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

• Preface ixAcronyms xiNotation xiii1 Introduction 11.1 Energy Transition 11.2 Problem Description 51.3 Methodological Framework 91.4 Topics of this Book 122 Modeling of Wind Turbines 152.1 Introduction 152.2 First-Principle Modeling 162.2.1 Energy Capturing: Actuator Disc Concept 162.2.1.1 Power Coefficient 182.2.1.2 Thrust Coefficient 202.2.2 Essentials of Rotor Blade Theory for Control Purpose 212.2.3 The c P –λ, c Q –λ, and c T –λ Curves 272.2.4 Wind Turbine Models with 1- and 4-DOF 322.2.5 Simulation-Based Model Validation 382.3 Control-Oriented Models in TS Form 412.3.1 Partial- and Full-Load Operating Region 412.3.2 Single-Region 1-DOF Models 422.3.3 Single-Region 2- and 3-DOF Models 472.3.3.1 Model with Tower and Rotor DOF 472.3.3.2 Model with Tower, Elastic Drive Train, and Rotor DOF 492.3.3.3 Model with Tower, Blades, and Rotor DOF 502.3.4 Multi-region Model for Disturbance Observer Design 532.3.5 Multi-region Model for Controller Design 572.4 Summary 602.5 Problems 602.6 Bibliography 613 Control of Wind Turbines 633.1 Introduction 633.2 Baseline Generator-Torque and Blade-Pitch Controller 633.3 Model-Based Control of WTs 723.3.1 Control Scheme 723.3.2 Effective Wind Speed and State Observer 723.3.3 State Feedback Design for Partial- and Full-Load Operating Region 793.3.3.1 Design of a Full-Load Region Control with State Feedback 823.3.3.2 Control-Design of Partial-Load Operating Region 853.3.3.3 Control Concept for Bumpless Transition Between Operating Regions 933.4 Model-Based Power Tracking 953.4.1 Introduction 953.4.2 Governor Concept of Synchronous Machines 963.4.3 Control-Oriented Models and Schemes 983.4.3.1 Control-oriented Model and Control Scheme for V ≥ V Rated 993.4.3.2 Control-oriented Model and Scheme for V < V Rated 1003.4.4 State Feedback and Feedforward Design for Power Tracking 1043.4.4.1 Controller Design for V ≥ V Rated 1053.4.4.2 Controller Design for V < V Rated 1093.5 Summary 1113.6 Problems 1123.7 Bibliography 1134 Modeling and Control of Photovoltaic Power Plants 1154.1 Introduction 1154.2 Modeling of PV Generators 1164.3 DC–DC Converter Modeling 1214.3.1 Overview of Switched-Mode Converter 1214.3.2 Generic State-Space Average Models 1244.3.3 Circuit Design and Simulation 1274.4 Voltage Control of PV Generators 1314.4.1 Control-Oriented State-Space Model 1314.4.2 State-Feedback Design 1364.5 Demanded Power Tracking 1474.5.1 Overall Control Structure 1484.5.2 Model-Based Power Tracking 1494.5.2.1 Performance and Robustness Analysis of the Cascaded Controller 1524.5.3 Model-Free Power Tracking 1544.6 Summary 1604.7 Problems 1604.8 Bibliography 1615 Modeling and Control of Voltage Source Converters 1635.1 Introduction 1635.2 Three-Phase Signals and Systems 1655.3 Average and Instantaneous Power 1695.4 Reduced-Order VSC Model 1735.5 Power Injection in the Steady State 1755.6 Voltage Drop in the Steady State 1765.7 Selected Control Concepts 1795.7.1 Control and Functional Requirements 1795.7.2 Control Scheme of Grid-Following VSC 1815.7.2.1 PQ Control of Grid-Following VSC 1835.7.2.2 Current Control of GFL Voltage Source Converter 1845.7.3 Control Scheme of Grid-Forming VSC 1855.7.3.1 PQ Control by Direct Droop-Based Voltage Control 1865.7.4 Grid-Forming VSC Control With Inner-Loop Current Regulator 1885.7.4.1 PQ Control as Reference Signal Generator for Lower-Level Control 1895.8 Summary 1905.9 Problems 1905.10 Bibliography 1916 Advanced Grid Integration of PV and Wind Power Plants 1936.1 Introduction 1936.2 Description of Test Scenarios 1946.3 Integration of Wind Power Plants 1976.3.1 Response to Active Power Request 1986.3.2 Decrease in Wind Inflow 1996.3.3 Response to Reactive Power Request 1996.3.4 Grid Disturbance Rejection 2026.4 Integration of PV Power Plants 2056.4.1 Response to Active Power Request 2056.4.2 RES Fluctuation: Irradiation Step 2076.4.3 Response to Reactive Power Request 2076.4.4 Grid Disturbance Rejection 2076.5 Summary 2106.6 Problems 2116.7 Bibliography 212A Modeling in the Takagi–Sugeno Framework 213A.1 Introduction 213A.2 Constructing TS Systems 214A.2.1 Sector-Nonlinearity Approach 214A.2.2 Taylor Linearization and Interpolation 215B LMI Conditions for Stability Analysis and Controller Design 219B.1 Introduction 219B.2 Linear Matrix Inequalities 220B.2.1 Basics 220B.2.2 Suitable Auxiliary Lemmas 222B.3 Stability Analysis of TS Systems 223B.3.1 Stability of Unforced TS Systems 223B.3.1.1 Asymptotic Stability 223B.3.1.2 D-Stability 224B.4 Relaxations 229B.5 State Feedback Design for TS Systems 230B.5.1 Pole Region Specification 231B.5.2 Minimization of M j 233B.5.3 Stability of Forced Systems 233B.5.3.1 Disturbance Rejection 233B.5.3.2 Input-to-State Stability 234B.6 Observer Design for TS Systems 236B.6.1 Pole Region Specification for Observer Design 237C Renewable Energy Sources 239C.1 Wind Energy Systems 239C.1.1 Froude’s Actuator Disc Theory (Froude–Rankine Theorem) 239C.1.2 Rotor-Equivalent Wind Speed 240C.1.3 Membership Functions and Matrices of TS Multi-region Model 241D Parameters of Renewable Energy Power Plants 243D.1 Physical Constants 243D.2 Wind Power Plant Parameters 243D.3 PV Power Plant Parameters 243D.4 VSC Parameters 245D.5 Equivalent Grid Model Parameters 246E Control Concept for Bumpless Transition Between Operating Regions 247References 251Index 265

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

• Preface ixAcronyms xiNotation xiii1 Introduction 11.1 Energy Transition 11.2 Problem Description 51.3 Methodological Framework 91.4 Topics of this Book 122 Modeling of Wind Turbines 152.1 Introduction 152.2 First-Principle Modeling 162.2.1 Energy Capturing: Actuator Disc Concept 162.2.1.1 Power Coefficient 182.2.1.2 Thrust Coefficient 202.2.2 Essentials of Rotor Blade Theory for Control Purpose 212.2.3 The c P –λ, c Q –λ, and c T –λ Curves 272.2.4 Wind Turbine Models with 1- and 4-DOF 322.2.5 Simulation-Based Model Validation 382.3 Control-Oriented Models in TS Form 412.3.1 Partial- and Full-Load Operating Region 412.3.2 Single-Region 1-DOF Models 422.3.3 Single-Region 2- and 3-DOF Models 472.3.3.1 Model with Tower and Rotor DOF 472.3.3.2 Model with Tower, Elastic Drive Train, and Rotor DOF 492.3.3.3 Model with Tower, Blades, and Rotor DOF 502.3.4 Multi-region Model for Disturbance Observer Design 532.3.5 Multi-region Model for Controller Design 572.4 Summary 602.5 Problems 602.6 Bibliography 613 Control