FACTS Modelling and Simulation in Power Networks

, by Acha, Enrique; Fuerte-Esquivel, Claudio R.; Ambriz-Pé; rez, Hugo; Angeles-Camacho, Cesar

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ISBN: 9780470852712 | 0470852712
Cover: Hardcover
Copyright: 3/26/2004

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The first book to provide comprehensive coverage of FACTS power systems modeling and simulation.* Detailed coverage of the development of FACTS controllers and guidance on the selection of appropriate equipment* Computer modelling examples of the FACTS controllers for steady-state and transient stability systems* Numerous case studies and practical examples

Preface

xiii

1 Introduction

(8)

1.1 Background

(1)

1.2 Flexible Alternating Current Transmission Systems

(1)

1.3 Inherent Limitations of Transmission Systems

(1)

1.4 FACTS Controllers

(3)

1.5 Steady-state Power System Analysis

(1)

References

(3)

2 Modelling of FACTS Controllers

(34)

2.1 Introduction

(2)

2.2 Modelling Philosophy

(1)

2.3 Controllers Based on Conventional Thyristors

(17)

2.3.1 The Thyristor-controlled Reactor

(4)

2.3.2 The Static VAR Compensator

(2)

2.3.3 The Thyristor-controlled Series Compensator

(10)

2.3.3.1 Thyristor-controlled Series Capacitor Equivalent Circuit

(1)

2.3.3.2 Steady-state Current and Voltage Equations

(4)

2.3.3.3 Thyristor-controlled Series Capacitor Fundamental Frequency Impedance

(4)

2.4 Power Electronic Controllers Based on Fully Controlled Semiconductor Devices

(12)

2.4.1 The Voltage Source Converter

(5)

2.4.1.1 Pulse-width Modulation Control

(3)

2.4.1.2 Principles of Voltage Source Converter Operation

(1)

2.4.2 The Static Compensator

(1)

2.4.3 The Solid State Series Compensator

(1)

2.4.4 The Unified Power Flow Controller

(2)

2.4.5 The High-voltage Direct-current Based on Voltage Source Converters

(2)

2.5 Control Capabilities of Controllers Based on Voltage Source Converters

(1)

2.6 Summary

(1)

References

(2)

3 Modelling of Conventional Power Plant

(50)

3.1 Introduction

(1)

3.2 Transmission Line Modelling

(26)

3.2.1 The Voltage-drop Equation

(5)

3.2.1.1 Calculation of Lumped RLC Parameters

(2)

3.2.1.2 Shunt Admittances

(1)

3.2.1.3 Internal Impedances

(1)

3.2.1.4 Ground Return Impedances

(2)

3.2.2 Ground Wires

(1)

3.2.3 Bundle Conductors

(3)

3.2.4 Double Circuit Transmission Lines

(1)

3.2.5 The Per-unit System

(1)

3.2.6 Transmission-line Program: Basic Parameters

(3)

3.2.7 Numerical Example of Transmission Line Parameter Calculation

(1)

3.2.8 Long Line Effects

(2)

3.2.9 Transmission Line Transpositions

(1)

3.2.10 Transmission Line Program: Distributed Parameters

(3)

3.2.11 Numerical Example of Long Line Parameter Calculation

(1)

3.2.12 Symmetrical Components and Sequence Domain Parameters

(2)

3.2.13 Transmission Line Program: Sequence Parameters

(1)

3.2.14 Numerical Example of Sequence Parameter Calculation

(1)

3.3 Power Transformer Modelling

(12)

3.3.1 Single-phase Transformers

(2)

3.3.2 Simple Tap-changing Transformer

(1)

3.3.3 Advanced Tap-changing Transformer

(2)

3.3.4 Three-phase Transformers

(4)

3.3.4.1 Star-Star Connection

(2)

3.3.4.2 Delta-Delta Connection

(1)

3.3.4.3 Star-Delta Connection

(1)

3.3.5 Sequence Domain Parameters

(3)

3.4 Rotating Machinery Modelling

(4)

3.4.1 Machine Voltage Equation

(3)

3.5 System Load

(3)

3.6 Summary

(1)

References

(3)

4 Conventional Power Flow

(60)

4.1 Introduction

(1)

