Doubly Fed Induction Machine: Modeling and Control for Wind Energy Generation

Preface xiii

1 Introduction to A Wind Energy Generation System 1

1.1 Introduction 1

1.2 Basic Concepts of a Fixed Speed Wind Turbine (FSWT) 2

1.2.1 Basic Wind Turbine Description 2

1.2.2 Power Control of Wind Turbines 5

1.2.3 Wind Turbine Aerodynamics 7

1.2.4 Example of a Commercial Wind Turbine 9

1.3 Variable Speed Wind Turbines (VSWTs) 10

1.3.1 Modeling of Variable Speed Wind Turbine 11

1.3.2 Control of a Variable Speed Wind Turbine 15

1.3.3 Electrical System of a Variable Speed Wind Turbine 22

1.4 Wind Energy Generation System Based on DFIM VSWT 25

1.4.1 Electrical Configuration of a VSWT Based on the DFIM 25

1.4.2 Electrical Configuration of a Wind Farm 33

1.4.3 WEGS Control Structure 34

1.5 Grid Code Requirements 39

1.5.1 Frequency and Voltage Operating Range 40

1.5.2 Reactive Power and Voltage Control Capability 41

1.5.3 Power Control 43

1.5.4 Power System Stabilizer Function 45

1.5.5 Low Voltage Ride Through (LVRT) 46

1.6 Voltage Dips and LVRT 46

1.6.1 Electric Power System 47

1.6.2 Voltage Dips 50

1.6.3 Spanish Verification Procedure 55

1.7 VSWT Based on DFIM Manufacturers 57

1.7.1 Industrial Solutions: Wind Turbine Manufacturers 57

1.7.2 Modeling a 2.4 MW Wind Turbine 72

1.7.3 Steady State Generator and Power Converter Sizing 79

1.8 Introduction to the Next Chapters 83

Bibliography 85

2 Back-to-Back Power Electronic Converter 87

2.1 Introduction 87

2.2 Back-to-Back Converter based on Two-Level VSC Topology 88

2.2.1 Grid Side System 89

2.2.2 Rotor Side Converter and dv/dt Filter 96

2.2.3 DC Link 99

2.2.4 Pulse Generation of the Controlled Switches 101

2.3 Multilevel VSC Topologies 114

2.3.1 Three-Level Neutral Point Clamped VSC Topology (3L-NPC) 116

2.4 Control of Grid Side System 133

2.4.1 Steady State Model of the Grid Side System 133

2.4.2 Dynamic Modeling of the Grid Side System 139

2.4.3 Vector Control of the Grid Side System 143

2.5 Summary 152

References 153

3 Steady State of the Doubly Fed Induction Machine 155

3.1 Introduction 155

3.2 Equivalent Electric Circuit at Steady State 156

3.2.1 Basic Concepts on DFIM 156

3.2.2 Steady State Equivalent Circuit 158

3.2.3 Phasor Diagram 163

3.3 Operation Modes Attending to Speed and Power Flows 165

3.3.1 Basic Active Power Relations 165

3.3.2 Torque Expressions 168

3.3.3 Reactive Power Expressions 170

3.3.4 Approximated Relations Between Active Powers, Torque, and Speeds 170

3.3.5 Four Quadrant Modes of Operation 171

3.4 Per Unit Transformation 173

3.4.1 Base Values 175

3.4.2 Per Unit Transformation of Magnitudes and Parameters 176

3.4.3 Steady State Equations of the DFIM in p.u 177

3.4.4 Example 3.1: Parameters of a 2 MW DFIM 179

3.4.5 Example 3.2: Parameters of Different Power DFIM 180

3.4.6 Example 3.3: Phasor Diagram of a 2 MW DFIM and p.u. Analysis 181

3.5 Steady State Curves: Performance Evaluation 184

3.5.1 Rotor Voltage Variation: Frequency, Amplitude, and Phase Shift 185

3.5.2 Rotor Voltage Variation: Constant Voltage–Frequency (V-F) Ratio 192

3.5.3 Rotor Voltage Variation: Control of Stator Reactive Power and Torque 195

3.6 Design Requirements for the DFIM in Wind Energy Generation Applications 202

3.7 Summary 207

References 208

4 Dynamic Modeling of the Doubly Fed Induction Machine 209

4.1 Introduction 209

4.2 Dynamic Modeling of the DFIM 210

4.2.1 ab Model 212

4.2.2 dq Model 214

4.2.3 State-Space Representation of ab Model 216

4.2.4 State-Space Representation of dq Model 229

4.2.5 Relation Between the Steady State Model and the Dynamic Model 234

4.3 Summary 238

References 238

5 Testing the DFIM 241

5.1 Introduction 241

5.2 Off-Line Estimation of DFIM Model Parameters 242

