Preface xiii

Acknowledgements xv

1 Introduction 1

1.1 Present Status of Grid Operation 1

1.1.1 General 1

1.1.2 HVDC Transmission 4

1.1.3 Reliability of Electricity Supply 4

1.2 Overview of System Dynamics and Control 4

1.2.1 Power System Stability 4

1.2.2 Mathematical Preliminaries 6

Stability of Equilibrium Point 6

Steady-State Behavior 8

1.2.3 Power System Security 8

1.3 Monitoring and Enhancing System Security 10

1.4 Emergency Control and System Protection 11

1.5 Recent Developments 12

1.5.1 Power System Protection 12

1.5.2 Development of Smart Grids 13

1.5.3 Microgrids 14

1.5.4 Role of System Dynamics and Control 14

1.6 Outline of Chapters 14

References 17

2 Grid Characteristics and Operation 19

2.1 Description of Electric Grids 19

2.2 Detailed Modeling of Three-Phase AC Lines 21

2.3 Circuit Models of Symmetric Networks 22

2.4 Network Equations in DQo and 𝛼𝛽o Components 23

2.4.1 Transformation to Park (dqo) Components 24

2.4.2 Steady-State Equations 25

2.4.3 D-Q Transformation using 𝛼-𝛽 Variables 26

2.5 Frequency and Power Control 28

2.5.1 Tie-Line Bias Frequency Control 31

2.6 Dynamic Characteristics of AC Grids 33

2.6.1 Grid Response to Frequency Modulation 33

2.6.2 Grid Response to Injection of Reactive Current 35

2.7 Control of Power Flow in AC Grids 38

2.7.1 Power Transfer Capability of a Line 38

2.7.2 Power Flow in a Line connected to an AC Transmission Grid 41

2.8 Analysis of Electromagnetic Transients 42

2.8.1 Modeling of Lumped Parameter Components 42

2.8.2 Modeling of a Single-Phase Line 43

2.8.3 Approximation of Series Resistance of Line 44

2.8.4 Modeling of Lossless Multiphase Line 45

2.8.5 Modeling of Multiphase Networks with Lumped Parameters 46

2.9 Transmission Expansion Planning 47

2.10 Reliability in Distribution Systems 48

2.11 Reliable Power Flows in a Transmission Network 48

2.12 Reliability Analysis of Transmission Networks 50

2.A Analysis of a Distributed Parameter Single-Phase Line in Steady State 51

2.A.1 Expressions for a Lossless Line 53

2.A.2 Performance of a Symmetrical Line 54

2.B Computation of Electrical Torque 55

References 57

3 Modeling and Simulation of Synchronous Generator Dynamics 59

3.1 Introduction 59

3.2 Detailed Model of a Synchronous Machine 59

3.2.1 Flux Linkage Equations 60

3.2.2 Voltage equations 61

3.3 Park’s Transformation 62

3.4 Per-Unit Quantities 69

3.5 Equivalent Circuits of a Synchronous Machine 72

3.6 Synchronous Machine Models for Stability Analysis 76

3.6.1 Application of Model (2.1) 80

3.6.2 Application of Model (1.1) 80

3.6.3 Modeling of Saturation 82

3.7 An Exact Circuit Model of a Synchronous Machine for Electromagnetic Transient Analysis 82

3.7.1 Derivation of the Circuit Model 83

3.7.2 Transformation of the Circuit Model 87

3.7.3 Modeling of a Synchronous Generator in the Simulation of Electromagnetic Transients 91

3.7.4 Treatment of Dynamic Saliency 92

3.8 Excitation and Prime Mover Controllers 93

3.8.1 Excitation Systems 93

3.8.2 Modeling of Prime-Mover Control Systems 98

3.9 Transient Instability due to Loss of Synchronism 101

3.10 Extended Equal Area Criterion 103

3.11 Dynamics of a Synchronous Generator 104

Network Equations 104

Calculation of Initial Conditions 106

