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Cover image for Structure preserving energy functions in power systems : theory and applications
Title:
Structure preserving energy functions in power systems : theory and applications
Personal Author:
Publication Information:
Boca Raton : Taylor & Francis, 2013
Physical Description:
xxii, 358 p. : ill. ; 24 cm.
ISBN:
9781439879368

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30000010322207 TK1007 P33 2013 Open Access Book Book
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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 components

The 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

Prefacep. xiii
Acknowledgmentsp. xvii
Authorp. xix
Abbreviations and Acronymsp. xxi
1 Introductionp. 1
1.1 Generalp. 1
1.2 Power System Stabilityp. 2
1.3 Power System Securityp. 3
1.4 Monitoring and Enhancing System Securityp. 6
1.5 Emergency Control and System Protectionp. 7
1.6 Application of Energy Functionsp. 8
1.7 Scope of This Bookp. 14
2 Review of Direct Methods for Transient Stability Evaluations for Systems with Simplified Modelsp. 17
2.1 Introductionp. 17
2.2 System Modelp. 18
2.2.1 Synchronous Generatorsp. 18
2.2.2 Network Equationsp. 21
2.2.3 Load Modelp. 22
2.2.4 Expressions for Electrical Powerp. 23
2.3 Mathematical Preliminariesp. 25
2.3.1 Equilibrium Pointsp. 26
2.3.2 Stability of Equilibrium Pointp. 27
2.3.3 Lyapunov Stabilityp. 27
2.3.4 Theorem on Lyapunov Stabilityp. 27
2.4 Two-Machine System and Equal Area Criterionp. 30
2.4.1 Equal Area Criterionp. 31
2.4.2 Energy Function Analysis of an SMIB Systemp. 32
2.5 Lyapunov Functions for Direct Stability Evaluationp. 34
2.5.1 Construction of Lyapunov Functionp. 38
2.6 Energy Functions for Multimachine Power Systemsp. 39
2.6.1 Characterization of Transient Stabilityp. 39
2.6.2 Center of Inertia Formulationsp. 40
2.6.3 Energy Function Using COI Formulationp. 43
2.7 Estimation of Stability Domainp. 44
2.7.1 Incorporating Transfer Conductances in Energy Functionp. 44
2.7.2 Determination of Critical Energyp. 46
2.7.2.1 Single-Machine Systemp. 46
2.7.2.2 Multimachine Systemp. 48
2.7.3 Potential Energy Boundary Surfacep. 48
2.7.4 Controlling UEP Methodp. 50
2.7.5 BCU Methodp. 51
2.8 Extended Equal Area Criterionp. 53
2.8.1 Formulationp. 53
2.8.2 Approximation of Faulted Trajectoryp. 54
2.8.3 Identification of Critical Clusterp. 55
3 Structure Preserving Energy Functions for Systems with Nonlinear Load Models and Generator Flux Decayp. 57
3.1 Introductionp. 57
3.2 Structure Preserving Modelp. 57
3.3 Inclusion of Voltage-Dependent Power Loadsp. 61
3.4 SPEF with Voltage-Dependent Load Modelsp. 62
3.4.1 Dynamic Equations of Generatorp. 62
3.4.2 Load Modelp. 63
3.4.3 Power Flow Equationsp. 64
3.4.4 Structure Preserving Energy Functionsp. 64
3.4.5 Computation of Stability Regionp. 68
3.5 Case Studies on IEEE Test Systemsp. 69
3.5.1 Seventeen-Generator Systemp. 70
3.5.2 Fifty-Generator Systemp. 74
3.6 Solution of System Equations during a Transientp. 76
3.7 Noniterative Solution of Networks with Nonlinear Loadsp. 77
3.7.1 System Equationsp. 78
3.7.2 Dynamic Equations of Generatorsp. 78
3.7.3 Power Flow Equations during a Transientp. 79
3.7.4 Special Casesp. 81
3.7.5 Solutions of the Quartic Equationp. 82
3.7.6 Network Transformation for Decoupling of Load Busesp. 83
3.7.7 Transformation of the Load Characteristicsp. 84
3.8 Inclusion of Transmission Losses in Energy Functionp. 85
3.8.1 Transformation of a Lossy Networkp. 85
