This book will be focused on the modeling and control of the DFIM based wind turbines. In the first part of the book, the mathematical description of different basic dynamic models of the DFIM will be carried out. It will be accompanied by a detailed steady-state analysis of the machine. After that, a more sophisticated model of the machine that considers grid disturbances, such as voltage dips and unbalances will be also studied. The second part of the book surveys the most relevant control strategies used for the DFIM when it operates at the wind energy generation application. The control techniques studied, range from standard solutions used by wind turbine manufacturers, to the last developments oriented to improve the behavior of high power wind turbines, as well as control and hardware based solutions to address different faulty scenarios of the grid. In addition, the standalone DFIM generation system will be also analyzed.

GONZALO ABAD, PhD, is an Associate Professor in the
Electronics Department at the Mondragon University, where he
teaches modeling, control, and power electronics.

JESÚS LÓPEZ, PhD, is an Assistant Professor in
the Electrical and Electronic Engineering Department of the Public
University of Navarra, where he teaches subjects related to the
electrical drives and the processing of electrical power in wind
turbines.

MIGUEL RODRÍGUEZ, PhD, is the Power Electronics
Systems Manager at Ingeteam Technology, responsible for developing
new power electronics for transmission and distribution grid
applications.

LUIS MARROYO, PhD, is an Associate Professor in the
Electrical and Electronic Engineering Department of the Public
University of Navarra, where he teaches courses on electrical
machines and power electronics.

GRZEGORZ IWANSKI, PhD, is an Associate Professor in the
Institute of Control and Industrial Electronics at the Warsaw
University of Technology, where he teaches courses on power
electronics drives and conversion systems.

Doubly Fed Induction Machine (DFIM)based wind turbines have proven to be a cost-effective, efficient, and reliable method for generating power. Readers interested in DFIM technology can turn to this text to discover not only the current state of the technology and future directions for research and development, but also learn the tools they need to devise their own innovations and solutions.

Doubly Fed Induction Machine offers clear mathematical descriptions of basic dynamic DFIM models as well as a detailed steady-state analysis. The authors provide a more sophisticated model of a DFIM that takes into account grid disturbances such as voltage dips and balance disruptions.

The second part of the book surveys DFIM control strategies. Readers will learn about standard solutions used by wind turbine manufacturers, new developments designed to improve the behavior of high-power wind turbines, as well as hardware-based solutions that address faulty grid scenarios. The book concludes with a forecast of the future of DFIMs.

This book is an ideal, practical reference for engineers, researches, and students interested in fully learning the power generation capabilities of DFIM technology. This book helps readers grasp and apply complex concepts by using numerous aids throughout including:

• Diagrams and graphs

• Step-by-step calculations

• Illustrations and photos of DFIM components and systems

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 VoltageFrequency (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...