Doubly Fed Induction Machine

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.

• Preface xiii 1 Introduction to A Wind Energy Generation System 11.1 Introduction 11.2 Basic Concepts of a Fixed Speed Wind Turbine (FSWT) 21.2.1 Basic Wind Turbine Description 21.2.2 Power Control of Wind Turbines 51.2.3 Wind Turbine Aerodynamics 71.2.4 Example of a Commercial Wind Turbine 91.3 Variable Speed Wind Turbines (VSWTs) 101.3.1 Modeling of Variable Speed Wind Turbine 111.3.2 Control of a Variable Speed Wind Turbine 151.3.3 Electrical System of a Variable Speed Wind Turbine 221.4 Wind Energy Generation System Based on DFIM VSWT 251.4.1 Electrical Configuration of a VSWT Based on the DFIM 251.4.2 Electrical Configuration of a Wind Farm 331.4.3 WEGS Control Structure 341.5 Grid Code Requirements 391.5.1 Frequency and Voltage Operating Range 401.5.2 Reactive Power and Voltage Control Capability 411.5.3 Power Control 431.5.4 Power System Stabilizer Function 451.5.5 Low Voltage Ride Through (LVRT) 461.6 Voltage Dips and LVRT 461.6.1 Electric Power System 471.6.2 Voltage Dips 501.6.3 Spanish Verification Procedure 551.7 VSWT Based on DFIM Manufacturers 571.7.1 Industrial Solutions: Wind Turbine Manufacturers 571.7.2 Modeling a 2.4 MW Wind Turbine 721.7.3 Steady State Generator and Power Converter Sizing 791.8 Introduction to the Next Chapters 83Bibliography 852 Back-to-Back Power Electronic Converter 872.1 Introduction 872.2 Back-to-Back Converter based on Two-Level VSC Topology 882.2.1 Grid Side System 892.2.2 Rotor Side Converter and dv/dt Filter 962.2.3 DC Link 992.2.4 Pulse Generation of the Controlled Switches 1012.3 Multilevel VSC Topologies 1142.3.1 Three-Level Neutral Point Clamped VSC Topology (3L-NPC) 1162.4 Control of Grid Side System 1332.4.1 Steady State Model of the Grid Side System 1332.4.2 Dynamic Modeling of the Grid Side System 1392.4.3 Vector Control of the Grid Side System 1432.5 Summary 152References 1533 Steady State of the Doubly Fed Induction Machine 1553.1 Introduction 1553.2 Equivalent Electric Circuit at Steady State 1563.2.1 Basic Concepts on DFIM 1563.2.2 Steady State Equivalent Circuit 1583.2.3 Phasor Diagram 1633.3 Operation Modes Attending to Speed and Power Flows 1653.3.1 Basic Active Power Relations 1653.3.2 Torque Expressions 1683.3.3 Reactive Power Expressions 1703.3.4 Approximated Relations Between Active Powers, Torque, and Speeds 1703.3.5 Four Quadrant Modes of Operation 1713.4 Per Unit Transformation 1733.4.1 Base Values 1753.4.2 Per Unit Transformation of Magnitudes and Parameters 1763.4.3 Steady State Equations of the DFIM in p.u 1773.4.4 Example 3.1: Parameters of a 2 MW DFIM 1793.4.5 Example 3.2: Parameters of Different Power DFIM 1803.4.6 Example 3.3: Phasor Diagram of a 2 MW DFIM and p.u. Analysis 1813.5 Steady State Curves: Performance Evaluation 1843.5.1 Rotor Voltage Variation: Frequency, Amplitude, and Phase Shift 1853.5.2 Rotor Voltage Variation: Constant Voltage–Frequency (V-F) Ratio 1923.5.3 Rotor Voltage Variation: Control of Stator Reactive Power and Torque 1953.6 Design Requirements for the DFIM in Wind Energy Generation Applications 2023.7 Summary 207References 2084 Dynamic Modeling of the Doubly Fed Induction Machine 2094.1 Introduction 2094.2 Dynamic Modeling of the DFIM 2104.2.1 ab Model 2124.2.2 dq Model 2144.2.3 State-Space Representation of ab Model 2164.2.4 State-Space Representation of dq Model 2294.2.5 Relation Between the Steady State Model and the Dynamic Model 2344.3 Summary 238References 2385 Testing the DFIM 