Modern power systems analysis

The capability of effectively analyzing complex systems is fundamental to the operation, management and planning of power systems. This book offers broad coverage of essential power system concepts and features a complete and in-depth account of all the latest developments, including Power Flow Analysis in Market Environment; Power Flow Calculation of AC/DC Interconnected Systems and Power Flow Control and Calculation for Systems Having FACTS Devices and recent results in system stability.

1 Mathematical Model and Solution of Electric Network	p. 1
1.1 Introduction	p. 1
1.2 Basic Concepts	p. 2
1.2.1 Node Equation and Loop Equation	p. 2
1.2.2 Equivalent Circuit of Transformer and Phase Shift Transformer	p. 9
1.3 Nodal Admittance Matrix	p. 13
1.3.1 Basic Concept of Nodal Admittance Matrix	p. 13
1.3.2 Formulation and Modification of Nodal Admittance Matrix	p. 17
1.4 Solution to Electric Network Equations	p. 22
1.4.1 Gauss Elimination Method	p. 22
1.4.2 Triangular Decomposition and Factor Table	p. 27
1.4.3 Sparse Techniques	p. 34
1.4.4 Sparse Vector Method	p. 38
1.4.5 Optimal Ordering Schemes of Electric Network Nodes	p. 43
1.5 Nodal Impedance Matrix	p. 48
1.5.1 Basic Concept of Nodal Impedance Matrix	p. 48
1.5.2 Forming Nodal Impedance Matrix Using Admittance Matrix	p. 50
1.5.3 Forming Nodal Impedance Matrix by Branch Addition Method	p. 56
2 Load Flow Analysis	p. 71
2.1 Introduction	p. 71
2.2 Formulation of Load Flow Problem	p. 73
2.2.1 Classification of Node Types	p. 73
2.2.2 Node Power Equations	p. 76
2.3 Load Flow Solution by Newton Method	p. 79
2.3.1 Basic Concept of Newton Method	p. 79
2.3.2 Correction Equations	p. 83
2.3.3 Solution Process of Newton Method	p. 88
2.3.4 Solution of Correction Equations	p. 89
2.4 Fast Decoupled Method	p. 101
2.4.1 Introduction to Fast Decoupled Method	p. 101
2.4.2 Correction Equations of Fast Decoupled method	p. 104
2.4.3 Flowchart of Fast Decoupled Method	p. 107
2.5 Static Security Analysis and Compensation Method	p. 113
2.5.1 Survey of Static Security Analysis	p. 113
2.5.2 Compensation Method	p. 114
2.6 DC Load Flow Method	p. 119
2.6.1 Model of DC Load Flow	p. 120
2.6.2 Outage Analysis by DC Load Flow Method	p. 122
2.6.3 N-1 Checking and Contingency Ranking Method	p. 123
3 Stochastic Security Analysis of Electrical Power Systems	p. 129
3.1 Introduction	p. 129
3.2 Basic Concepts of Probability Theory	p. 130
3.2.1 Probability of Stochastic Events	p. 130
3.2.2 Random Variables and its Distribution	p. 132
3.2.3 Numeral Character of Random Variable	p. 133
3.2.4 Convolution of Random Variables	p. 135
3.2.5 Several Usual Random Variable Distributions	p. 136
3.2.6 Markov Process	p. 138
3.3 Probabilistic Model of Power Systems	p. 140
3.3.1 Probabilistic Model of Load	p. 140
3.3.2 Probabilistic Model of Power System Components	p. 141
3.3.3 Outage Table of Power System Components	p. 142
3.4 Monte Carlo Simulation Method	p. 145
3.4.1 Fundamental Theory of Monte Carlo Simulation Method	p. 145
3.4.2 Sampling of System Operation State	p. 148
3.4.3 State Evaluation Model	p. 150
3.4.4 Indices of Reliability Evaluation	p. 151
3.4.5 Flowchart of Composite System Adequacy Evaluation	p. 152
3.4.6 Markov Chain Monte Carlo (MCMC) Simulation Method	p. 156
3.5 Probabilistic Load Flow Analysis	p. 161
3.5.1 Cumulants of Random Distribution	p. 162
3.5.2 Linearization of Load Flow Equation	p. 168
3.5.3 Computing Process of Probabilistic Load Flow	p. 171
3.6 Probabilistic Network-Flow Analysis	p. 178
3.6.1 Introduction	p. 178
3.6.2 Network-Flow Model	p. 180
3.6.3 Lower Boundary Points of Feasible Flow Solutions	p. 186
3.6.4 Reliability of Transmission System	p. 188
4 Power Flow Analysis in Market Environment	p. 193
4.1 Introduction	p. 193
4.1.1 Transmission Owner	p. 193
4.1.2 Independent Operator	p. 194
4.1.3 Power Exchange	p. 194
4.1.4 Ancillary Service	p. 195
4.1.5 Scheduling Coordinator	p. 195
4.2 Optimal Power Flow	p. 196
4.2.1 General Formulation of OPF Problem	p. 196
4.2.2 Approaches to OPF	p. 198
4.2.3 Interior Point Method (IPM) for OPF Problem	p. 202
4.3 Application of Optimal Power Flow in Electricity Market	p. 217
4.3.1 Survey	p. 217
4.3.2 Congestion Management Method Based On OPF	p. 223
4.4 Power Flow Tracing	p. 228
4.4.1 Current Decomposition Axioms	p. 230
4.4.2 Mathematical Model of Loss Allocation	p. 232
4.4.3 Usage Sharing Problem of Transmission Facilities	p. 234
4.4.4 Methodology of Graph Theory	p. 238
4.5 Available Transfer Capability of Transmission System	p. 241
4.5.1 Introduction To Available Transfer Capability	p. 241
4.5.2 Application of Monte Carlo Simulation in ATC Calculation	p. 245
