Modern Power Systems Analysis (eBook)

139544_Wang_FM 2
Preface 5
Contents 5
139544_Wang_CH01 12
Chapter 1: Mathematical Model and Solution of Electric Network 12
1.1 Introduction 12
1.2 Basic Concepts 13
1.2.1 Node Equation and Loop Equation 13
1.2.2 Equivalent Circuit of Transformer and Phase-Shift Transformer 20
1.3 Nodal Admittance Matrix 24
1.3.1 Basic Concept of Nodal Admittance Matrix 24
1.3.2 Formulation and Modification of Nodal Admittance Matrix 28
1.4 Solution to Electric Network Equations 33
1.4.1 Gauss Elimination Method 33
1.4.2 Triangular Decomposition and Factor Table 38
1.4.3 Sparse Techniques 45
1.4.4 Sparse Vector Method 49
1.4.5 Optimal Ordering Schemes of Electric Network Nodes 54
1.5 Nodal Impedance Matrix 59
1.5.1 Basic Concept of Nodal Impedance Matrix 59
1.5.2 Forming Nodal Impedance Matrix by Using Nodal Admittance Matrix 61
1.5.3 Forming Nodal Impedance Matrix by Branch Addition Method 67
Thinking and Problem Solving 80
139544_Wang_CH02 82
Chapter 2: Load Flow Analysis 82
2.1 Introduction 82
2.2 Formulation of Load Flow Problem 84
2.2.1 Classification of Node Types 84
2.2.2 Node Power Equations 87
2.3 Load Flow Solution by Newton Method 89
2.3.1 Basic Concept of Newton Method 89
2.3.2 Correction Equations 94
2.3.3 Solution Process of Newton Method 99
2.3.4 Solution of Correction Equations 100
2.4 Fast Decoupled Method 112
2.4.1 Introduction to Fast Decoupled Method 112
2.4.2 Correction Equations of Fast Decoupled Method 115
2.4.3 Flowchart of Fast Decoupled Method 118
2.5 Static Security Analysis and Compensation Method 124
2.5.1 Survey of Static Security Analysis 124
2.5.2 Compensation Method 125
2.6 DC Load Flow Method 130
2.6.1 Model of DC Load Flow 131
2.6.2 Outage Analysis by DC Load Flow Method 133
2.6.3 N-1 Checking and Contingency Ranking Method 134
Thinking and Problem Solving 138
139544_Wang_CH03 140
Chapter 3: Stochastic Security Analysis of Electrical Power Systems 140
3.1 Introduction 140
3.2 Basic Concepts of Probability Theory 141
3.2.1 Probability of Stochastic Events 141
3.2.2 Random Variable and its Distribution 143
3.2.3 Numeral Characteristics of Random Variable 144
3.2.4 Convolution of Random Variable 146
3.2.5 Several Usual Random Variable Distributions 147
3.2.6 Markov Process 149
3.3 Probabilistic Model of Power Systems 151
3.3.1 Probabilistic Model of Load 151
3.3.2 Probabilistic Models of Power System Components 152
3.3.3 Outage Table of Power System Components 153
3.4 Monte Carlo Simulation Method 156
3.4.1 Fundamental Theory of Monte Carlo Simulation Method 156
3.4.2 Sampling of System Operation State 159
3.4.3 State Evaluation Model 161
3.4.4 Indices of Reliability Evaluation 162
3.4.5 Flowchart of Composite System Adequacy Evaluation 163
3.4.6 Markov Chain Monte Carlo (MCMC) Simulation Method 167
3.5 Probabilistic Load Flow Analysis 172
3.5.1 Cumulants of Random Distribution 173
3.5.2 Linearization of Load Flow Equation 179
3.5.3 Computing Process of Probabilistic Load Flow 182
3.6 Probabilistic Network-Flow Analysis 189
3.6.1 Introduction 189
3.6.2 Network-Flow Model 191
3.6.3 Lower Boundary Points of Feasible Flow Solutions 197
3.6.4 Reliability of Transmission System 199
Thinking and Problem Solving 202
139544_Wang_CH04 204
Chapter 4: Power Flow Analysis in Market Environment 204
4.1 Introduction 204
4.1.1 Transmission Owner 204
4.1.2 Independent Operator 205
4.1.3 Power Exchange 205
4.1.4 Ancillary Service 206
4.1.5 Scheduling Coordinator 206
4.2 Optimal Power Flow 207
4.2.1 General Formulation of OPF Problem 207
4.2.2 Approaches to OPF 209
4.2.3 Interior Point Method for OPF Problem 213
4.3 Application of OPF in Electricity Market 228
4.3.1 Survey 228
4.3.2 Congestion Management Method Based on OPF 234
4.4 Power Flow Tracing 239
4.4.1 Current Decomposition Axioms 241
4.4.2 Mathematical Model of Loss Allocation 243
4.4.3 Usage Sharing Problem of Transmission Facilities 245
4.4.4 Methodology of Graph Theory 249
4.5 Available Transfer Capability of Transmission System 252
4.5.1 Introduction to Available Transfer Capability 252
4.5.2 Application of Monte Carlo Simulation in ATC Calculation 256
4.5.3 ATC Calculation with Sensitivity Analysis Method 257
Thinking and Problem Solving 265
139544_Wang_CH05 266
Chapter 5: HVDC and FACTS 266
5.1 Introduction 266
5.2 HVDC Basic Principles and Mathematical Models 269
5.2.1 HVDC Basic Principles 269