System Simulation 108

3.A Derivation of Electrical Torque 110

References 112

4 Modeling and Simulation of Wind Power Generators 115

4.1 Introduction 115

4.2 Power Extraction byWind Turbines 116

4.2.1 Wind Speed Characteristics 117

4.2.2 Control of Power Extraction 118

4.3 Generator and Power Electronic Configurations 120

4.3.1 Wind Farm Configurations 122

4.4 Modeling of the Rotating System 122

4.5 Induction Generator Model 124

4.5.1 Rotor Speed Instability 127

4.5.2 Modeling Issues 130

4.5.3 Frequency Conversion Using Voltage Source Converters 132

4.6 Control of Type IIIWTG System 133

4.6.1 Rotor-Side Converter Control 133

4.6.2 Grid-Side Converter Control 136

4.6.3 Overall Control Scheme for a Type III WTG system 137

4.6.4 Simplified Modeling of the Controllers for Slow Transient Studies 141

4.7 Control of Type IVWTG System 142

References 143

5 Modeling and Analysis of FACTS and HVDC Controllers 145

5.1 Introduction 145

5.2 FACTS Controllers 146

5.2.1 Description 146

5.2.2 A General Equivalent Circuit for FACTS Controllers 147

5.2.3 Benefits of the Application of FACTS Controllers 148

5.2.4 Application of FACTS Controllers in Distribution Systems 150

5.3 Reactive Power Control 150

Control Characteristics 153

5.4 Thyristor-Controlled Series Capacitor 153

5.4.1 Basic Concepts of Controlled Series Compensation 155

5.4.2 Operation of a TCSC 157

5.4.3 Analysis of a TCSC 158

5.4.4 Computation of the TCSC Reactance (XTCSC) 159

5.4.5 Control of the TCSC 161

5.5 Static Synchronous Compensator 166

5.5.1 General 166

5.5.2 Two-Level (Graetz Bridge) Voltage Source Converter 168

5.5.3 Pulse0020Width Modulation 169

5.5.4 Analysis of a Voltage Source Converter 171

5.5.5 Control of VSC 175

5.6 HVDC Power Transmission 177

5.6.1 Application of DC Transmission 178

5.6.2 Description of HVDC Transmission Systems 178

5.6.3 Analysis of a Line Commutated Converter 180

5.6.4 Introduction of VSC-HVDC Transmission 186

5.A Case Study of a VSC-HVDC Link 190

References 193

6 Damping of Power Swings 195

6.1 Introduction 195

6.2 Origin of Power Swings 196

6.3 SMIB Model with Field Flux Dynamics and AVR 199

6.3.1 Small-Signal Model and Eigenvalue Analysis 201

6.4 Damping and Synchronizing Torque Analysis 205

6.5 Analysis of Multi-Machine Systems 210

6.5.1 Electro-Mechanical Modes in a Multi-Machine System 210

6.5.2 Analysis with Detailed Models 216

6.6 Principles of Damping Controller Design 225

6.6.1 Actuator Location and Choice of Feedback Signals 229

6.6.2 Components of a PSDC 230

6.6.3 PSDCs based on Generator Excitation Systems: Power System Stabilizers 231

6.6.4 Adverse Torsional Interactions with the Speed/Slip Signal 237

6.6.5 Damping of Swings using Grid-Connected Power Electronic Systems 237

6.7 Concluding Remarks 241

6.A Eigenvalues of the Stiffness matrix K of Section 6.5.1 242

6.B Three-Machine Data 244

References 244

7 Analysis and Control of Loss of Synchronism 247

7.1 Introduction 247

7.2 Effect of LoS 247

7.3 Understanding the LoS Phenomenon 249

7.4 Criteria for Assessment of Stability 251

7.5 Power System Modeling and Simulation for Analysis of LoS 252

7.5.1 Effect of System Model 254

7.5.2 Effect of Changing Operating Conditions 255

7.6 Loss of Synchronism in Multi-Machine Systems 256

