. 22 |
2.2.4 Expressions for Electrical Power | p. 23 |
2.3 Mathematical Preliminaries | p. 25 |
2.3.1 Equilibrium Points | p. 26 |
2.3.2 Stability of Equilibrium Point | p. 27 |
2.3.3 Lyapunov Stability | p. 27 |
2.3.4 Theorem on Lyapunov Stability | p. 27 |
2.4 Two-Machine System and Equal Area Criterion | p. 30 |
2.4.1 Equal Area Criterion | p. 31 |
2.4.2 Energy Function Analysis of an SMIB System | p. 32 |
2.5 Lyapunov Functions for Direct Stability Evaluation | p. 34 |
2.5.1 Construction of Lyapunov Function | p. 38 |
2.6 Energy Functions for Multimachine Power Systems | p. 39 |
2.6.1 Characterization of Transient Stability | p. 39 |
2.6.2 Center of Inertia Formulations | p. 40 |
2.6.3 Energy Function Using COI Formulation | p. 43 |
2.7 Estimation of Stability Domain | p. 44 |
2.7.1 Incorporating Transfer Conductances in Energy Function | p. 44 |
2.7.2 Determination of Critical Energy | p. 46 |
2.7.2.1 Single-Machine System | p. 46 |
2.7.2.2 Multimachine System | p. 48 |
2.7.3 Potential Energy Boundary Surface | p. 48 |
2.7.4 Controlling UEP Method | p. 50 |
2.7.5 BCU Method | p. 51 |
2.8 Extended Equal Area Criterion | p. 53 |
2.8.1 Formulation | p. 53 |
2.8.2 Approximation of Faulted Trajectory | p. 54 |
2.8.3 Identification of Critical Cluster | p. 55 |
3 Structure Preserving Energy Functions for Systems with Nonlinear Load Models and Generator Flux Decay | p. 57 |
3.1 Introduction | p. 57 |
3.2 Structure Preserving Model | p. 57 |
3.3 Inclusion of Voltage-Dependent Power Loads | p. 61 |
3.4 SPEF with Voltage-Dependent Load Models | p. 62 |
3.4.1 Dynamic Equations of Generator | p. 62 |
3.4.2 Load Model | p. 63 |
3.4.3 Power Flow Equations | p. 64 |
3.4.4 Structure Preserving Energy Functions | p. 64 |
3.4.5 Computation of Stability Region | p. 68 |
3.5 Case Studies on IEEE Test Systems | p. 69 |
3.5.1 Seventeen-Generator System | p. 70 |
3.5.2 Fifty-Generator System | p. 74 |
3.6 Solution of System Equations during a Transient | p. 76 |
3.7 Noniterative Solution of Networks with Nonlinear Loads | p. 77 |
3.7.1 System Equations | p. 78 |
3.7.2 Dynamic Equations of Generators | p. 78 |
3.7.3 Power Flow Equations during a Transient | p. 79 |
3.7.4 Special Cases | p. 81 |
3.7.5 Solutions of the Quartic Equation | p. 82 |
3.7.6 Network Transformation for Decoupling of Load Buses | p. 83 |
3.7.7 Transformation of the Load Characteristics | p. 84 |
3.8 Inclusion of Transmission Losses in Energy Function | p. 85 |
3.8.1 Transformation of a Lossy Network | p. 85 |
3.8.2 Structure Preserving Energy Function Incorporating Transmission Line Resistances | p. 87 |
3.9 SPEF for Systems with Generator Flux Decay | p. 90 |
3.9.1 System Model | p. 90 |
3.9.1.1 Generator Model | p. 91 |
3.9.1.2 Load Model | p. 92 |
3.9.1.3 Power Flow Equations | p. 92 |
3.9.2 Structure Preserving Energy Function | p. 93 |
3.9.3 Example | p. 96 |
3.10 Network Analogy for System Stability Analysis | p. 97 |
4 Structure Preserving Energy Functions for Systems with Detailed Generator and Load Models | p. 105 |
4.1 Introduction | p. 105 |
4.2 System Model | p. 106 |
4.2.1 Generator Model | p. 106 |
4.2.2 Excitation System Model | p. 107 |
4.2.3 Load Model | p. 108 |
4.2.4 Power Flow Equations | p. 108 |
4.3 Structure Preserving Energy Function with Detailed Generator Models | p. 109 |
4.3.1 Structure Preserving Energy Function | p. 109 |
4.3.2 Simpler Expression for SPEF | p. 112 |
