Advanced Control of Grid-Integrated Renewable Energy Power Plants

Horst Schulte, PhD, is the Head of Control Engineering Group, HTW Berlin, Germany.

Preface ix

Acronyms xi

Notation xiii

1 Introduction 1

1.1 Energy Transition 1

1.2 Problem Description 5

1.3 Methodological Framework 9

1.4 Topics of this Book 12

2 Modeling of Wind Turbines 15

2.1 Introduction 15

2.2 First-Principle Modeling 16

2.2.1 Energy Capturing: Actuator Disc Concept 16

2.2.1.1 Power Coefficient 18

2.2.1.2 Thrust Coefficient 20

2.2.2 Essentials of Rotor Blade Theory for Control Purpose 21

2.2.3 The c P –λ, c Q –λ, and c T –λ Curves 27

2.2.4 Wind Turbine Models with 1- and 4-DOF 32

2.2.5 Simulation-Based Model Validation 38

2.3 Control-Oriented Models in TS Form 41

2.3.1 Partial- and Full-Load Operating Region 41

2.3.2 Single-Region 1-DOF Models 42

2.3.3 Single-Region 2- and 3-DOF Models 47

2.3.3.1 Model with Tower and Rotor DOF 47

2.3.3.2 Model with Tower, Elastic Drive Train, and Rotor DOF 49

2.3.3.3 Model with Tower, Blades, and Rotor DOF 50

2.3.4 Multi-region Model for Disturbance Observer Design 53

2.3.5 Multi-region Model for Controller Design 57

2.4 Summary 60

2.5 Problems 60

2.6 Bibliography 61

3 Control of Wind Turbines 63

3.1 Introduction 63

3.2 Baseline Generator-Torque and Blade-Pitch Controller 63

3.3 Model-Based Control of WTs 72

3.3.1 Control Scheme 72

3.3.2 Effective Wind Speed and State Observer 72

3.3.3 State Feedback Design for Partial- and Full-Load Operating Region 79

3.3.3.1 Design of a Full-Load Region Control with State Feedback 82

3.3.3.2 Control-Design of Partial-Load Operating Region 85

3.3.3.3 Control Concept for Bumpless Transition Between Operating Regions 93

3.4 Model-Based Power Tracking 95

3.4.1 Introduction 95

3.4.2 Governor Concept of Synchronous Machines 96

3.4.3 Control-Oriented Models and Schemes 98

3.4.3.1 Control-oriented Model and Control Scheme for V ≥ V Rated 99

3.4.3.2 Control-oriented Model and Scheme for V < V Rated 100

3.4.4 State Feedback and Feedforward Design for Power Tracking 104

3.4.4.1 Controller Design for V ≥ V Rated 105

3.4.4.2 Controller Design for V < V Rated 109

3.5 Summary 111

3.6 Problems 112

3.7 Bibliography 113

4 Modeling and Control of Photovoltaic Power Plants 115

4.1 Introduction 115

4.2 Modeling of PV Generators 116

4.3 DC–DC Converter Modeling 121

4.3.1 Overview of Switched-Mode Converter 121

4.3.2 Generic State-Space Average Models 124

4.3.3 Circuit Design and Simulation 127

4.4 Voltage Control of PV Generators 131

4.4.1 Control-Oriented State-Space Model 131

4.4.2 State-Feedback Design 136

4.5 Demanded Power Tracking 147

4.5.1 Overall Control Structure 148

4.5.2 Model-Based Power Tracking 149

4.5.2.1 Performance and Robustness Analysis of the Cascaded Controller 152

4.5.3 Model-Free Power Tracking 154

4.6 Summary 160

4.7 Problems 160

4.8 Bibliography 161

5 Modeling and Control of Voltage Source Converters 163

5.1 Introduction 163

5.2 Three-Phase Signals and Systems 165

5.3 Average and Instantaneous Power 169

5.4 Reduced-Order VSC Model 173

5.5 Power Injection in the Steady State 175

5.6 Voltage Drop in the Steady State 176

5.7 Selected Control Concepts 179

5.7.1 Control and Functional Requirements 179

5.7.2 Control Scheme of Grid-Following VSC 181

5.7.2.1 PQ Control of Grid-Following VSC 183

5.7.2.2 Current Control of GFL Voltage Source Converter 184

5.7.3 Control Scheme of Grid-Forming VSC 185

5.7.3.1 PQ Control by Direct Droop-Based Voltage Control 186

5.7.4 Grid-Forming VSC Control With Inner-Loop Current Regulator 188

5.7.4.1 PQ Control as Reference Signal Generator for Lower-Level Control 189

5.8 Summary 190

5.9 Problems 190

5.10 Bibliography 191

6 Advanced Grid Integration of PV and Wind Power Plants 193

6.1 Introduction 193

6.2 Description of Test Scenarios 194

6.3 Integration of Wind Power Plants 197

6.3.1 Response to Active Power Request 198

6.3.2 Decrease in Wind Inflow 199

6.3.3 Response to Reactive Power Request 199

6.3.4 Grid Disturbance Rejection 202

6.4 Integration of PV Power Plants 205

6.4.1 Response to Active Power Request 205

6.4.2 RES Fluctuation: Irradiation Step 207

6.4.3 Response to Reactive Power Request 207

6.4.4 Grid Disturbance Rejection 207

6.5 Summary 210

6.6 Problems 211

6.7 Bibliography 212

A Modeling in the Takagi–Sugeno Framework 213

A.1 Introduction 213

A.2 Constructing TS Systems 214

A.2.1 Sector-Nonlinearity Approach 214

A.2.2 Taylor Linearization and Interpolation 215

B LMI Conditions for Stability Analysis and Controller Design 219

B.1 Introduction 219

B.2 Linear Matrix Inequalities 220

B.2.1 Basics 220

B.2.2 Suitable Auxiliary Lemmas 222

B.3 Stability Analysis of TS Systems 223

B.3.1 Stability of Unforced TS Systems 223

B.3.1.1 Asymptotic Stability 223

B.3.1.2 D-Stability 224

B.4 Relaxations 229

B.5 State Feedback Design for TS Systems 230

B.5.1 Pole Region Specification 231

B.5.2 Minimization of M j 233

B.5.3 Stability of Forced Systems 233

B.5.3.1 Disturbance Rejection 233

B.5.3.2 Input-to-State Stability 234

B.6 Observer Design for TS Systems 236

B.6.1 Pole Region Specification for Observer Design 237

C Renewable Energy Sources 239

C.1 Wind Energy Systems 239

C.1.1 Froude’s Actuator Disc Theory (Froude–Rankine Theorem) 239

C.1.2 Rotor-Equivalent Wind Speed 240

C.1.3 Membership Functions and Matrices of TS Multi-region Model 241

D Parameters of Renewable Energy Power Plants 243

D.1 Physical Constants 243

D.2 Wind Power Plant Parameters 243

D.3 PV Power Plant Parameters 243

D.4 VSC Parameters 245

D.5 Equivalent Grid Model Parameters 246

E Control Concept for Bumpless Transition Between Operating Regions 247

References 251

Index 265