2415.1 Introduction 2415.2 Off-Line Estimation of DFIM Model Parameters 2425.2.1 Considerations About the Model Parameters of the DFIM 2435.2.2 Stator and Rotor Resistances Estimation by VSC 2455.2.3 Leakage Inductances Estimation by VSC 2505.2.4 Magnetizing Inductance and Iron Losses Estimation with No-Load Test by VSC 2565.3 Summary 262References 2626 Analysis of the DFIM Under Voltage Dips 2656.1 Introduction 2656.2 Electromagnetic Force Induced in the Rotor 2666.3 Normal Operation 2676.4 Three-Phase Voltage Dips 2686.4.1 Total Voltage Dip, Rotor Open-Circuited 2686.4.2 Partial Voltage Dip, Rotor Open-Circuited 2736.5 Asymmetrical Voltage Dips 2786.5.1 Fundamentals of the Symmetrical Component Method 2786.5.2 Symmetrical Components Applied to the DFIM 2816.5.3 Single-Phase Dip 2836.5.4 Phase-to-Phase Dip 2866.6 Influence of the Rotor Currents 2906.6.1 Influence of the Rotor Current in a Total Three-Phase Voltage Dip 2916.6.2 Rotor Voltage in a General Case 2946.7 DFIM Equivalent Model During Voltage Dips 2976.7.1 Equivalent Model in Case of Linearity 2976.7.2 Equivalent Model in Case of Nonlinearity 2996.7.3 Model of the Grid 3006.8 Summary 300References 3017 Vector Control Strategies for Grid-Connected DFIM Wind Turbines 3037.1 Introduction 3037.2 Vector Control 3047.2.1 Calculation of the Current References 3057.2.2 Limitation of the Current References 3077.2.3 Current Control Loops 3087.2.4 Reference Frame Orientations 3117.2.5 Complete Control System 3137.3 Small Signal Stability of the Vector Control 3147.3.1 Influence of the Reference Frame Orientation 3147.3.2 Influence of the Tuning of the Regulators 3207.4 Vector Control Behavior Under Unbalanced Conditions 3277.4.1 Reference Frame Orientation 3287.4.2 Saturation of the Rotor Converter 3287.4.3 Oscillations in the Stator Current and in the Electromagnetic Torque 3287.5 Vector Control Behavior Under Voltage Dips 3317.5.1 Small Dips 3337.5.2 Severe Dips 3367.6 Control Solutions for Grid Disturbances 3407.6.1 Demagnetizing Current 3407.6.2 Dual Control Techniques 3467.7 Summary 358References 3608 Direct Control of the Doubly Fed Induction Machine 3638.1 Introduction 3638.2 Direct Torque Control (DTC) of the Doubly Fed Induction Machine 3648.2.1 Basic Control Principle 3658.2.2 Control Block Diagram 3718.2.3 Example 8.1: Direct Torque Control of a 2 MW DFIM 3778.2.4 Study of Rotor Voltage Vector Effect in the DFIM 3798.2.5 Example 8.2: Spectrum Analysis in Direct Torque Control of a 2 MW DFIM 3848.2.6 Rotor Flux Amplitude Reference Generation 3868.3 Direct Power Control (DPC) of the Doubly Fed Induction Machine 3878.3.1 Basic Control Principle 3878.3.2 Control Block Diagram 3908.3.3 Example 8.3: Direct Power Control of a 2 MW DFIM 3958.3.4 Study of Rotor Voltage Vector Effect in the DFIM 3958.4 Predictive Direct Torque Control (P-DTC) of the Doubly Fed Induction Machine at Constant Switching Frequency 3998.4.1 Basic Control Principle 3998.4.2 Control Block Diagram 4028.4.3 Example 8.4: Predictive Direct Torque Control of 15kW and 2 MW DFIMs at 800 Hz ConstantSwitching Frequency 4118.4.4 Example 8.5: Predictive Direct Torque Control of a 15kW DFIM at 4 kHz Constant Switching Frequency 4158.5 Predictive Direct Power Control (P-DPC) of the Doubly Fed Induction Machine at Constant Switching Frequency 4168.5.1 Basic Control Principle 4178.5.2 Control Block Diagram 4198.5.3 Example 8.6: Predictive Direct Power Control of a 15 kW DFIM at 1 kHz Constant Switching Frequency 4248.6 Multilevel Converter Based Predictive