5.2.1 Considerations About the Model Parameters of the DFIM 243

5.2.2 Stator and Rotor Resistances Estimation by VSC 245

5.2.3 Leakage Inductances Estimation by VSC 250

5.2.4 Magnetizing Inductance and Iron Losses Estimation with No-Load Test by VSC 256

5.3 Summary 262

References 262

6 Analysis of the DFIM Under Voltage Dips 265

6.1 Introduction 265

6.2 Electromagnetic Force Induced in the Rotor 266

6.3 Normal Operation 267

6.4 Three-Phase Voltage Dips 268

6.4.1 Total Voltage Dip, Rotor Open-Circuited 268

6.4.2 Partial Voltage Dip, Rotor Open-Circuited 273

6.5 Asymmetrical Voltage Dips 278

6.5.1 Fundamentals of the Symmetrical Component Method 278

6.5.2 Symmetrical Components Applied to the DFIM 281

6.5.3 Single-Phase Dip 283

6.5.4 Phase-to-Phase Dip 286

6.6 Influence of the Rotor Currents 290

6.6.1 Influence of the Rotor Current in a Total Three-Phase Voltage Dip 291

6.6.2 Rotor Voltage in a General Case 294

6.7 DFIM Equivalent Model During Voltage Dips 297

6.7.1 Equivalent Model in Case of Linearity 297

6.7.2 Equivalent Model in Case of Nonlinearity 299

6.7.3 Model of the Grid 300

6.8 Summary 300

References 301

7 Vector Control Strategies for Grid-Connected DFIM Wind Turbines 303

7.1 Introduction 303

7.2 Vector Control 304

7.2.1 Calculation of the Current References 305

7.2.2 Limitation of the Current References 307

7.2.3 Current Control Loops 308

7.2.4 Reference Frame Orientations 311

7.2.5 Complete Control System 313

7.3 Small Signal Stability of the Vector Control 314

7.3.1 Influence of the Reference Frame Orientation 314

7.3.2 Influence of the Tuning of the Regulators 320

7.4 Vector Control Behavior Under Unbalanced Conditions 327

7.4.1 Reference Frame Orientation 328

7.4.2 Saturation of the Rotor Converter 328

7.4.3 Oscillations in the Stator Current and in the Electromagnetic Torque 328

7.5 Vector Control Behavior Under Voltage Dips 331

7.5.1 Small Dips 333

7.5.2 Severe Dips 336

7.6 Control Solutions for Grid Disturbances 340

7.6.1 Demagnetizing Current 340

7.6.2 Dual Control Techniques 346

7.7 Summary 358

References 360

8 Direct Control of the Doubly Fed Induction Machine 363

8.1 Introduction 363

8.2 Direct Torque Control (DTC) of the Doubly Fed Induction Machine 364

8.2.1 Basic Control Principle 365

8.2.2 Control Block Diagram 371

8.2.3 Example 8.1: Direct Torque Control of a 2 MW DFIM 377

8.2.4 Study of Rotor Voltage Vector Effect in the DFIM 379

8.2.5 Example 8.2: Spectrum Analysis in Direct Torque Control of a 2 MW DFIM 384

8.2.6 Rotor Flux Amplitude Reference Generation 386

8.3 Direct Power Control (DPC) of the Doubly Fed Induction Machine 387

8.3.1 Basic Control Principle 387

8.3.2 Control Block Diagram 390

8.3.3 Example 8.3: Direct Power Control of a 2 MW DFIM 395

8.3.4 Study of Rotor Voltage Vector Effect in the DFIM 395

8.4 Predictive Direct Torque Control (P-DTC) of the Doubly Fed Induction Machine at Constant Switching Frequency 399

8.4.1 Basic Control Principle 399

8.4.2 Control Block Diagram 402

8.4.3 Example 8.4: Predictive Direct Torque Control of 15kW and 2 MW DFIMs at 800 Hz Constant

Switching Frequency 411

8.4.4 Example 8.5: Predictive Direct Torque Control of a 15kW DFIM at 4 kHz Constant Switching Frequency 415

8.5 Predictive Direct Power Control (P-DPC) of the Doubly Fed Induction Machine at Constant Switching Frequency 416

8.5.1 Basic Control Principle 417

8.5.2 Control Block Diagram 419

8.5.3 Example 8.6: Predictive Direct Power Control of a 15 kW DFIM at 1 kHz Constant Switching Frequency 424

8.6 Multilevel Converter Based Predictive Direct Power and Direct Torque Control of the Doubly Fed Induction Machine at Constant Switching Frequency 425