4.4 Numerical Examples | p. 114 |
4.4.1 SMIB System | p. 114 |
4.4.2 Ten-Generator, 39-Bus New England Test System | p. 115 |
4.4.3 Variation of Total Energy and Its Components | p. 121 |
4.5 Modeling of Dynamic Loads | p. 122 |
4.5.1 Induction Motor Model | p. 124 |
4.5.2 Voltage Instability in Induction Motors | p. 126 |
4.5.3 Simpler Models of Induction Motors | p. 128 |
4.5.4 Energy Function Analysis of Synchronous and Voltage Stability | p. 128 |
4.5.4.1 Computation of Equilibrium Points | p. 130 |
4.5.4.2 Computation of Energy at UEP | p. 132 |
4.5.5 Dynamic Load Models in Multimachine Power Systems | p. 135 |
4.6 New Results on SPEF Based on Network Analogy | p. 136 |
4.6.1 Potential Energy Contributed by Considering the Two-Axis Model of the Synchronous Generator | p. 140 |
4.7 Unstable Modes and Parametric Resonance | p. 144 |
4.7.1 Normal Forms | p. 145 |
4.7.2 Fast Fourier Transform of Potential Energy | p. 146 |
4.7.2.1 Results of the Case Study | p. 146 |
5 Structure Preserving Energy Functions for Systems with HVDC and FACTS Controllers | p. 149 |
5.1 Introduction | p. 149 |
5.2 HVDC Power Transmission Links | p. 149 |
5.2.1 HVDC Systems and Energy Functions | p. 149 |
5.2.2 HVDC System Model | p. 150 |
5.2.2.1 Converter Model | p. 150 |
5.2.2.2 DC Network Equations | p. 152 |
5.2.2.3 Converter Control Model | p. 152 |
5.2.3 AC System Model | p. 155 |
5.2.3.1 Generator Model | p. 155 |
5.2.3.2 Load Model | p. 156 |
5.2.3.3 AC Network Equations | p. 156 |
5.2.4 Structure Preserving Energy Function | p. 156 |
5.2.5 Example | p. 160 |
5.2.5.1 Auxiliary Controller | p. 161 |
5.2.5.2 Emergency Controller | p. 162 |
5.2.5.3 Case Study and Results | p. 162 |
5.3 Static Var Compensator | p. 163 |
5.3.1 Description | p. 163 |
5.3.2 Control Characteristics and Modeling of SVC Controller | p. 164 |
5.3.3 Network Solution with SVC: Application of Compensation Theorem | p. 166 |
5.3.3.1 Calculation of ¿ SVC in Control Region | p. 167 |
5.3.3.2 Network Solution | p. 168 |
5.3.4 Potential Energy Function for SVC | p. 169 |
5.3.5 Example | p. 171 |
5.3.6 Case Study of New England Test System | p. 172 |
5.3.6.1 Network Calculation with Multiple SVCs | p. 173 |
5.3.6.2 Structure Preserving Energy Function | p. 174 |
5.3.6.3 Results and Discussion | p. 175 |
5.4 Static Synchronous Compensator | p. 175 |
5.4.1 General | p. 175 |
5.4.2 Modeling of a STATCOM | p. 176 |
5.4.3 STATCOM Controller | p. 178 |
5.4.4 Potential Energy Function for a STATCOM | p. 180 |
5.5 Series-Connected FACTS Controllers | p. 181 |
5.5.1 Thyristor-Controlled Series Capacitor | p. 182 |
5.5.1.1 Power Scheduling Control | p. 182 |
5.5.1.2 Power Swing Damping Control | p. 183 |
5.5.1.3 Transient Stability Control | p. 183 |
5.5.2 Static Synchronous Series Compensator | p. 184 |
5.6 Potential Energy in a Line with Series FACTS Controllers | p. 185 |
5.6.1 Thyristor-Controlled Series Capacitor | p. 186 |
5.6.2 Static Synchronous Series Compensator | p. 187 |
5.6.3 Potential Energy in the Presence of CC and CA Controllers | p. 188 |
5.6.3.1 Potential Energy with CC Control | p. 188 |
5.6.3.2 Potential Energy with CA Control | p. 189 |
5.7 Unified Power Flow Controller | p. 189 |
5.7.1 Description | p. 189 |
5.7.2 Energy Function with Unified Power Flow Controller | p. 191 |
6 Detection of Instability Based on Identification of Critical Cutsets | p. 195 |
6.1 Introduction | p. 195 |
6.2 Basic Concepts | p. 196 |