of Wind Turbines 633.1 Introduction 633.2 Baseline Generator-Torque and Blade-Pitch Controller 633.3 Model-Based Control of WTs 723.3.1 Control Scheme 723.3.2 Effective Wind Speed and State Observer 723.3.3 State Feedback Design for Partial- and Full-Load Operating Region 793.3.3.1 Design of a Full-Load Region Control with State Feedback 823.3.3.2 Control-Design of Partial-Load Operating Region 853.3.3.3 Control Concept for Bumpless Transition Between Operating Regions 933.4 Model-Based Power Tracking 953.4.1 Introduction 953.4.2 Governor Concept of Synchronous Machines 963.4.3 Control-Oriented Models and Schemes 983.4.3.1 Control-oriented Model and Control Scheme for V ≥ V Rated 993.4.3.2 Control-oriented Model and Scheme for V < V Rated 1003.4.4 State Feedback and Feedforward Design for Power Tracking 1043.4.4.1 Controller Design for V ≥ V Rated 1053.4.4.2 Controller Design for V < V Rated 1093.5 Summary 1113.6 Problems 1123.7 Bibliography 1134 Modeling and Control of Photovoltaic Power Plants 1154.1 Introduction 1154.2 Modeling of PV Generators 1164.3 DC–DC Converter Modeling 1214.3.1 Overview of Switched-Mode Converter 1214.3.2 Generic State-Space Average Models 1244.3.3 Circuit Design and Simulation 1274.4 Voltage Control of PV Generators 1314.4.1 Control-Oriented State-Space Model 1314.4.2 State-Feedback Design 1364.5 Demanded Power Tracking 1474.5.1 Overall Control Structure 1484.5.2 Model-Based Power Tracking 1494.5.2.1 Performance and Robustness Analysis of the Cascaded Controller 1524.5.3 Model-Free Power Tracking 1544.6 Summary 1604.7 Problems 1604.8 Bibliography 1615 Modeling and Control of Voltage Source Converters 1635.1 Introduction 1635.2 Three-Phase Signals and Systems 1655.3 Average and Instantaneous Power 1695.4 Reduced-Order VSC Model 1735.5 Power Injection in the Steady State 1755.6 Voltage Drop in the Steady State 1765.7 Selected Control Concepts 1795.7.1 Control and Functional Requirements 1795.7.2 Control Scheme of Grid-Following VSC 1815.7.2.1 PQ Control of Grid-Following VSC 1835.7.2.2 Current Control of GFL Voltage Source Converter 1845.7.3 Control Scheme of Grid-Forming VSC 1855.7.3.1 PQ Control by Direct Droop-Based Voltage Control 1865.7.4 Grid-Forming VSC Control With Inner-Loop Current Regulator 1885.7.4.1 PQ Control as Reference Signal Generator for Lower-Level Control 1895.8 Summary 1905.9 Problems 1905.10 Bibliography 1916 Advanced Grid Integration of PV and Wind Power Plants 1936.1 Introduction 1936.2 Description of Test Scenarios 1946.3 Integration of Wind Power Plants 1976.3.1 Response to Active Power Request 1986.3.2 Decrease in Wind Inflow 1996.3.3 Response to Reactive Power Request 1996.3.4 Grid Disturbance Rejection 2026.4 Integration of PV Power Plants 2056.4.1 Response to Active Power Request 2056.4.2 RES Fluctuation: Irradiation Step 2076.4.3 Response to Reactive Power Request 2076.4.4 Grid Disturbance Rejection 2076.5 Summary 2106.6 Problems 2116.7 Bibliography 212A Modeling in the Takagi–Sugeno Framework 213A.1 Introduction 213A.2 Constructing TS Systems 214A.2.1 Sector-Nonlinearity Approach 214A.2.2 Taylor Linearization and Interpolation 215B LMI Conditions for Stability Analysis and Controller Design 219B.1 Introduction 