Modern power systems analysis / Xi-Fan Wang, Yonghua Song, Malcolm Irving.

Format:

Book

Author/Creator:

Wang, Xi-Fan.

Contributor:

Song, Yong-Hua.

Irving, Malcolm

Louis A. Duhring Fund.

Language:

English

Subjects (All):

Electric power systems.

System analysis.

Physical Description:

xi, 559 pages : illustrations ; 24 cm

Place of Publication:

New York : Springer, [2008]

Summary:

Modern Power Systems Analysis provides new theories, models, and algorithms for the analysis of electrical power systems. It features recent developments in this area such as power flow analysis in a market environment, calculation of AC/DC interconnected systems, control and calculation for FACTS devices, and stochastic security analysis. This work serves as a useful reference for the professional engineer and researcher involved in the operation and control of electrical power systems.

Contents:

1 Mathematical Model and Solution of Electric Network 1

1.2.1 Node Equation and Loop Equation 2

1.2.2 Equivalent Circuit of Transformer and Phase Shift Transformer 9

1.3 Nodal Admittance Matrix 13

1.3.1 Basic Concept of Nodal Admittance Matrix 13

1.3.2 Formulation and Modification of Nodal Admittance Matrix 17

1.4 Solution to Electric Network Equations 22

1.4.1 Gauss Elimination Method 22

1.4.2 Triangular Decomposition and Factor Table 27

1.4.3 Sparse Techniques 34

1.4.4 Sparse Vector Method 38

1.4.5 Optimal Ordering Schemes of Electric Network Nodes 43

1.5 Nodal Impedance Matrix 48

1.5.1 Basic Concept of Nodal Impedance Matrix 48

1.5.2 Forming Nodal Impedance Matrix Using Admittance Matrix 50

1.5.3 Forming Nodal Impedance Matrix by Branch Addition Method 56

2 Load Flow Analysis 71

2.2 Formulation of Load Flow Problem 73

2.2.1 Classification of Node Types 73

2.2.2 Node Power Equations 76

2.3 Load Flow Solution by Newton Method 79

2.3.1 Basic Concept of Newton Method 79

2.3.2 Correction Equations 83

2.3.3 Solution Process of Newton Method 88

2.3.4 Solution of Correction Equations 89

2.4 Fast Decoupled Method 101

2.4.1 Introduction to Fast Decoupled Method 101

2.4.2 Correction Equations of Fast Decoupled method 104

2.4.3 Flowchart of Fast Decoupled Method 107

2.5 Static Security Analysis and Compensation Method 113

2.5.1 Survey of Static Security Analysis 113

2.5.2 Compensation Method 114

2.6 DC Load Flow Method 119

2.6.1 Model of DC Load Flow 120

2.6.2 Outage Analysis by DC Load Flow Method 122

2.6.3 N-1 Checking and Contingency Ranking Method 123

3 Stochastic Security Analysis of Electrical Power Systems 129

3.2 Basic Concepts of Probability Theory 130

3.2.1 Probability of Stochastic Events 130

3.2.2 Random Variables and its Distribution 132

3.2.3 Numeral Character of Random Variable 133

3.2.4 Convolution of Random Variables 135

3.2.5 Several Usual Random Variable Distributions 136

3.2.6 Markov Process 138

3.3 Probabilistic Model of Power Systems 140

3.3.1 Probabilistic Model of Load 140

3.3.2 Probabilistic Model of Power System Components 141

3.3.3 Outage Table of Power System Components 142

3.4 Monte Carlo Simulation Method 145

3.4.1 Fundamental Theory of Monte Carlo Simulation Method 145

3.4.2 Sampling of System Operation State 148

3.4.3 State Evaluation Model 150

3.4.4 Indices of Reliability Evaluation 151

3.4.5 Flowchart of Composite System Adequacy Evaluation 152

3.4.6 Markov Chain Monte Carlo (MCMC) Simulation Method 156

3.5 Probabilistic Load Flow Analysis 161

3.5.1 Cumulants of Random Distribution 162

3.5.2 Linearization of Load Flow Equation 168

3.5.3 Computing Process of Probabilistic Load Flow 171

3.6 Probabilistic Network-Flow Analysis 178

3.6.2 Network-Flow Model 180

3.6.3 Lower Boundary Points of Feasible Flow Solutions 186

3.6.4 Reliability of Transmission System 188

4 Power Flow Analysis in Market Environment 193

4.1.1 Transmission Owner 193

4.1.2 Independent Operator 194

4.1.3 Power Exchange 194

4.1.4 Ancillary Service 195

4.1.5 Scheduling Coordinator 195

4.2 Optimal Power Flow 196

4.2.1 General Formulation of OPF Problem 196

4.2.2 Approaches to OPF 198

4.2.3 Interior Point Method (IPM) for OPF Problem 202

4.3 Application of Optimal Power Flow in Electricity Market 217

4.3.1 Survey 217

4.3.2 Congestion Management Method Based On OPF 223

4.4 Power Flow Tracing 228

4.4.1 Current Decomposition Axioms 230

4.4.2 Mathematical Model of Loss Allocation 232

4.4.3 Usage Sharing Problem of Transmission Facilities 234

4.4.4 Methodology of Graph Theory 238

4.5 Available Transfer Capability of Transmission System 241