4.2 General Power Flow Concepts

(4)

4.2.1 Basic Formulation

(3)

4.2.2 Variables and Bus Classification

(1)

4.3 Power Flow Solution Methods

(22)

4.3.1 Early Power Flow Algorithms

(1)

4.3.2 The Newton-Raphson Algorithm

(3)

4.3.3 State Variable Initialisation

101

(1)

4.3.4 Generator Reactive Power Limits

101

(1)

4.3.5 Linearised Frame of Reference

102

(2)

4.3.6 Newton-Raphson Computer Program in Matlab® Code

104

(7)

4.3.7 The Fast Decoupled Algorithm

111

(1)

4.3.8 Fast Decoupled Computer Program in Matlab® Code

112

(3)

4.3.9 A Benchmark Numerical Example

115

(4)

4.4 Constrained Power Flow Solutions

119

(25)

4.4.1 Load Tap-changing Transformers

119

(13)

4.4.1.1 State Variable Initialisation and Limit Checking

121

(1)

4.4.1.2 Load Tap Changer Computer Program in Matlab® Code

122

(5)

4.4.1.3 Test Case of Voltage Magnitude Control with Load Tap-changing

127

(3)

4.4.1.4 Combined Voltage Magnitude Control by Means of Generators and Load Tap Changers

130

(1)

4.4.1.5 Control Coordination between One Load Tap Changer and One Generator

130

(2)

4.4.2 Phase-shifting Transformer

132

(12)

4.4.2.1 State Variable Initialisation and Limit Checking

134

(1)

4.4.2.2 Phase-shifter Computer Program in Matlab® Code

135

(5)

4.4.2.3 Test Cases for Phase-shifting Transformers

140

(4)

4.5 Further Concepts in Power Flows

144

(5)

4.5.1 Sparsity-oriented Solutions

144

(1)

4.5.2 Truncated Adjustments

145

(2)

4.5.2.1 Test Case of Truncated Adjustments Involving Three Load Tap-changing Transformers

145

(2)

4.5.3 Special Load Tap Changer Configurations

147

(8)

4.5.3.1 Test Case of Sensitivity Factors in Parallel Load Tap-changing Operation

148

(1)

4.6 Summary

149

(1)

References

150

(3)

5 Power Flow Including FACTS Controllers

153

(78)

5.1 Introduction

153

(1)

5.2 Power Flow Solutions Including FACTS Controllers

154

(1)

5.3 Static VAR Compensator

155

(16)

5.3.1 Conventional Power Flow Models

155

(3)

5.3.2 Shunt Variable Susceptance Model

158

(1)

5.3.3 Static VAR Compensator Computer Program in Matlab® Code

159

(3)

5.3.4 Firing-angle Model

162

(1)

5.3.5 Static VAR Compensator Firing-angle Computer Program in Matlab® Code

162

(4)

5.3.6 Integrated Transformer Firing-angle Model

166

(1)

5.3.7 Nodal Voltage Magnitude Control using Static VAR Compensators

167

(1)

5.3.8 Control Coordination between Reactive Sources

168

(1)

5.3.9 Numerical Example of Voltage Magnitude Control using One Static VAR Compensator

168

(3)

5.4 Thyristor-controlled Series Compensator

171

(20)

5.4.1 Variable Series Impedance Power Flow Model

171

(2)

5.4.2 Thyristor-controlled Series Compensator Computer Program in Matlab® Code

173

(5)

5.4.3 Numerical Example of Active Power Flow Control using One Thyristor-controlled Series Compensator: Variable Series Compensator Model

178

(2)

5.4.4 Firing-angle Power Flow Model

180

(2)

5.4.5 Thyristor-controlled Series Compensator Firing-angle Computer Program in Matlab® Code

182

(5)

5.4.6 Numerical Example of Active Power Flow Control using One Thyristor-controlled Series Compensator: Firing-angle Model

187

(2)

5.4.7 Numerical Properties of the Thyristor-controlled Series Compensator Power Flow Model

189

(2)

5.5 Static Synchronous Compensator

191

(9)

5.5.1 Power Flow Model

191

(1)

5.5.2 Static Compensator Computer Program in Matlab® Code

192

(6)

