Wind Energy Generation: Modelling and Control

About the Authors xi

Preface xiii

Acronyms and Symbols xv

1 Electricity Generation from Wind Energy 1

1.1 Wind Farms 2

1.2 Wind Energy-generating Systems 3

1.2.1 Wind Turbines 3

1.2.2 Wind Turbine Architectures 7

1.3 Wind Generators Compared with Conventional Power Plant 10

1.3.1 Local Impacts 11

1.3.2 System-wide Impacts 13

1.4 Grid Code Regulations for the Integration of Wind Generation 14

References 17

2 Power Electronics for Wind Turbines 19

2.1 Soft-starter for FSIG Wind Turbines 21

2.2 Voltage Source Converters (VSCs) 21

2.2.1 The Two-level VSC 21

2.2.2 Square-wave Operation 24

2.2.3 Carrier-based PWM (CB-PWM) 25

2.2.4 Switching Frequency Optimal PWM (SFO-PWM) 27

2.2.5 Regular and Non-regular Sampled PWM (RS-PWM and NRS-PWM) 28

2.2.6 Selective Harmonic Elimination PWM (SHEM) 29

2.2.7 Voltage Space Vector Switching (SV-PWM) 30

2.2.8 Hysteresis Switching 33

2.3 Application of VSCs for Variable-speed Systems 33

2.3.1 VSC with a Diode Bridge 34

2.3.2 Back-to-Back VSCs 34

References 36

3 Modelling of Synchronous Generators 39

3.1 Synchronous Generator Construction 39

3.2 The Air-gap Magnetic Field of the Synchronous Generator 39

3.3 Coil Representation of the Synchronous Generator 42

3.4 Generator Equations in the dq Frame 44

3.4.1 Generator Electromagnetic Torque 47

3.5 Steady-state Operation 47

3.6 Synchronous Generator with Damper Windings 49

3.7 Non-reduced Order Model 51

3.8 Reduced-order Model 52

3.9 Control of Large Synchronous Generators 53

3.9.1 Excitation Control 53

3.9.2 Prime Mover Control 55

References 56

4 Fixed-speed Induction Generator (FSIG)-based Wind Turbines 57

4.1 Induction Machine Construction 57

4.1.1 Squirrel-cage Rotor 58

4.1.2 Wound Rotor 58

4.2 Steady-state Characteristics 58

4.2.1 Variations in Generator Terminal Voltage 61

4.3 FSIG Configurations for Wind Generation 61

4.3.1 Two-speed Operation 62

4.3.2 Variable-slip Operation 63

4.3.3 Reactive Power Compensation Equipment 64

4.4 Induction Machine Modelling 64

4.4.1 FSIG Model as a Voltage Behind a Transient Reactance 65

4.5 Dynamic Performance of FSIG Wind Turbines 70

4.5.1 Small Disturbances 70

4.5.2 Performance During Network Faults 73

References 76

5 Doubly Fed Induction Generator (DFIG)-based Wind Turbines 77

5.1 Typical DFIG Configuration 77

5.2 Steady-state Characteristics 77

5.2.1 Active Power Relationships in the Steady State 80

5.2.2 Vector Diagram of Operating Conditions 81

5.3 Control for Optimum Wind Power Extraction 83

5.4 Control Strategies for a DFIG 84

5.4.1 Current-mode Control (PVdq) 84

5.4.2 Rotor Flux Magnitude and Angle Control 89

5.5 Dynamic Performance Assessment 90

5.5.1 Small Disturbances 91

5.5.2 Performance During Network Faults 94

References 96

6 Fully Rated Converter-based (FRC) Wind Turbines 99

6.1 FRC Synchronous Generator-based (FRC-SG) Wind Turbine 100

6.1.1 Direct-driven Wind Turbine Generators 100

6.1.2 Permanent Magnets Versus Electrically Excited Synchronous Generators 101

6.1.3 Permanent Magnet Synchronous Generator 101

6.1.4 Wind Turbine Control and Dynamic Performance Assessment 103

6.2 FRC Induction Generator-based (FRC-IG) Wind Turbine 113

6.2.1 Steady-state Performance 113

6.2.2 Control of the FRC-IG Wind Turbine 114

6.2.3 Performance Characteristics of the FRC-IG Wind Turbine 119

References 119

7 Influence of Rotor Dynamics on Wind Turbine Operation 121

