Stability Analysis of Converter-Rich Power Grids

Jun Liang, PhD, is a Chair Professor at Cardiff University’s School of Engineering, United Kingdom. A Fellow of the IET and Senior Member of IEEE, he has extensive expertise in power electronics and HVDC systems. He co-authored the Wiley-IEEE Press title HVDC Grids: For Offshore and Supergrid of the Future (2016) and has held leadership roles in IEEE and CIGRE, contributing significantly to power system stability research. Chuanyue Li, PhD, is a Research Associate at Cardiff University’s School of Engineering, specializing in power systems, renewable energy integration, and transportation electrification. He has co-authored multiple high-impact journal articles in leading IEEE publications. His research focuses on developing advanced analytical tools and solutions to address converter-driven instability and grid integration challenges.

• Foreword xiPreface xiiiAcknowledgments xviiAcronyms xixIntroduction xxi1 Drives of High Penetration of Converters 11.1 High-voltage Direct Current 11.1.1 LCC-HVDC 11.1.2 VSC-HVDC 31.2 Renewable Energy 51.2.1 Wind Generation 51.2.2 Solar Photovoltaic 71.3 Energy Storage System 9References 102 Challenges and Future Development of Grid-connected Converters 132.1 Conventional Classification of Power System Stability Based on Disturbances 132.1.1 Steady-state Stability Condition (Without Considering Damping Characteristics) 142.1.2 Steady-state Stability Condition (Considering Damping Characteristics) 162.1.3 Subsynchronous Resonance 162.1.4 Transient Stability 172.2 Overview of VSC-induced Oscillation Events 182.2.1 Oscillation Frequency of Different Electrical Quantities 202.3 Subsynchronous Oscillations 222.3.1 Subsynchronous Resonance 232.3.2 Power Electronic Device Interactions 242.4 Classification of Power System Stability 242.4.1 Classification of Power System Stability in 1982 242.4.2 Classification of Power System Stability in 2004 252.4.3 Classification of Power System Stability in 2020 262.5 Control Interaction of CIG 272.5.1 Past Experiences with Control Interactions from Power Electronic Devices 272.5.2 Control Interaction of VSCs 282.6 Overview of Weak-grid Caused Instabilities 312.6.1 Past Experiences with Weak-grid Instabilities 322.6.2 VSC: Weak-grid Instabilities 32References 343 Fundamental Stability Criteria for Feedback Systems 373.1 The Mathematical Mechanism of System Stability 373.2 Stability Criterion via Pole Map 393.3 Stability Criterion via Bode Plot Analysis 413.4 Stability Criterion via Nyquist Plot Analysis 43Reference 464 Modeling of Grid-connected Converters 474.1 Basic Control Configurations of VSCs 474.2 Linearization of VSC Control Systems 484.2.1 Linearization of Frame Transformation for Single-phase Systems 504.2.2 Linearization of Reference Frame Transformation for Three-phase Systems 524.2.3 Summary of the Linearization of the Frame Transformation 544.3 Modeling of Frame Transformation with Frequency Alignment Control 554.3.1 Modeling of Phase-locked Loops 564.3.2 Modeling of Power-frequency Droop Control 574.4 Modeling and Stability Analysis of a VSC System 604.4.1 Modeling a VSC System 604.4.2 Transfer-function-based Stability Analysis Method for Converter Systems 624.4.3 Case Study on Stability Analysis of the PLL 634.4.4 Stability Analysis of the P−ω Droop Control 66Reference 675 Stability Analysis Methods 695.1 State-space Stability Analysis Method 695.1.1 Typical State-space Stability Analysis Method 705.1.2 Sensitivity Stability Analysis 705.1.3 Demonstration of State-space Stability Analysis Method 715.2 Impedance Stability Analysis Method 755.2.1 Impedance Representation of Converters Based on Norton and Thevenin Equivalent Circuits 755.2.2 Demonstration of How to Derive Converter Impedance 765.2.3 Impedance Stability Analysis Method Based on Generalized Nyquist Criterion and Bode Criterion 775.2.4 dq-sequence Impedance 825.2.5 αβ Impedance 845.3 Comparison Among Stability Analysis Methods 86References 886 Impedance Interaction Analysis for Converter-integrated Power Systems 896.1 Impedance Interaction Analysis 896.1.1 Negative Resistor Criterion in an Equivalent RLC Circuit 896.1.2 Stability Impact of Negative Inductors and Capacitors in an RLC Circuit 916.1.3 Effective Frequency Range of a Negative Resistor, Inductor, and Capacitor in an RLC Circuit 936.2 Impedance Interaction in a High-order System 976.2.1 Impedance Interaction Criterion 976.2.2 Modified Impedance Interaction Criterion 986.2.3 Case Study for Impedance Interaction Analysis 1006.2.4 Why Is the Impedance in the Form of a 2 × 2 Matrix? 