6.3 Prediction of the Critical Cutset | p. 198 |
6.3.1 Analysis | p. 198 |
6.3.2 Case Study | p. 203 |
6.3.3 Discussion | p. 203 |
6.4 Detection of Instability by Monitoring Critical Cutset | p. 203 |
6.4.1 Criterion for Instability | p. 204 |
6.4.2 Modification of the Instability Criterion | p. 206 |
6.5 Algorithm for Identification of Critical Cutset | p. 207 |
6.6 Prediction of Instability | p. 209 |
6.7 Case Studies | p. 210 |
6.7.1 Ten-Generator New England Test System | p. 210 |
6.7.2 Seventeen-Generator IEEE Test System | p. 213 |
6.7.3 Discussion | p. 214 |
6.8 Study of a Practical System | p. 215 |
6.8.1 Discussion | p. 217 |
6.9 Adaptive System Protection | p. 219 |
6.9.1 Discussion | p. 225 |
7 Sensitivity Analysis for Dynamic Security and Preventive Control Using Damping Controllers Based on FACTS | p. 227 |
7.1 Introduction | p. 227 |
7.2 Basic Concepts in Sensitivity Analysis | p. 228 |
7.3 Dynamic Security Assessment Based on Energy Margin | p. 229 |
7.3.1 Transient Energy Margin | p. 229 |
7.3.2 Computation of Energy Margin | p. 229 |
7.3.2.1 Evaluation of Path-Dependent Integrals | p. 231 |
7.3.2.2 Computation of Energy Margin Based on Critical Cutsets | p. 231 |
7.4 Energy Margin Sensitivity | p. 232 |
7.4.1 Application to Structure Preserving Model | p. 232 |
7.5 Trajectory Sensitivity | p. 235 |
7.5.1 Sensitivity to Initial Condition Variations | p. 235 |
7.5.2 Discussion | p. 236 |
7.6 Energy Function-Based Design of Damping Controllers | p. 236 |
7.6.1 Series FACTS Controllers | p. 237 |
7.6.1.1 Linearized System Equations | p. 238 |
7.6.1.2 Synthesis of the Control Signal | p. 242 |
7.6.1.3 Case Study of a 10-Machine System | p. 244 |
7.6.2 Shunt FACTS Controllers | p. 245 |
7.6.2.1 Linear Network Model for Reactive Current | p. 247 |
7.7 Damping Controllers for UPFC | p. 251 |
7.7.1 Discussion | p. 254 |
8 Application of FACTS Controllers for Emergency Control-I | p. 255 |
8.1 Introduction | p. 255 |
8.2 Basic Concepts | p. 256 |
8.3 Switched Series Compensation | p. 257 |
8.3.1 Time-Optimal Control | p. 257 |
8.4 Control Strategy for a Two-Machine System | p. 260 |
8.5 Comparative Study of TCSC and SSSC | p. 264 |
8.5.1 Control Strategy | p. 265 |
8.6 Discrete Control of STATCOM | p. 269 |
8.7 Discrete Control of UPFC | p. 272 |
8.7.1 Application of Control Strategy to SMIB System with UPFC | p. 278 |
8.7.2 Discussion | p. 278 |
8.8 Improvement of Transient Stability by Static Phase-Shifting Transformer | p. 280 |
8.9 Emergency Control Measures | p. 282 |
8.9.1 Controlled System Separation and Load Shedding | p. 283 |
8.9.2 Generator Tripping | p. 284 |
9 Application of FACTS Controllers for Emergency Control-II | p. 285 |
9.1 Introduction | p. 285 |
9.2 Discrete Control Strategy | p. 285 |
9.3 Case Study I: Application of TCSC | p. 289 |
9.3.1 Fault at Bus 26: Without Line Tripping | p. 289 |
9.3.2 Fault at Bus 26: Cleared by Line Tripping | p. 292 |
9.4 Case Study II: Application of UPFC | p. 292 |
9.4.1 Single UPFC | p. 293 |
9.4.2 Multiple UPFC | p. 298 |
9.4.3 Practical Implementation | p. 299 |
9.5 Discussion and Directions for Further Research | p. 302 |
References | p. 305 |
Appendix A Synchronous Generator Model | p. 315 |
Appendix B Boundary of Stability Region: Theoretical Results | p. 327 |
Appendix C Network Solution for Transient Stability Analysis | p. 331 |
Appendix D Data for 10-Generator System | p. 341 |
Index | p. 345 |