219B.2 Linear Matrix Inequalities 220B.2.1 Basics 220B.2.2 Suitable Auxiliary Lemmas 222B.3 Stability Analysis of TS Systems 223B.3.1 Stability of Unforced TS Systems 223B.3.1.1 Asymptotic Stability 223B.3.1.2 D-Stability 224B.4 Relaxations 229B.5 State Feedback Design for TS Systems 230B.5.1 Pole Region Specification 231B.5.2 Minimization of M j 233B.5.3 Stability of Forced Systems 233B.5.3.1 Disturbance Rejection 233B.5.3.2 Input-to-State Stability 234B.6 Observer Design for TS Systems 236B.6.1 Pole Region Specification for Observer Design 237C Renewable Energy Sources 239C.1 Wind Energy Systems 239C.1.1 Froude’s Actuator Disc Theory (Froude–Rankine Theorem) 239C.1.2 Rotor-Equivalent Wind Speed 240C.1.3 Membership Functions and Matrices of TS Multi-region Model 241D Parameters of Renewable Energy Power Plants 243D.1 Physical Constants 243D.2 Wind Power Plant Parameters 243D.3 PV Power Plant Parameters 243D.4 VSC Parameters 245D.5 Equivalent Grid Model Parameters 246E Control Concept for Bumpless Transition Between Operating Regions 247References 251Index 265

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

• Preface ixAcronyms xiNotation xiii1 Introduction 11.1 Energy Transition 11.2 Problem Description 51.3 Methodological Framework 91.4 Topics of this Book 122 Modeling of Wind Turbines 152.1 Introduction 152.2 First-Principle Modeling 162.2.1 Energy Capturing: Actuator Disc Concept 162.2.1.1 Power Coefficient 182.2.1.2 Thrust Coefficient 202.2.2 Essentials of Rotor Blade Theory for Control Purpose 212.2.3 The c P –λ, c Q –λ, and c T –λ Curves 272.2.4 Wind Turbine Models with 1- and 4-DOF 322.2.5 Simulation-Based Model Validation 382.3 Control-Oriented Models in TS Form 412.3.1 Partial- and Full-Load Operating Region 412.3.2 Single-Region 1-DOF Models 422.3.3 Single-Region 2- and 3-DOF Models 472.3.3.1 Model with Tower and Rotor DOF 472.3.3.2 Model with Tower, Elastic Drive Train, and Rotor DOF 492.3.3.3 Model with Tower, Blades, and Rotor DOF 502.3.4 Multi-region Model for Disturbance Observer Design 532.3.5 Multi-region Model for Controller Design 572.4 Summary 602.5 Problems 602.6 Bibliography 613 Control of Wind Turbines 633.1 Introduction 633.2 Baseline Generator-Torque and Blade-Pitch Controller 633.3 Model-Based Control of WTs 723.3.1 Control Scheme 723.3.2 Effective Wind Speed and State Observer 723.3.3 State Feedback Design for Partial- and Full-Load Operating Region 793.3.3.1 Design of a Full-Load Region Control with State Feedback 823.3.3.2 Control-Design of Partial-Load Operating Region 853.3.3.3 Control Concept for Bumpless Transition Between Operating Regions 933.4 Model-Based Power Tracking 953.4.1 Introduction 953.4.2 Governor Concept of Synchronous Machines 963.4.3 Control-Oriented Models and Schemes 983.4.3.1 Control-oriented Model and Control Scheme for V ≥ V Rated 993.4.3.2 Control-oriented Model and Scheme for V < V Rated 1003.4.4 State Feedback and Feedforward Design for Power Tracking 1043.4.4.1 Controller Design for V ≥ V Rated 1053.4.4.2 Controller Design for V < V Rated 1093.5 Summary 1113.6 Problems 1123.7 Bibliography 1134 Modeling and Control of Photovoltaic Power Plants 1154.1 Introduction 1154.2 Modeling of PV Generators 1164.3 DC–DC