4.5.3 ATC Calculation with Sensitivity Analysis Method	p. 246
5 HVDC and FACTS	p. 255
5.1 Introduction	p. 255
5.2 HVDC Basic Principles and Mathematical Models	p. 258
5.2.1 HVDC Basic Principles	p. 258
5.2.2 Converter Basic Equations Neglecting Lc	p. 261
5.2.3 Converter Basic Equations Considering Lc	p. 267
5.2.4 Converter Equivalent Circuits	p. 273
5.2.5 Multiple Bridge Operation	p. 276
5.2.6 Converter Control	p. 279
5.3 Power Flow Calculation of AC/DC Interconnected Systems	p. 281
5.3.1 Converter Basic Equations in per Unit System	p. 282
5.3.2 Power Flow Equations	p. 283
5.3.3 Jacobian Matrix of Power Flow Equations	p. 286
5.3.4 Integrated Iteration formula of AC/DC Interconnected Systems	p. 289
5.3.5 Alternating Iteration for AC/DC Interconnected Systems	p. 294
5.4 HVDC Dynamic Mathematical Models	p. 299
5.5 Basic Principles and Mathematical Models of FACTS	p. 301
5.5.1 Basic Principle and Mathematical Model of SVC	p. 302
5.5.2 Basic Principle and Mathematical Model of STATCOM	p. 308
5.5.3 Basic Principle and Mathematical Model of TCSC	p. 313
5.5.4 Basic Principle and Mathematical Model of SSSC	p. 319
5.5.5 Basic Principle and Mathematical Model of TCPST	p. 322
5.5.6 Basic Principle and Mathematical Model of UPFC	p. 325
6 Mathematical Model of Synchronous Generator and Load	p. 333
6.1 Introduction	p. 333
6.2 Mathematical Model of Synchronous Generator	p. 335
6.2.1 Basic Mathematical Equations of Synchronous Generator	p. 336
6.2.2 Mathematical Equations of Synchronous Generator Using Machine Parameters	p. 343
6.2.3 Simplified Mathematical Model of Synchronous Generator	p. 351
6.2.4 Steady-State Equations and Phasor Diagram	p. 354
6.2.5 Mathematical Equations Considering Effect of Saturation	p. 357
6.2.6 Rotor Motion Equation of Synchronous Generator	p. 360
6.3 Mathematical Model of Generator Excitation Systems	p. 363
6.3.1 Mathematical Model of Exciter	p. 365
6.3.2 Voltage Measurement and Load Compensation Unit	p. 375
6.3.3 Limiters	p. 376
6.3.4 Mathematical Model of Power System Stabilizer	p. 377
6.3.5 Mathematical Model of Excitation Systems	p. 377
6.4 Mathematical Model of Prime Mover and Governing System	p. 381
6.4.1 Mathematical Model of Hydro-Turbine and Governing System	p. 382
6.4.2 Mathematical Model of Steam Turbine and Governing System	p. 389
6.5 Mathematical Model of Load	p. 393
6.5.1 Static Load Model	p. 395
6.5.2 Dynamic Load Model	p. 397
7 Power System Transient Stability Analysis	p. 405
7.1 Introduction	p. 405
7.2 Numerical Methods for Transient Stability Analysis	p. 407
7.2.1 Numerical Methods for Ordinary Differential Equations	p. 408
7.2.2 Numerical Methods for Differential-Algebraic Equations	p. 425
7.2.3 General Procedure for Transient Stability Analysis	p. 427
7.3 Network Mathematical Model for Transient Stability Analysis	p. 430
7.3.1 The Relationship Between Network and Dynamic Devices	p. 431
7.3.2 Modeling Network Switching and Faults	p. 439
7.4 Transient Stability Analysis with Simplified Model	p. 446
7.4.1 Computing Initial Values	p. 447
7.4.2 Solving Network Equations with Direct Method	p. 448
7.4.3 Solving Differential Equations by Modified Euler Method	p. 450
7.4.4 Numerical Integration Methods for Transient Stability Analysis under Classical Model	p. 457
7.5 Transient Stability Analysis with FACTS Devices	p. 463
7.5.1 Initial Values and Difference Equations of Generators	p. 464
7.5.2 Initial Values and Difference Equations of FACTS and HVDC	p. 475
7.5.3 Forming Network Equations	p. 484
7.5.4 Simultaneous Solution of Difference and Network Equations	p. 487
8 Small-Signal Stability Analysis of Power Systems	p. 489
8.1 Introduction	p. 489
8.2 Linearized Equations of Power System Dynamic Components	p. 493
8.2.1 Linearized Equation of Synchronous Generator	p. 493
8.2.2 Linearized Equation of Load	p. 500
8.2.3 Linearized Equation of FACTS Components	p. 502
8.2.4 Linearized Equation of HVDC Transmission System	p. 503
8.3 Steps in Small-Signal Stability Analysis	p. 506
8.3.1 Network Equation	p. 506
8.3.2 Linearized Differential Equations of Whole Power System	p. 508
8.3.3 Program Package for Small-Signal Stability Analysis	p. 510
8.4 Eigenvalue Problem in Small-Signal Stability Analysis	p. 519
8.4.1 Characteristics of State Matrix Given by Its Eigensolution	p. 519
8.4.2 Modal Analysis of Linear Systems	p. 523
8.4.3 Computation of Eigenvalues	p. 526
8.4.4 Eigensolution of Sparse Matrix	p. 530
8.4.5 Application of Eigenvalue Sensitivity Analysis	p. 533
8.5 Oscillation Analysis of Power Systems	p. 534
References	p. 543
Index	p. 555

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