7.6.1 Effect of Disturbance Location on Mode of Separation: 258

7.6.2 Effect of the Load Model 258

7.6.3 Effect of Series Compensation in a Critical Line 260

7.6.4 Effect of a Change in the Pre-fault Generation Schedule 261

7.6.5 Voltage Phase Angular Differences across Critical Lines/Apparent Impedance seen by Relays 261

7.7 Measures to Avoid LoS 263

7.7.1 System Planning and Design 263

7.7.2 Preventive Control During Actual Operation 264

7.7.3 Emergency Control 264

7.8 Assessment and Control of LoS Using Energy Functions 265

7.8.1 Energy Function Method Applied to an SMIB System 266

7.8.2 Energy Function Method Applied to Multi-Machine Systems/Detailed Models 270

7.8.3 Evaluation of Critical Energy in a Multi-Machine System 274

7.9 Generation Rescheduling Using Energy Margin Sensitivities 274

7.9.1 Case Study: Generation Rescheduling 276

7.A Simulation Methods for Transient Stability Studies 276

7.A.1 Simultaneous Implicit Method 277

7.A.2 Partitioned Explicit Method 277

7.B Ten-Machine System Data 279

References 281

8 Analysis of Voltage Stability and Control 283

8.1 Introduction 283

8.2 Definitions of Voltage Stability 284

8.3 Comparison of Angle and Voltage Stability 286

8.3.1 Analysis of the SMLB System 287

8.4 Mathematical Preliminaries 290

8.5 Factors Affecting Instability and Collapse 292

8.5.1 Induction Motor Loads 292

8.5.2 HVDC Converter 293

8.5.3 Overexcitation Limiters 294

8.5.4 OLTC Transformers 295

8.5.5 A Nonlinear Dynamic Load Model 296

8.6 Dynamics of Load Restoration 296

8.7 Analysis of Voltage Stability and Collapse 298

8.7.1 Simulation 298

8.7.2 Small Signal (Linear) Analysis 298

8.8 Integrated Analysis of Voltage and Angle Stability 301

8.9 Analysis of Small Signal Voltage Instability Decoupled from Angle Instability 303

8.9.1 Decoupling of Angle and Voltage Variables 304

8.9.2 Incremental RCFN 305

8.9.3 Nonlinear Reactive Loads 306

8.9.4 Generator Model 306

Discussion 307

8.10 Control of Voltage Instability 308

References 308

9 Wide-AreaMeasurements and Applications 311

9.1 Introduction 311

9.2 Technology and Standards 311

9.2.1 Synchrophasor Definition 313

9.2.2 Reporting Rates 314

9.2.3 Latency and Data Loss 315

9.3 Modeling ofWAMS in Angular Stability Programs 315

9.4 Online Monitoring of Power Swing Damping 316

9.4.1 Modal Estimation based on Ringdown Analysis 317

9.4.2 Modal Estimation based on Probing Signals 319

9.4.3 Modal Estimation based on Ambient Data Analysis 323

9.5 WAMS Applications in Power Swing Damping Controllers 327

9.6 WAMS Applications in Emergency Control 330

9.7 Generator Parameter Estimation 335

9.8 Electro-MechanicalWave Propagation and Other Observations in Large Grids 335

References 338

10 Analysis of Subsynchronous Resonance 341

10.1 Introduction 341

10.2 Analysis of Electrical Network Dynamics 342

10.2.1 Equations in DQo Variables 344

10.2.2 Interfacing a DQ Network Model with a Generator Model 346

10.3 Torsional Dynamics of a Generator-Turbine System 353

10.3.1 Damping of Torsional Oscillations 359

10.3.2 Sensitivity of the Torsional Modes to the External Electrical System 360

10.4 Generator-Turbine and Network Interactions: Subsynchronous Resonance 362

10.4.1 Torsional Modes in Multi-Generator Systems 368