5.2.2 Converter Basic Equations Neglecting Lc 272
5.2.3 Converter Basic Equations Considering Lc 278
5.2.4 Converter Equivalent Circuits 284
5.2.5 Multiple Bridge Operation 287
5.2.6 Converter Control 290
5.3 Power Flow Calculation of AC/DC Interconnected Systems 292
5.3.1 Converter Basic Equations in the per Unit System 293
5.3.2 Power Flow Equations 294
5.3.3 Jacobian Matrix of Power Flow Equations 297
5.3.4 Integrated Iteration Formula of AC/DC Interconnected Systems 300
5.3.5 Alternating Iteration for AC/DC Interconnected Systems 305
5.4 HVDC Dynamic Mathematical Models 310
5.5 Basic Principles and Mathematical Models of FACTS 312
5.5.1 Basic Principle and Mathematical Model of SVC 313
5.5.2 Basic Principle and Mathematical Model of STATCOM 319
5.5.3 Basic Principle and Mathematical Model of TCSC 324
5.5.4 Basic Principle and Mathematical Model of SSSC 330
5.5.5 Basic Principle and Mathematical Model of TCPST 333
5.5.6 Basic Principle and Mathematical Model of UPFC 336
Thinking and Problem Solving 342
139544_Wang_CH06 344
Chapter 6: Mathematical Model of Synchronous Generator and Load 344
6.1 Introduction 344
6.2 Mathematical Model of Synchronous Generator 346
6.2.1 Basic Mathematical Equations of Synchronous Generator 347
6.2.2 Mathematical Equations of Synchronous Generator Using Machine Parameters 354
6.2.3 Simplified Mathematical Model of Synchronous Generator 362
6.2.4 Steady-State Equations and Phasor Diagram 365
6.2.5 Mathematical Equations Considering Effect of Saturation• 368
6.2.6 Rotor Motion Equation of Synchronous Generator 371
6.3 Mathematical Model of Generator Excitation Systems 374
6.3.1 Mathematical Model of Exciter 376
6.3.2 Voltage Measurement and Load Compensation Unit 386
6.3.3 Limiters 387
6.3.4 Mathematical Model of Power System Stabilizer 388
6.3.5 Mathematical Model of Excitation Systems 388
6.4 Mathematical Model of Prime Mover and Governing System 392
6.4.1 Mathematical Model of Hydroturbine and Governing System 393
6.4.2 Mathematical Model of Steam Turbine and Governing System 400
6.5 Mathematical Model of Load 404
6.5.1 Static Load Model 406
6.5.2 Dynamic Load Model 408
Thinking and Problem Solving 414
139544_Wang_CH07 416
Chapter 7: Power System Transient Stability Analysis 416
7.1 Introduction 416
7.2 Numerical Methods for Transient Stability Analysis 418
7.2.1 Numerical Methods for Ordinary Differential Equations 419
7.2.2 Numerical Methods for Differential-Algebraic Equations 436
7.2.3 General Procedure for Transient Stability Analysis 438
7.3 Network Mathematical Model for Transient Stability Analysis 441
7.3.1 The Relationship Between Network and Dynamic Devices 442
7.3.2 Modeling Network Switching and Faults 450
7.4 Transient Stability Analysis with Simplified Model 457
7.4.1 Computing Initial Values 458
7.4.2 Solving Network Equations with Gauss Elimination Method 459
7.4.3 Solving Differential Equations by Modified Euler´s Method 461
7.4.4 Numerical Integration Methods for Transient Stability Analysis Under Classical Model 468
7.5 Transient Stability Analysis with FACTS Devices 474
7.5.1 Initial Values and Difference Equations of Generators 475
7.5.2 Initial Values and Difference Equations of FACTS and HVDC 486
7.5.3 Forming Network Equations 495
7.5.4 Simultaneous Solution of Difference and Network Equations 498
Thinking and Problem Solving 499
139544_Wang_CH08 500
Chapter 8: Small-Signal Stability Analysis of Power Systems 500
8.1 Introduction 500
8.2 Linearized Equations of Power System Dynamic Components 504
8.2.1 Linearized Equation of Synchronous Generator 504
8.2.2 Linearized Equation of Load 511
8.2.3 Linearized Equation of FACTS Components 513
8.2.4 Linearized Equation of HVDC Transmission System 514
8.3 Steps in Small-Signal Stability Analysis 517
8.3.1 Network Equation 517
8.3.2 Linearized Differential Equations of Whole Power System 519
8.3.3 Program Package for Small-Signal Stability Analysis 521
8.4 Eigenvalue Problem in Small-Signal Stability Analysis 530
8.4.1 Characteristics of State Matrix Given by Its Eigensolution 530
8.4.2 Modal Analysis of Linear Systems 534
8.4.3 Computation of Eigenvalues 537
8.4.4 Eigensolution of Sparse Matrix 541
8.4.5 Application of Eigenvalue Sensitivity Analysis 544
8.5 Oscillation Analysis of Power Systems 545
HeadingsSec31_8 545
139544_Wang_Ref 554
References 554
139544_Wang_Index 565
: Index 565