7.1 Blade Bending Dynamics 122

7.2 Derivation of Three-mass Model 123

7.2.1 Example: 300 kW FSIG Wind Turbine 124

7.3 Effective Two-mass Model 126

7.4 Assessment of FSIG and DFIG Wind Turbine Performance 128

Acknowledgement 132

References 132

8 Influence of Wind Farms on Network Dynamic Performance 135

8.1 Dynamic Stability and its Assessment 135

8.2 Dynamic Characteristics of Synchronous Generation 136

8.3 A Synchronizing Power and Damping Power Model of a Synchronous Generator 137

8.4 Influence of Automatic Voltage Regulator on Damping 139

8.5 Influence on Damping of Generator Operating Conditions 141

8.6 Influence of Turbine Governor on Generator Operation 143

8.7 Transient Stability 145

8.8 Voltage Stability 147

8.9 Generic Test Network 149

8.10 Influence of Generation Type on Network Dynamic Stability 150

8.10.1 Generator 2 – Synchronous Generator 151

8.10.2 Generator 2 – FSIG-based Wind Farm 152

8.10.3 Generator 2 – DFIG-based Wind Farm (PVdq Control) 152

8.10.4 Generator 2 – DFIG-based Wind Farm (FMAC Control) 152

8.10.5 Generator 2 – FRC-based Wind Farm 152

8.11 Dynamic Interaction of Wind Farms with the Network 153

8.11.1 FSIG Influence on Network Damping 153

8.11.2 DFIG Influence on Network Damping 158

8.12 Influence of Wind Generation on Network Transient Performance 161

8.12.1 Generator 2 – Synchronous Generator 161

8.12.2 Generator 2 – FSIG Wind Farm 162

8.12.3 Generator 2 – DFIG Wind Farm 163

8.12.4 Generator 2 – FRC Wind Farm 165

References 165

9 Power Systems Stabilizers and Network Damping Capability of Wind Farms 167

9.1 A Power System Stabilizer for a Synchronous Generator 167

9.1.1 Requirements and Function 167

9.1.2 Synchronous Generator PSS and its Performance Contributions 169

9.2 A Power System Stabilizer for a DFIG 172

9.2.1 Requirements and Function 172

9.2.2 DFIG-PSS and its Performance Contributions 178

9.3 A Power System Stabilizer for an FRC Wind Farm 182

9.3.1 Requirements and Functions 182

9.3.2 FRC–PSS and its Performance Contributions 186

References 191

10 The Integration of Wind Farms into the Power System 193

10.1 Reactive Power Compensation 193

10.1.1 Static Var Compensator (SVC) 194

10.1.2 Static Synchronous Compensator (STATCOM) 195

10.1.3 STATCOM and FSIG Stability 197

10.2 HVAC Connections 198

10.3 HVDC Connections 198

10.3.1 LCC–HVDC 200

10.3.2 VSC–HVDC 201

10.3.3 Multi-terminal HVDC 203

10.3.4 HVDC Transmission – Opportunities and Challenges 204

10.4 Example of the Design of a Submarine Network 207

10.4.1 Beatrice Offshore Wind Farm 207

10.4.2 Onshore Grid Connection Points 208

10.4.3 Technical Analysis 210

10.4.4 Cost Analysis 212

10.4.5 Recommended Point of Connection 213

Acknowledgement 214

References 214

11 Wind Turbine Control for System Contingencies 217

11.1 Contribution of Wind Generation to Frequency Regulation 217

11.1.1 Frequency Control 217

11.1.2 Wind Turbine Inertia 218

11.1.3 Fast Primary Response 219

11.1.4 Slow Primary Response 222

11.2 Fault Ride-through (FRT) 228

11.2.1 FSIGs 228

11.2.2 DFIGs 229

11.2.3 FRCs 231

11.2.4 VSC–HVDC with FSIG Wind Farm 233

11.2.5 FRC Wind Turbines Connected Via a VSC–HVDC 234

References 237

Appendix A: State–Space Concepts and Models 241

Appendix B: Introduction to Eigenvalues and Eigenvectors 249

Appendix C: Linearization of State Equations 255

Appendix D: Generic Network Model Parameters 259

Index 265