Converter Modeling 1214.3.1 Overview of Switched-Mode Converter 1214.3.2 Generic State-Space Average Models 1244.3.3 Circuit Design and Simulation 1274.4 Voltage Control of PV Generators 1314.4.1 Control-Oriented State-Space Model 1314.4.2 State-Feedback Design 1364.5 Demanded Power Tracking 1474.5.1 Overall Control Structure 1484.5.2 Model-Based Power Tracking 1494.5.2.1 Performance and Robustness Analysis of the Cascaded Controller 1524.5.3 Model-Free Power Tracking 1544.6 Summary 1604.7 Problems 1604.8 Bibliography 1615 Modeling and Control of Voltage Source Converters 1635.1 Introduction 1635.2 Three-Phase Signals and Systems 1655.3 Average and Instantaneous Power 1695.4 Reduced-Order VSC Model 1735.5 Power Injection in the Steady State 1755.6 Voltage Drop in the Steady State 1765.7 Selected Control Concepts 1795.7.1 Control and Functional Requirements 1795.7.2 Control Scheme of Grid-Following VSC 1815.7.2.1 PQ Control of Grid-Following VSC 1835.7.2.2 Current Control of GFL Voltage Source Converter 1845.7.3 Control Scheme of Grid-Forming VSC 1855.7.3.1 PQ Control by Direct Droop-Based Voltage Control 1865.7.4 Grid-Forming VSC Control With Inner-Loop Current Regulator 1885.7.4.1 PQ Control as Reference Signal Generator for Lower-Level Control 1895.8 Summary 1905.9 Problems 1905.10 Bibliography 1916 Advanced Grid Integration of PV and Wind Power Plants 1936.1 Introduction 1936.2 Description of Test Scenarios 1946.3 Integration of Wind Power Plants 1976.3.1 Response to Active Power Request 1986.3.2 Decrease in Wind Inflow 1996.3.3 Response to Reactive Power Request 1996.3.4 Grid Disturbance Rejection 2026.4 Integration of PV Power Plants 2056.4.1 Response to Active Power Request 2056.4.2 RES Fluctuation: Irradiation Step 2076.4.3 Response to Reactive Power Request 2076.4.4 Grid Disturbance Rejection 2076.5 Summary 2106.6 Problems 2116.7 Bibliography 212A Modeling in the Takagi–Sugeno Framework 213A.1 Introduction 213A.2 Constructing TS Systems 214A.2.1 Sector-Nonlinearity Approach 214A.2.2 Taylor Linearization and Interpolation 215B LMI Conditions for Stability Analysis and Controller Design 219B.1 Introduction 219B.2 Linear Matrix Inequalities 220B.2.1 Basics 220B.2.2 Suitable Auxiliary Lemmas 222B.3 Stability Analysis of TS Systems 223B.3.1 Stability of Unforced TS Systems 223B.3.1.1 Asymptotic Stability 223B.3.1.2 D-Stability 224B.4 Relaxations 229B.5 State Feedback Design for TS Systems 230B.5.1 Pole Region Specification 231B.5.2 Minimization of M j 233B.5.3 Stability of Forced Systems 233B.5.3.1 Disturbance Rejection 233B.5.3.2 Input-to-State Stability 234B.6 Observer Design for TS Systems 236B.6.1 Pole Region Specification for Observer Design 237C Renewable Energy Sources 239C.1 Wind Energy Systems 239C.1.1 Froude’s Actuator Disc Theory (Froude–Rankine Theorem) 239C.1.2 Rotor-Equivalent Wind Speed 240C.1.3 Membership Functions and Matrices of TS Multi-region Model 241D Parameters of Renewable Energy Power Plants 243D.1 Physical Constants 243D.2 Wind Power Plant Parameters 243D.3 PV Power Plant Parameters 243D.4 VSC Parameters 245D.5 Equivalent Grid Model Parameters 246E Control Concept for Bumpless Transition Between Operating Regions 247References 251Index 265