3.8.2 Structure Preserving Energy Function Incorporating Transmission Line Resistancesp. 87
3.9 SPEF for Systems with Generator Flux Decayp. 90
3.9.1 System Modelp. 90
3.9.1.1 Generator Modelp. 91
3.9.1.2 Load Modelp. 92
3.9.1.3 Power Flow Equationsp. 92
3.9.2 Structure Preserving Energy Functionp. 93
3.9.3 Examplep. 96
3.10 Network Analogy for System Stability Analysisp. 97
4 Structure Preserving Energy Functions for Systems with Detailed Generator and Load Modelsp. 105
4.1 Introductionp. 105
4.2 System Modelp. 106
4.2.1 Generator Modelp. 106
4.2.2 Excitation System Modelp. 107
4.2.3 Load Modelp. 108
4.2.4 Power Flow Equationsp. 108
4.3 Structure Preserving Energy Function with Detailed Generator Modelsp. 109
4.3.1 Structure Preserving Energy Functionp. 109
4.3.2 Simpler Expression for SPEFp. 112
4.4 Numerical Examplesp. 114
4.4.1 SMIB Systemp. 114
4.4.2 Ten-Generator, 39-Bus New England Test Systemp. 115
4.4.3 Variation of Total Energy and Its Componentsp. 121
4.5 Modeling of Dynamic Loadsp. 122
4.5.1 Induction Motor Modelp. 124
4.5.2 Voltage Instability in Induction Motorsp. 126
4.5.3 Simpler Models of Induction Motorsp. 128
4.5.4 Energy Function Analysis of Synchronous and Voltage Stabilityp. 128
4.5.4.1 Computation of Equilibrium Pointsp. 130
4.5.4.2 Computation of Energy at UEPp. 132
4.5.5 Dynamic Load Models in Multimachine Power Systemsp. 135
4.6 New Results on SPEF Based on Network Analogyp. 136
4.6.1 Potential Energy Contributed by Considering the Two-Axis Model of the Synchronous Generatorp. 140
4.7 Unstable Modes and Parametric Resonancep. 144
4.7.1 Normal Formsp. 145
4.7.2 Fast Fourier Transform of Potential Energyp. 146
4.7.2.1 Results of the Case Studyp. 146
5 Structure Preserving Energy Functions for Systems with HVDC and FACTS Controllersp. 149
5.1 Introductionp. 149
5.2 HVDC Power Transmission Linksp. 149
5.2.1 HVDC Systems and Energy Functionsp. 149
5.2.2 HVDC System Modelp. 150
5.2.2.1 Converter Modelp. 150
5.2.2.2 DC Network Equationsp. 152
5.2.2.3 Converter Control Modelp. 152
5.2.3 AC System Modelp. 155
5.2.3.1 Generator Modelp. 155
5.2.3.2 Load Modelp. 156
5.2.3.3 AC Network Equationsp. 156
5.2.4 Structure Preserving Energy Functionp. 156
5.2.5 Examplep. 160
5.2.5.1 Auxiliary Controllerp. 161
5.2.5.2 Emergency Controllerp. 162
5.2.5.3 Case Study and Resultsp. 162
5.3 Static Var Compensatorp. 163
5.3.1 Descriptionp. 163
5.3.2 Control Characteristics and Modeling of SVC Controllerp. 164
5.3.3 Network Solution with SVC: Application of Compensation Theoremp. 166
5.3.3.1 Calculation of ¿ SVC in Control Regionp. 167
5.3.3.2 Network Solutionp. 168
5.3.4 Potential Energy Function for SVCp. 169
5.3.5 Examplep. 171
5.3.6 Case Study of New England Test Systemp. 172
5.3.6.1 Network Calculation with Multiple SVCsp. 173
5.3.6.2 Structure Preserving Energy Functionp. 174
5.3.6.3 Results and Discussionp. 175
5.4 Static Synchronous Compensatorp. 175
5.4.1 Generalp. 175
5.4.2 Modeling of a STATCOMp. 176
5.4.3 STATCOM Controllerp. 178
5.4.4 Potential Energy Function for a STATCOMp. 180
5.5 Series-Connected FACTS Controllersp. 181
5.5.1 Thyristor-Controlled Series Capacitorp. 182
5.5.1.1 Power Scheduling Controlp. 182
5.5.1.2 Power Swing Damping Controlp. 183
5.5.1.3 Transient Stability Controlp. 183
5.5.2 Static Synchronous Series Compensatorp. 184
5.6 Potential Energy in a Line with Series FACTS Controllersp. 185
5.6.1 Thyristor-Controlled Series Capacitorp. 186
5.6.2 Static Synchronous Series Compensatorp. 187