5.5.3 Numerical Example of Voltage Magnitude Control using One Static Compensator

198

(2)

5.6 Unified Power Flow Controller

200

(16)

5.6.1 Power Flow Model

201

(2)

5.6.2 Unified Power Flow Controller Computer Program in Matlab®Code

203

(10)

5.6.3 Numerical Example of Power Flow Control using One Unified Power Flow Controller

213

(3)

5.7 High-voltage Direct-current-based Voltage Source Converter

216

(11)

5.7.1 Power Equations

217

(1)

5.7.2 High-voltage Direct-current-based Voltage Source-Converter Computer Program in Matlab® Code

218

(7)

5.7.3 Numerical Example of Power Flow Control using One HVDC-VSC

225

(2)

5.7.3.1 HVDC-VSC Back-to-back Model

225

(1)

5.7.3.2 HVDC-VSC Full Model

225

(2)

5.8 Effective Initialisation of FACTS Controllers

227

(1)

5.8.1 Controllers Represented by Shunt Synchronous Voltage Sources

227

(1)

5.8.2 Controllers Represented by Shunt Admittances

227

(1)

5.8.3 Controllers Represented by Series Reactances

227

(1)

5.8.4 Controllers Represented by Series Synchronous Voltage Sources

228

(1)

5.9 Summary

228

(1)

References

229

(2)

6 Three-phase Power Flow

231

(36)

6.1 Introduction

231

(1)

6.2 Power Flow in the Phase Frame of Reference

232

(17)

6.2.1 Power Flow Equations

233

(1)

6.2.2 Newton-Raphson Power Flow Algorithm

234

(2)

6.2.3 Matlab® Code of a Power Flow Program in the Phase Frame of Reference

236

(8)

6.2.4 Numerical Example of a Three-phase Network

244

(5)

6.3 Static VAR Compensator

249

(4)

6.3.1 Variable Susceptance Model

250

(1)

6.3.2 Firing-angle Model

251

(1)

6.3.3 Numerical Example: Static VAR Compensator Voltage Magnitude Balancing Capability

252

(1)

6.4 Thyristor-controlled Series Compensator

253

(4)

6.4.1 Variable Susceptance Model

253

(2)

6.4.2 Firing-angle Model

255

(2)

6.4.3 Numerical Example: Power Flow Control using One Thyristor-controlled Series Compensator

257

(1)

6.5 Static Compensator

257

(4)

6.5.1 Static Compensator Three-phase Numerical Example

260

(1)

6.6 Unified Power Flow Controller

261

(3)

6.6.1 Numerical Example of Power Flow Control using One Unified Power Flow Controller

264

(1)

6.7 Summary

264

(1)

References

265

(2)

7 Optimal Power Flow

267

(44)

7.1 Introduction

267

(1)

7.2 Optimal Power Flow using Newton's Method

268

(10)

7.2.1 General Formulation

268

(2)

7.2.1.1 Variables

268

(1)

7.2.1.2 Objective Function

269

(1)

7.2.1.3 Equality Constraints

269

(1)

7.2.1.4 Inequality Constraints

270

(1)

7.2.2 Application of Newton's Method to Optimal Power Flow

270

(1)

7.2.3 Linearised System Equations

271

(1)

7.2.4 Optimality Conditions for Newton's Method

272

(1)

7.2.5 Conventional Power Plant Modelling in Optimal Power Flow

272

(3)

7.2.5.1 Transmission Lines

273

(1)

7.2.5.2 Shunt Elements

274

(1)

7.2.5.3 Synchronous Generators

275

(1)

7.2.6 Handling of Inequality Constraints

275

(3)

7.2.6.1 Handling of Inequality Constraints on Variables

275

(2)

7.2.6.2 Handling of Inequality Constraints on Functions

277

(1)

7.3 Implementation of Optimal Power Flow using Newton's Method

278

(5)

7.3.1 Initial Conditions in Optimal Power Flow Solutions

279

(1)

7.3.2 Active Power Schedule

279

(1)

7.3.3 Lagrange Multipliers

280

(1)

7.3.4 Penalty Weighting Factors

280

(1)

7.3.5 Conjugated Variables

280

(1)