103Reference 1057 Mirror-frequency Oscillation Due to Converters 1077.1 Mirror-frequency Effect of Converter Systems 1077.1.1 Mirror-frequency Effect in a Single-phase Control 1087.1.2 Mirror Frequency in a Three-phase System 1097.2 The Difference Between Mirror-frequency Oscillations and Positive/ Negative Sequence Oscillations 1157.3 The Performance of Mirror-frequency Oscillations Across Different Electrical Quantities 1177.4 Understanding Balanced and Unbalanced Control Systems and Their Role in the Mirror-frequency Effect 1197.5 Why Is Converter Control an Unbalanced System? 1228 Impedance Measurement Techniques for Power System Stability Analysis 1258.1 Stability Analysis Method Based on Measurement 1258.1.1 Mechanism of Impedance Measurement 1258.2 Impedance Measurement Methods 1268.2.1 DC Impedance Measurement 1268.2.2 AC System Impedance Measurement 1278.3 Impact of Noise on Measurement Accuracy and Elimination Methods 1308.3.1 Impact of Noise on DC Impedance Measurements and Elimination Methods 1318.3.2 Impact of Noise on AC Impedance Measurements and Elimination Methods 1338.4 Impedance Measurement of dq-sequence Impedance or αβ Impedance 1359 Stability Analysis of Grid-following Converters 1399.1 Instability Causes of PLL-based Control 1399.1.1 Stability Performance Comparison Between Current Control and PLL 1399.1.2 Dominant Factor of Current Control Causing PCC Voltage Fluctuation 1429.1.3 Instability Cause of Outer Loop 1449.2 A Tuning Method for PLL-based Current Control 1469.2.1 Solution for the Dominant Instability 1469.2.2 The Relationship Between Current Control and PLLs 1499.2.3 Tuning Strategies 1539.3 Overall Tuning Strategy for PLL-based PV Control Systems 1549.3.1 Outer-loop Tuning Strategy 1549.3.2 Coordinated Tuning of PLL and Current Control 1569.3.3 Overall Tuning Strategy 1569.4 Summary 158References 15810 Stability Analysis of Grid-forming Converters 15910.1 Development of Grid-forming Converters 15910.1.1 Connection with Synchronous Generators 15910.1.2 Development of GFM Control 16110.1.3 GFM Capabilities 16210.2 Definition and Variants of GFM Control 16310.3 Brief Comparative Analysis of Stability Characteristics: GFM Converters and SGs in Strong and Weak Grids 16710.3.1 Causes of GFM Converter Instability in Strong Grids 16710.3.2 A Brief Discussion on the Stability of SGs Under Weak Grid Conditions 16910.4 Comparative Analysis of PLL-based Grid-supporting Control and P−ω Droop-based GFM Controls 17010.4.1 Island Operation of a PLL-based Grid-supporting Converter 17010.4.2 Control Conflict Analysis: P−ω Droop and Inner Current Control in GFM Converters 17110.4.3 Comparative Analysis of Grid-supporting and GFM Control Strategies 17210.4.4 Challenges of Current-source-based GFM Control 17310.5 Comparative Analysis of Stability in GFL and GFM Converters 17510.5.1 Stability Analysis Under Various Grid Strength Conditions 17610.5.2 Stability Analysis with Various Cutoff Frequencies of the Inner Current Control Loop 17710.5.3 Stability Enhancement Using Virtual Impedance 17810.5.4 Summary 180References 18211 Transient Stability Analysis of Grid-following and Grid-forming Converters 18511.1 Transient Stability of Conventional Synchronous Generators Based Power Systems 18511.1.1 Introduction of Transient Stability 18511.1.2 Transient Stability Analysis Approaches 18611.1.3 Transient Stability Enhancement Methods 18811.2 Transient Stability of Grid-following Converters 18911.2.1 Overview of Transient Stability of Grid-following Converters 18911.2.2 Control Structure 19111.2.3 Transient Stability Analysis 19211.2.4 Simulation Verifications 19611.3 Transient Stability of Grid-forming Converters 19811.3.1 Overview of Transient Stability of Grid-forming Converters 19811.3.2 Control Structure 20011.3.3 Transient Stability Analysis 20111.3.4 Simulation Verifications 20611.4 Summary 211References 212Appendix A: Small-signal Model of Grid-following Converters 215Index 227