Direct Power and Direct Torque Control of the Doubly Fed Induction Machine at Constant Switching Frequency 4258.6.1 Introduction 4258.6.2 Three-Level NPC VSC Based DPC of the DFIM 4288.6.3 Three-Level NPC VSC Based DTC of the DFIM 4478.7 Control Solutions for Grid Voltage Disturbances, Based on Direct Control Techniques 4518.7.1 Introduction 4518.7.2 Control for Unbalanced Voltage Based on DPC 4528.7.3 Control for Unbalanced Voltage Based on DTC 4608.7.4 Control for Voltage Dips Based on DTC 4678.8 Summary 473References 4749 Hardware Solutions for LVRT 4799.1 Introduction 4799.2 Grid Codes Related to LVRT 4799.3 Crowbar 4819.3.1 Design of an Active Crowbar 4849.3.2 Behavior Under Three-Phase Dips 4869.3.3 Behavior Under Asymmetrical Dips 4889.3.4 Combination of Crowbar and Software Solutions 4909.4 Braking Chopper 4929.4.1 Performance of a Braking Chopper Installed Alone 4929.4.2 Combination of Crowbar and Braking Chopper 4939.5 Other Protection Techniques 4959.5.1 Replacement Loads 4959.5.2 Wind Farm Solutions 4969.6 Summary 497References 49810 Complementary Control Issues: Estimator Structures and Start-Up of Grid-Connected DFIM 50110.1 Introduction 50110.2 Estimator and Observer Structures 50210.2.1 General Considerations 50210.2.2 Stator Active and Reactive Power Estimation for Rotor Side DPC 50310.2.3 Stator Flux Estimator from Stator Voltage for Rotor Side Vector Control 50310.2.4 Stator Flux Synchronization from Stator Voltage for Rotor Side Vector Control 50610.2.5 Stator and Rotor Fluxes Estimation for Rotor Side DPC, DTC, and Vector Control 50710.2.6 Stator and Rotor Flux Full Order Observer 50810.3 Start-up of the Doubly Fed Induction Machine Based Wind Turbine 51210.3.1 Encoder Calibration 51410.3.2 Synchronization with the Grid 51810.3.3 Sequential Start-up of the DFIM Based Wind Turbine 52310.4 Summary 534References 53511 Stand-Alone DFIM Based Generation Systems 53711.1 Introduction 53711.1.1 Requirements of Stand-alone DFIM Based System 53711.1.2 Characteristics of DFIM Supported by DC Coupled Storage 54011.1.3 Selection of Filtering Capacitors 54111.2 Mathematical Description of the Stand-Alone DFIM System 54411.2.1 Model of Stand-alone DFIM 54411.2.2 Model of Stand-alone DFIM Fed from Current Source 54911.2.3 Polar Frame Model of Stand-alone DFIM 55111.2.4 Polar Frame Model of Stand-alone DFIM Fed from Current Source 55411.3 Stator Voltage Control 55811.3.1 Amplitude and Frequency Control by the Use of PLL 55811.3.2 Voltage Asymmetry Correction During Unbalanced Load Supply 56711.3.3 Voltage Harmonics Reduction During Nonlinear Load Supply 56911.4 Synchronization Before Grid Connection By Superior PLL 57311.5 Summary 576References 57712 New Trends on Wind Energy Generation 57912.1 Introduction 57912.2 Future Challenges for Wind Energy Generation: What must be Innovated 58012.2.1 Wind Farm Location 58012.2.2 Power, Efficiency, and Reliability Increase 58212.2.3 Electric Grid Integration 58312.2.4 Environmental Concerns 58312.3 Technological Trends: How They Can be Achieved 58412.3.1 Mechanical Structure of the Wind Turbine 58512.3.2 Power Train Technology 58612.4 Summary 599References 600Appendix 603A.1 Space Vector Representation 603A.1.1 Space Vector Notation 603A.1.2 Transformations to Different Reference Frames 606A.1.3 Power Expressions 609A.2 Dynamic Modeling of the DFIM Considering the Iron Losses 610A.2.1 ab Model 611A.2.2 dq Model 614A.2.3 State-Space Representation of ab Model 616References 618Index 619The IEEE Press Series on Power Engineering