7.3.6 An Optimal Power Flow Numerical Example

281

(2)

7.4 Power System Controller Representation in Optimal Power Flow Studies

283

(1)

7.5 Load Tap-changing Transformer

283

(3)

7.5.1 Load Tap-changing Lagrangian Function

283

(1)

7.5.2 Linearised System of Equations

284

(1)

7.5.3 Load Tap-changing Transformer Test Cases

285

(1)

7.6 Phase-shifting Transformer

286

(5)

7.6.1 Lagrangian Function

286

(1)

7.6.2 Linearised System of Equations

287

(2)

7.6.3 Phase-shifting Transformer Test Cases

289

(2)

7.6.3.1 Case 1: No Active Power Flow Regulation

289

(1)

7.6.3.2 Case 2: Active Power Flow Regulation at LakePS

290

(1)

7.7 Static VAR Compensator

291

(5)

7.7.1 Lagrangian Function

291

(1)

7.7.2 Linearised System of Equations

292

(1)

7.7.3 Static VAR Compensator Test Cases

293

(3)

7.7.3.1 Firing-angle Model

293

(2)

7.7.3.2 Susceptance Model

295

(1)

7.8 Thyristor-controlled Series Compensator

296

(5)

7.8.1 Lagrangian Function

296

(1)

7.8.2 Linearised System of Equations

297

(2)

7.8.3 Thyristor-controlled Series Compensator Test Cases

299

(2)

7.9 Unified Power Flow Controller

301

(6)

7.9.1 Unified Power Flow Controller Lagrangian Function

301

(1)

7.9.2 Direct-current Link Lagrangian Function

301

(1)

7.9.3 Unified Power Flow Controller Power Flow Constraints

302

(1)

7.9.4 Linearised System of Equations

302

(3)

7.9.5 Unified Power Flow Controller Test Cases

305

(2)

7.9.6 Unified Power Flow Controller Operating Modes

307

(1)

7.10 Summary

307

(1)

References

308

(3)

8 Power Flow Tracing

311

(32)

8.1 Introduction

311

(1)

8.2 Basic Assumptions

312

(1)

8.3 Mathematical Justification of the Proportional Sharing Principle

313

(2)

8.4 Dominions

315

(6)

8.4.1 Dominion Contributions to Active Power Flows

317

(2)

8.4.2 Dominion Contributions to Reactive Power Flows

319

(1)

8.4.3 Dominion Contributions to Loads and Sinks

320

(1)

8.5 Tracing Algorithm

321

(1)

8.6 Numerical Examples

322

(17)

8.6.1 Simple Radial Network

322

(2)

8.6.2 Simple Meshed Network: Active Power

324

(5)

8.6.3 Meshed Network with FACTS Controllers: Reactive Power

329

(2)

8.6.4 Large Network

331

(1)

8.6.5 Tracing the Power Output of a Wind Generator

331

(18)

8.6.5.1 The Wind Generator Model

335

(1)

8.6.5.2 Numerical Example

336

(3)

8.7 Summary

339

(1)

References

340

(3)

Appendix A: Jacobian Elements for FACTS Controllers in Positive Sequence Power Flow

343

(6)

A.1 Tap-changing Transformer

343

(1)

A.2 Thyristor-controlled Series Compensator

344

(1)

A.3 Static Synchronous Compensator

345

(1)

A.4 Unified Power Flow Controller

345

(2)

A.5 High-voltage Direct-current-based Voltage Source Converter

347

(2)

Appendix B: Gradient and Hessian Elements for Optimal Power Flow Newton's Method

349

(16)

B.1 First and Second Partial Derivatives for Transmission Lines

349

(3)

B.1.1 The Gradient Vector

349

(1)

B.1.2 The Matrix W

350

(2)

B.2 Phase Shifter Transformer

352

(3)

B.3 Static VAR Compensator

355

(1)

B.4 Thyristor-controlled Series Compensator

356

(1)

B.5 Unified Power Flow Controller

357

(8)

Appendix C: Matlab® Computer Program for Optimal Power Flow Solutions using Newton's Method

365

(34)

Index

399

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FACTS Modelling and Simulation in Power Networks

Summary

Author Biography

Table of Contents

Supplemental Materials