5.6.3 Potential Energy in the Presence of CC and CA Controllersp. 188
5.6.3.1 Potential Energy with CC Controlp. 188
5.6.3.2 Potential Energy with CA Controlp. 189
5.7 Unified Power Flow Controllerp. 189
5.7.1 Descriptionp. 189
5.7.2 Energy Function with Unified Power Flow Controllerp. 191
6 Detection of Instability Based on Identification of Critical Cutsetsp. 195
6.1 Introductionp. 195
6.2 Basic Conceptsp. 196
6.3 Prediction of the Critical Cutsetp. 198
6.3.1 Analysisp. 198
6.3.2 Case Studyp. 203
6.3.3 Discussionp. 203
6.4 Detection of Instability by Monitoring Critical Cutsetp. 203
6.4.1 Criterion for Instabilityp. 204
6.4.2 Modification of the Instability Criterionp. 206
6.5 Algorithm for Identification of Critical Cutsetp. 207
6.6 Prediction of Instabilityp. 209
6.7 Case Studiesp. 210
6.7.1 Ten-Generator New England Test Systemp. 210
6.7.2 Seventeen-Generator IEEE Test Systemp. 213
6.7.3 Discussionp. 214
6.8 Study of a Practical Systemp. 215
6.8.1 Discussionp. 217
6.9 Adaptive System Protectionp. 219
6.9.1 Discussionp. 225
7 Sensitivity Analysis for Dynamic Security and Preventive Control Using Damping Controllers Based on FACTSp. 227
7.1 Introductionp. 227
7.2 Basic Concepts in Sensitivity Analysisp. 228
7.3 Dynamic Security Assessment Based on Energy Marginp. 229
7.3.1 Transient Energy Marginp. 229
7.3.2 Computation of Energy Marginp. 229
7.3.2.1 Evaluation of Path-Dependent Integralsp. 231
7.3.2.2 Computation of Energy Margin Based on Critical Cutsetsp. 231
7.4 Energy Margin Sensitivityp. 232
7.4.1 Application to Structure Preserving Modelp. 232
7.5 Trajectory Sensitivityp. 235
7.5.1 Sensitivity to Initial Condition Variationsp. 235
7.5.2 Discussionp. 236
7.6 Energy Function-Based Design of Damping Controllersp. 236
7.6.1 Series FACTS Controllersp. 237
7.6.1.1 Linearized System Equationsp. 238
7.6.1.2 Synthesis of the Control Signalp. 242
7.6.1.3 Case Study of a 10-Machine Systemp. 244
7.6.2 Shunt FACTS Controllersp. 245
7.6.2.1 Linear Network Model for Reactive Currentp. 247
7.7 Damping Controllers for UPFCp. 251
7.7.1 Discussionp. 254
8 Application of FACTS Controllers for Emergency Control-Ip. 255
8.1 Introductionp. 255
8.2 Basic Conceptsp. 256
8.3 Switched Series Compensationp. 257
8.3.1 Time-Optimal Controlp. 257
8.4 Control Strategy for a Two-Machine Systemp. 260
8.5 Comparative Study of TCSC and SSSCp. 264
8.5.1 Control Strategyp. 265
8.6 Discrete Control of STATCOMp. 269
8.7 Discrete Control of UPFCp. 272
8.7.1 Application of Control Strategy to SMIB System with UPFCp. 278
8.7.2 Discussionp. 278
8.8 Improvement of Transient Stability by Static Phase-Shifting Transformerp. 280
8.9 Emergency Control Measuresp. 282
8.9.1 Controlled System Separation and Load Sheddingp. 283
8.9.2 Generator Trippingp. 284
9 Application of FACTS Controllers for Emergency Control-IIp. 285
9.1 Introductionp. 285
9.2 Discrete Control Strategyp. 285
9.3 Case Study I: Application of TCSCp. 289
9.3.1 Fault at Bus 26: Without Line Trippingp. 289
9.3.2 Fault at Bus 26: Cleared by Line Trippingp. 292
9.4 Case Study II: Application of UPFCp. 292
9.4.1 Single UPFCp. 293
9.4.2 Multiple UPFCp. 298
9.4.3 Practical Implementationp. 299
9.5 Discussion and Directions for Further Researchp. 302
Referencesp. 305
Appendix A Synchronous Generator Modelp. 315
Appendix B Boundary of Stability Region: Theoretical Resultsp. 327
Appendix C Network Solution for Transient Stability Analysisp. 331
Appendix D Data for 10-Generator Systemp. 341
Indexp. 345
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