10.4.2 Adverse Interactions with Turbine-Generator Controllers 371

10.4.3 Detection of SSR/Torsional Monitoring 373

10.4.4 Countermeasures for Subsynchronous Resonance and Subsynchronous Torsional Interactions 374

10.4.5 Case Study: TCSC-Based SSDC 377

10.5 Time-InvariantModels of Grid-Connected Power Electronic Systems 378

10.5.1 Discrete-Time DynamicModels using the PoincaréMapping Technique 380

10.5.2 Dynamic Phasor-Based Modeling 380

10.5.3 Numerical Derivation of PES Models: A Frequency Scanning Approach 383

10.A Transfer Function Representation of the Network 385

References 386

11 Solar Power Generation and Energy Storage 391

11.1 Introduction 391

11.2 Solar Thermal Power Generation 392

11.3 Solar PV Power Generation 392

11.3.1 Solar Module I-V Characteristics 393

11.3.2 Solar PV Connections and Power Extraction Strategies 393

11.3.3 Power Electronic Converters for Solar PV Applications 395

11.3.4 Maximum Power Point Tracking Algorithms 397

11.3.5 Control of Grid-Connected Solar PV Plants 398

11.3.6 Low-Voltage Ride Through and Voltage Support Capability 400

11.4 Energy Storage 403

11.4.1 Attributes of Energy Storage Devices 404

11.4.2 Energy Storage Technologies 404

11.4.3 Mapping to Applications 406

11.4.4 Battery Modeling 410

References 412

12 Microgrids: Operation and Control 415

12.1 Introduction 415

12.2 Microgrid Concept 416

12.2.1 Definition of a Microgrid 416

12.2.2 Control System 417

12.3 Microgrid Architecture 419

12.4 Distribution Automation and Control 420

12.5 Operation and Control of Microgrids 421

12.5.1 DER Units 421

12.5.2 Microgrid Loads 423

12.5.3 DER Controls 423

12.5.4 Control Strategies under Grid-Connected Operation 425

12.5.5 Control Strategy for an Islanded Microgrid 427

12.6 Energy Management System 428

12.6.1 Microgrid Supervisory Control 429

12.6.2 Decentralized Microgrid Control based on a Multi-Agent System 430

12.6.3 IndustrialMicrogrid Controllers 431

12.7 Adaptive Network Protection in Microgrids 432

12.7.1 Protection Issues 433

12.7.2 Adaptive Protection 434

12.8 Dynamic Modeling of Distributed Energy Resources 435

12.8.1 Photovoltaic Array with MPP Tracker 435

12.8.2 Fuel Cells 437

12.8.3 Natural Gas Generator Set 438

12.8.4 Fixed-SpeedWind Turbine Driving SCIG 439

12.9 Some Operating Problems in Microgirds 442

12.10 Integration of DG and DS in a Microgrid 444

12.11 DC Microgrids 444

12.12 Future Trends and Conclusions 445

12.A A Three-Phase Model of an Induction Machine 448

References 452

A Equal Area Criterion 455

An Interesting Network Analogy 456

References 458

B Grid Synchronization and Current Regulation 459

Choice of Reference Frames 459

References 462

C Fryze–Buchbolz–Depenbrock Method for Load Compensation 463

C.1 Introduction 463

C.2 Description of FBDTheory 463

C.3 Power Theory in Multiconductor Circuits 466

Virtual Star Point 466

Collective Quantities 467

C.4 Examples 469

C.5 Load Characterization over a Period 470

C.6 Compensation of Non-Active Currents 471

Discussion 472

References 472

D Symmetrical Components and Per-Unit Representation 473

D.1 Symmetrical Component Representation of Three-Phase Systems 473

D.2 Per-Unit Representation 476

References 478

Index 479