Provides a deep understanding of the mechanisms, analysis methods, stability criteria, and stabilization methods for converter-driven oscillations in power systems
The extensive integration of converter-interfaced resources into power systems has significantly increased the occurrences of converter-driven oscillations, posing a serious new challenge to power system stability over the past decade. Stability Analysis of Converter-Rich Power Grids offers a comprehensive understanding of converter interactions with power systems and their oscillation characteristics. Based on academic research, this book is to explicitly connect mathematical mechanism and converter-driven oscillation phenomena, helping readers with deep insight into converter-driven oscillations.
To provide a solid foundation for studying converter-driven oscillations, the book is organized into ten chapters, covering topics such as stability mechanisms, modeling, stability criteria, analysis methods, and stabilization techniques for different types of converters.
Equipping readers with the knowledge to design stable converter systems and tackle critical power system challenges, Stability Analysis of Converter-Rich Power Grids:
- Describes the history of converter-driven oscillations and presents recent understandings and categorizations of these oscillations in sub-synchronous oscillation classification and power system stability classification
- Presents modeling methods for typical converter control approaches, including grid-following and grid-forming converters
- Explains the mechanism of mirror-frequency oscillations induced by converters and clarifies the fundamental causes of converter-driven oscillations
- Provides comprehensive stability analysis methods and distinctions in their applications, including the impedance measurement methods for stability analysis for black-box systems
- Analyzes and specifies the stability characteristics of both grid-following and grid-forming converters, with relevant stabilization measures provided accordingly
Stability Analysis of Converter-Rich Power Grids is an essential resource for engineers, system operators, and converter designers addressing power system stability challenges. It is also an excellent supplementary text for graduate and advanced undergraduate courses in power systems, renewable energy integration, and power electronics.
Table of Contents:
Foreword xi
Preface xiii
Acknowledgments xvii
Acronyms xix
Introduction xxi
1 Drives of High Penetration of Converters 1
1.1 High-voltage Direct Current 1
1.1.1 LCC-HVDC 1
1.1.2 VSC-HVDC 3
1.2 Renewable Energy 5
1.2.1 Wind Generation 5
1.2.2 Solar Photovoltaic 7
1.3 Energy Storage System 9
References 10
2 Challenges and Future Development of Grid-connected Converters 13
2.1 Conventional Classification of Power System Stability Based on Disturbances 13
2.1.1 Steady-state Stability Condition (Without Considering Damping Characteristics) 14
2.1.2 Steady-state Stability Condition (Considering Damping Characteristics) 16
2.1.3 Subsynchronous Resonance 16
2.1.4 Transient Stability 17
2.2 Overview of VSC-induced Oscillation Events 18
2.2.1 Oscillation Frequency of Different Electrical Quantities 20
2.3 Subsynchronous Oscillations 22
2.3.1 Subsynchronous Resonance 23
2.3.2 Power Electronic Device Interactions 24
2.4 Classification of Power System Stability 24
2.4.1 Classification of Power System Stability in 1982 24
2.4.2 Classification of Power System Stability in 2004 25
2.4.3 Classification of Power System Stability in 2020 26
2.5 Control Interaction of CIG 27
2.5.1 Past Experiences with Control Interactions from Power Electronic Devices 27
2.5.2 Control Interaction of VSCs 28
2.6 Overview of Weak-grid Caused Instabilities 31
2.6.1 Past Experiences with Weak-grid Instabilities 32
2.6.2 VSC: Weak-grid Instabilities 32
References 34
3 Fundamental Stability Criteria for Feedback Systems 37
3.1 The Mathematical Mechanism of System Stability 37
3.2 Stability Criterion via Pole Map 39
3.3 Stability Criterion via Bode Plot Analysis 41
3.4 Stability Criterion via Nyquist Plot Analysis 43
Reference 46
4 Modeling of Grid-connected Converters 47
4.1 Basic Control Configurations of VSCs 47
4.2 Linearization of VSC Control Systems 48
4.2.1 Linearization of Frame Transformation for Single-phase Systems 50
4.2.2 Linearization of Reference Frame Transformation for Three-phase Systems 52
4.2.3 Summary of the Linearization of the Frame Transformation 54
4.3 Modeling of Frame Transformation with Frequency Alignment Control 55
4.3.1 Modeling of Phase-locked Loops 56
4.3.2 Modeling of Power-frequency Droop Control 57
4.4 Modeling and Stability Analysis of a VSC System 60
4.4.1 Modeling a VSC System 60
4.4.2 Transfer-function-based Stability Analysis Method for Converter Systems 62
4.4.3 Case Study on Stability Analysis of the PLL 63
4.4.4 Stability Analysis of the P−ω Droop Control 66
Reference 67
5 Stability Analysis Methods 69
5.1 State-space Stability Analysis Method 69
5.1.1 Typical State-space Stability Analysis Method 70
5.1.2 Sensitivity Stability Analysis 70