8.6.1 Introduction 425

8.6.2 Three-Level NPC VSC Based DPC of the DFIM 428

8.6.3 Three-Level NPC VSC Based DTC of the DFIM 447

8.7 Control Solutions for Grid Voltage Disturbances, Based on Direct Control Techniques 451

8.7.1 Introduction 451

8.7.2 Control for Unbalanced Voltage Based on DPC 452

8.7.3 Control for Unbalanced Voltage Based on DTC 460

8.7.4 Control for Voltage Dips Based on DTC 467

8.8 Summary 473

References 474

9 Hardware Solutions for LVRT 479

9.1 Introduction 479

9.2 Grid Codes Related to LVRT 479

9.3 Crowbar 481

9.3.1 Design of an Active Crowbar 484

9.3.2 Behavior Under Three-Phase Dips 486

9.3.3 Behavior Under Asymmetrical Dips 488

9.3.4 Combination of Crowbar and Software Solutions 490

9.4 Braking Chopper 492

9.4.1 Performance of a Braking Chopper Installed Alone 492

9.4.2 Combination of Crowbar and Braking Chopper 493

9.5 Other Protection Techniques 495

9.5.1 Replacement Loads 495

9.5.2 Wind Farm Solutions 496

9.6 Summary 497

References 498

10 Complementary Control Issues: Estimator Structures and Start-Up of Grid-Connected DFIM 501

10.1 Introduction 501

10.2 Estimator and Observer Structures 502

10.2.1 General Considerations 502

10.2.2 Stator Active and Reactive Power Estimation for Rotor Side DPC 503

10.2.3 Stator Flux Estimator from Stator Voltage for Rotor Side Vector Control 503

10.2.4 Stator Flux Synchronization from Stator Voltage for Rotor Side Vector Control 506

10.2.5 Stator and Rotor Fluxes Estimation for Rotor Side DPC, DTC, and Vector Control 507

10.2.6 Stator and Rotor Flux Full Order Observer 508

10.3 Start-up of the Doubly Fed Induction Machine Based Wind Turbine 512

10.3.1 Encoder Calibration 514

10.3.2 Synchronization with the Grid 518

10.3.3 Sequential Start-up of the DFIM Based Wind Turbine 523

10.4 Summary 534

References 535

11 Stand-Alone DFIM Based Generation Systems 537

11.1 Introduction 537

11.1.1 Requirements of Stand-alone DFIM Based System 537

11.1.2 Characteristics of DFIM Supported by DC Coupled Storage 540

11.1.3 Selection of Filtering Capacitors 541

11.2 Mathematical Description of the Stand-Alone DFIM System 544

11.2.1 Model of Stand-alone DFIM 544

11.2.2 Model of Stand-alone DFIM Fed from Current Source 549

11.2.3 Polar Frame Model of Stand-alone DFIM 551

11.2.4 Polar Frame Model of Stand-alone DFIM Fed from Current Source 554

11.3 Stator Voltage Control 558

11.3.1 Amplitude and Frequency Control by the Use of PLL 558

11.3.2 Voltage Asymmetry Correction During Unbalanced Load Supply 567

11.3.3 Voltage Harmonics Reduction During Nonlinear Load Supply 569

11.4 Synchronization Before Grid Connection By Superior PLL 573

11.5 Summary 576

References 577

12 New Trends on Wind Energy Generation 579

12.1 Introduction 579

12.2 Future Challenges for Wind Energy Generation: What must be Innovated 580

12.2.1 Wind Farm Location 580

12.2.2 Power, Efficiency, and Reliability Increase 582

12.2.3 Electric Grid Integration 583

12.2.4 Environmental Concerns 583

12.3 Technological Trends: How They Can be Achieved 584

12.3.1 Mechanical Structure of the Wind Turbine 585

12.3.2 Power Train Technology 586

12.4 Summary 599

References 600

Appendix 603

A.1 Space Vector Representation 603

A.1.1 Space Vector Notation 603

A.1.2 Transformations to Different Reference Frames 606

A.1.3 Power Expressions 609

A.2 Dynamic Modeling of the DFIM Considering the Iron Losses 610

A.2.1 ab Model 611

A.2.2 dq Model 614

A.2.3 State-Space Representation of ab Model 616

References 618

Index 619

The IEEE Press Series on Power Engineering