4.5.1 Introduction To Available Transfer Capability 241

4.5.2 Application of Monte Carlo Simulation in ATC Calculation 245

4.5.3 ATC Calculation with Sensitivity Analysis Method 246

5 HVDC and FACTS 255

5.2 HVDC Basic Principles and Mathematical Models 258

5.2.1 HVDC Basic Principles 258

5.2.2 Converter Basic Equations Neglecting Lc 261

5.2.3 Converter Basic Equations Considering Lc 267

5.2.4 Converter Equivalent Circuits 273

5.2.5 Multiple Bridge Operation 276

5.2.6 Converter Control 279

5.3 Power Flow Calculation of AC/DC Interconnected Systems 281

5.3.1 Converter Basic Equations in per Unit System 282

5.3.2 Power Flow Equations 283

5.3.3 Jacobian Matrix of Power Flow Equations 286

5.3.4 Integrated Iteration formula of AC/DC Interconnected Systems 289

5.3.5 Alternating Iteration for AC/DC Interconnected Systems 294

5.4 HVDC Dynamic Mathematical Models 299

5.5 Basic Principles and Mathematical Models of FACTS 301

5.5.1 Basic Principle and Mathematical Model of SVC 302

5.5.2 Basic Principle and Mathematical Model of STATCOM 308

5.5.3 Basic Principle and Mathematical Model of TCSC 313

5.5.4 Basic Principle and Mathematical Model of SSSC 319

5.5.5 Basic Principle and Mathematical Model of TCPST 322

5.5.6 Basic Principle and Mathematical Model of UPFC 325

6 Mathematical Model of Synchronous Generator and Load 333

6.2 Mathematical Model of Synchronous Generator 335

6.2.1 Basic Mathematical Equations of Synchronous Generator 336

6.2.2 Mathematical Equations of Synchronous Generator Using Machine Parameters 343

6.2.3 Simplified Mathematical Model of Synchronous Generator 351

6.2.4 Steady-State Equations and Phasor Diagram 354

6.2.5 Mathematical Equations Considering Effect of Saturation 357

6.2.6 Rotor Motion Equation of Synchronous Generator 360

6.3 Mathematical Model of Generator Excitation Systems 363

6.3.1 Mathematical Model of Exciter 365

6.3.2 Voltage Measurement and Load Compensation Unit 375

6.3.3 Limiters 376

6.3.4 Mathematical Model of Power System Stabilizer 377

6.3.5 Mathematical Model of Excitation Systems 377

6.4 Mathematical Model of Prime Mover and Governing System 381

6.4.1 Mathematical Model of Hydro-Turbine and Governing System 382

6.4.2 Mathematical Model of Steam Turbine and Governing System 389

6.5 Mathematical Model of Load 393

6.5.1 Static Load Model 395

6.5.2 Dynamic Load Model 397

7 Power System Transient Stability Analysis 405

7.2 Numerical Methods for Transient Stability Analysis 407

7.2.1 Numerical Methods for Ordinary Differential Equations 408

7.2.2 Numerical Methods for Differential-Algebraic Equations 425

7.2.3 General Procedure for Transient Stability Analysis 427

7.3 Network Mathematical Model for Transient Stability Analysis 430

7.3.1 The Relationship Between Network and Dynamic Devices 431

7.3.2 Modeling Network Switching and Faults 439

7.4 Transient Stability Analysis with Simplified Model 446

7.4.1 Computing Initial Values 447

7.4.2 Solving Network Equations with Direct Method 448

7.4.3 Solving Differential Equations by Modified Euler Method 450

7.4.4 Numerical Integration Methods for Transient Stability Analysis under Classical Model 457

7.5 Transient Stability Analysis with FACTS Devices 463

7.5.1 Initial Values and Difference Equations of Generators 464

7.5.2 Initial Values and Difference Equations of FACTS and HVDC 475

7.5.3 Forming Network Equations 484

7.5.4 Simultaneous Solution of Difference and Network Equations 487

8 Small-Signal Stability Analysis of Power Systems 489

8.2 Linearized Equations of Power System Dynamic Components 493

8.2.1 Linearized Equation of Synchronous Generator 493

8.2.2 Linearized Equation of Load 500

8.2.3 Linearized Equation of FACTS Components 502

8.2.4 Linearized Equation of HVDC Transmission System 503

8.3 Steps in Small-Signal Stability Analysis 506

8.3.1 Network Equation 506

8.3.2 Linearized Differential Equations of Whole Power System 508

8.3.3 Program Package for Small-Signal Stability Analysis 510

8.4 Eigenvalue Problem in

Small-Signal Stability Analysis 519

8.4.1 Characteristics of State Matrix Given by Its Eigensolution 519

8.4.2 Modal Analysis of Linear Systems 523

8.4.3 Computation of Eigenvalues 526

8.4.4 Eigensolution of Sparse Matrix 530

8.4.5 Application of Eigenvalue Sensitivity Analysis 533

8.5 Oscillation Analysis of Power Systems 534.

Notes:

Includes bibliographical referecnes (pages 543-553) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Louis A. Duhring Fund.

ISBN:

9780387728520

038772852X

OCLC:

154711992