5.1.3 Demonstration of State-space Stability Analysis Method 71
5.2 Impedance Stability Analysis Method 75
5.2.1 Impedance Representation of Converters Based on Norton and Thevenin Equivalent Circuits 75
5.2.2 Demonstration of How to Derive Converter Impedance 76
5.2.3 Impedance Stability Analysis Method Based on Generalized Nyquist Criterion and Bode Criterion 77
5.2.4 dq-sequence Impedance 82
5.2.5 αβ Impedance 84
5.3 Comparison Among Stability Analysis Methods 86
References 88
6 Impedance Interaction Analysis for Converter-integrated Power Systems 89
6.1 Impedance Interaction Analysis 89
6.1.1 Negative Resistor Criterion in an Equivalent RLC Circuit 89
6.1.2 Stability Impact of Negative Inductors and Capacitors in an RLC Circuit 91
6.1.3 Effective Frequency Range of a Negative Resistor, Inductor, and Capacitor in an RLC Circuit 93
6.2 Impedance Interaction in a High-order System 97
6.2.1 Impedance Interaction Criterion 97
6.2.2 Modified Impedance Interaction Criterion 98
6.2.3 Case Study for Impedance Interaction Analysis 100
6.2.4 Why Is the Impedance in the Form of a 2 × 2 Matrix? 103
Reference 105
7 Mirror-frequency Oscillation Due to Converters 107
7.1 Mirror-frequency Effect of Converter Systems 107
7.1.1 Mirror-frequency Effect in a Single-phase Control 108
7.1.2 Mirror Frequency in a Three-phase System 109
7.2 The Difference Between Mirror-frequency Oscillations and Positive/ Negative Sequence Oscillations 115
7.3 The Performance of Mirror-frequency Oscillations Across Different Electrical Quantities 117
7.4 Understanding Balanced and Unbalanced Control Systems and Their Role in the Mirror-frequency Effect 119
7.5 Why Is Converter Control an Unbalanced System? 122
8 Impedance Measurement Techniques for Power System Stability Analysis 125
8.1 Stability Analysis Method Based on Measurement 125
8.1.1 Mechanism of Impedance Measurement 125
8.2 Impedance Measurement Methods 126
8.2.1 DC Impedance Measurement 126
8.2.2 AC System Impedance Measurement 127
8.3 Impact of Noise on Measurement Accuracy and Elimination Methods 130
8.3.1 Impact of Noise on DC Impedance Measurements and Elimination Methods 131
8.3.2 Impact of Noise on AC Impedance Measurements and Elimination Methods 133
8.4 Impedance Measurement of dq-sequence Impedance or αβ Impedance 135
9 Stability Analysis of Grid-following Converters 139
9.1 Instability Causes of PLL-based Control 139
9.1.1 Stability Performance Comparison Between Current Control and PLL 139
9.1.2 Dominant Factor of Current Control Causing PCC Voltage Fluctuation 142
9.1.3 Instability Cause of Outer Loop 144
9.2 A Tuning Method for PLL-based Current Control 146
9.2.1 Solution for the Dominant Instability 146
9.2.2 The Relationship Between Current Control and PLLs 149
9.2.3 Tuning Strategies 153
9.3 Overall Tuning Strategy for PLL-based PV Control Systems 154
9.3.1 Outer-loop Tuning Strategy 154
9.3.2 Coordinated Tuning of PLL and Current Control 156
9.3.3 Overall Tuning Strategy 156
9.4 Summary 158
References 158
10 Stability Analysis of Grid-forming Converters 159
10.1 Development of Grid-forming Converters 159
10.1.1 Connection with Synchronous Generators 159
10.1.2 Development of GFM Control 161
10.1.3 GFM Capabilities 162
10.2 Definition and Variants of GFM Control 163
10.3 Brief Comparative Analysis of Stability Characteristics: GFM Converters and SGs in Strong and Weak Grids 167
10.3.1 Causes of GFM Converter Instability in Strong Grids 167
10.3.2 A Brief Discussion on the Stability of SGs Under Weak Grid Conditions 169
10.4 Comparative Analysis of PLL-based Grid-supporting Control and P−ω Droop-based GFM Controls 170
10.4.1 Island Operation of a PLL-based Grid-supporting Converter 170
10.4.2 Control Conflict Analysis: P−ω Droop and Inner Current Control in GFM Converters 171
10.4.3 Comparative Analysis of Grid-supporting and GFM Control Strategies 172
10.4.4 Challenges of Current-source-based GFM Control 173
10.5 Comparative Analysis of Stability in GFL and GFM Converters 175
10.5.1 Stability Analysis Under Various Grid Strength Conditions 176
10.5.2 Stability Analysis with Various Cutoff Frequencies of the Inner Current Control Loop 177
10.5.3 Stability Enhancement Using Virtual Impedance 178
10.5.4 Summary 180
References 182
11 Transient Stability Analysis of Grid-following and Grid-forming Converters 185
11.1 Transient Stability of Conventional Synchronous Generators Based Power Systems 185
11.1.1 Introduction of Transient Stability 185
11.1.2 Transient Stability Analysis Approaches 186
11.1.3 Transient Stability Enhancement Methods 188
11.2 Transient Stability of Grid-following Converters 189
11.2.1 Overview of Transient Stability of Grid-following Converters 189
11.2.2 Control Structure 191
11.2.3 Transient Stability Analysis 192
11.2.4 Simulation Verifications 196
11.3 Transient Stability of Grid-forming Converters 198
11.3.1 Overview of Transient Stability of Grid-forming Converters 198
11.3.2 Control Structure 200
11.3.3 Transient Stability Analysis 201
11.3.4 Simulation Verifications 206
11.4 Summary 211
References 212
Appendix A: Small-signal Model of Grid-following Converters 215
Index 227
