Механизмы возникновения субсинхронных колебаний в энергосистемах с силовыми инверторными преобразователями. Ч. 1
Ключевые слова:
сетевой инвертор, субсинхронные колебания, устойчивость, система автоматического управления, возобновляемые источники энергии
Аннотация
Современные энергосистемы меняются благодаря широкомасштабному внедрению силовых инверторных преобразователей. Уникальные свойства таких устройств изменяют динамику энергосистем и приводят к появлению новых процессов. Среди них выделяется явление, сопровождающееся возникновением широкого спектра субсинхронных колебаний, связанных с реакцией используемой системы управления сетевого инвертора во вращающихся координатах dq на различные схемно-режимные условия работы электрической сети. Учитывая существующие пробелы в понимании механизмов возникновения субсинхронных колебаний из-за различных комбинаций регуляторов, используемых в системе управления сетевым инвертором, и параметров электрической сети, первая часть статьи посвящена разработке упрощенных математических моделей сетевого инвертора с различной степенью детализации. Последовательно рассмотрены модели, отражающие влияние на субсинхронные колебания различных внешних регуляторов, блока фазовой автоподстройки частоты и их реакция на изменение плотности электрической сети, уровня загрузки сетевого инвертора по активной мощности и напряжения в точке подключения. Для полученных моделей проведен частотный анализ, на основе которого выявлены механизмы возникновения субсинхронных колебаний и влияющие факторы. Для каждого механизма возникновения субсинхронных колебаний обоснована необходимая степень детализации используемой математической модели.
Литература
1. Илюшин П.В., Георгиевский И.Д. Обзор возможностей для увеличения доли ветровых и солнечных электростанций в структуре генерирующих мощностей энергосистем. – Энергетик, 2023, № 5, с. 13–18.
2. Рубан Н.Ю. и др. Анализ влияния возобновляемых источников энергии с силовыми преобразователями на процессы в современных энергосистемах. – Вестник ПНИПУ. Электротехника, информационные технологии, системы управления, 2020, № 36, с. 7–30.
3. Cheng Y. et al. Real-World Subsynchronous Oscillation Events in Power Grids With High Penetrations of Inverter-Based Resources. – IEEE Transactions on Power Systems, 2023, 38(1), pp. 316–30, DOI: 10.1109/TPWRS.2022.3161418.
4. Xie X., Shair J. Introduction to Power System Oscillatory Stability. – Oscillatory Stability of Converter-Dominated Power Systems. Power Systems. Springer, Cham, 2024, DOI: 10.1007/978-3-031-53357-0_1.
5. Shair J. et al. Overview of Emerging Subsynchronous Oscillations in Practical Wind Power Systems. – Renewable and Sustainable Energy Reviews, 2019, vol. 99, pp. 159–168, DOI: 10.1016/j.rser.2018.09.047.
6. Xie X. et al. Guest Editorial: Control Interactions in Power Electronic Converter Dominated Power Systems. – International Journal of Electrical Power & Energy Systems, 2024, vol. 155, DOI: 10.1016/j.ijepes.2023.109553.
7. Суворов А.А. и др. Управление сетевым инвертором на основе виртуального синхронного генератора при изменении плотности электрической сети. – Электричество, 2023, № 3, с. 35–51.
8. Fan L. et al. Real-World 20-Hz IBR Subsynchronous Oscillations: Signatures and Mechanism Analysis. – IEEE Transactions on Energy Conversion, 2022, vol. 37(4), pp. 2863–2873, DOI: 10.1109/TEC.2022.3206795.
9. Zhou J.Z. et al. Impact of Short-Circuit Ratio and Phase-Locked-Loop Parameters on the Small-Signal Behavior of a VSC-HVDC Converter. – IEEE Transactions on Power Delivery, 2014, vol. 29, No. 5, pp. 2287–2296, DOI: 10.1109/TPWRD.2014.2330518.
10. Zhao M. et al. Voltage Dynamics of Current Control Time-Scale in A VSC-Connected Weak Grid. – IEEE Transactions on Power Systems, 2016, vol. 31, No. 4, pp. 2925–2937, DOI: 10.1109/TPWRS.2015.2482605.
11. Strachan N.P., Jovcic D. Stability of a Variable-Speed Permanent Magnet Wind Generator with Weak AC Grids. – IEEE Transactions on Power Delivery, 2010, 25(4), pp. 2779–2788, DOI: 10.1109/TPWRD.2010.2053723.
12. Zhou Y. et al. Connecting Wind Power Plant with Weak Grid-Challenges and Solutions. – 2013 IEEE Power & Energy Society General Meeting, 2013, DOI: 10.1109/PESMG.2013.6672755.
13. Hu J. et al. Small Signal Instability of PLL-Synchronized Type-4 Wind Turbines Connected to High-Impedance AC Grid During LVRT. – IEEE Transactions on Energy Conversion, 2016, vol. 31, No. 4, pp. 1676–1687, DOI: 10.1109/TEC.2016.2577606.
14. Булатов Ю.Н. и др. Регулирование напряжения в микросети постоянного и переменного тока на базе энергороутеров и накопителей электроэнергии. – Интеллектуальная электротехника, 2023, № 1 (21), c. 62–84.
15. Huang S.-H. et al. Voltage Control Challenges on Weak Grids with High Penetration of Wind Generation: ERCOT Experience. – 2012 IEEE Power and Energy Society General Meeting, 2012, DOI: 10.1109/PESGM.2012.6344713.
16. Bao L. et al. Hardware Demonstration of Weak Grid Oscillations in Grid-Following Converters. – 2021 North American Power Symposium (NAPS), 2021, DOI: 10.1109/NAPS52732.2021.9654557.
17. Papangelis L. et al. Stability of a Voltage Source Converter Subject to Decrease of Short-Circuit Capacity: A Case Study. – Power Systems Computation Conference (PSCC), 2018, DOI: 10.23919/PSCC.2018.8442773.
18. Fan L. Modeling Type-4 Wind in Weak Grids. – IEEE Transactions on Sustainable Energy, 2019, vol. 10, No. 2, pp. 853–864, DOI: 10.1109/TSTE.2018.2849849.
19. Alawasa K.M. et al. Modeling, Analysis, and Suppression of The Impact of Full-Scale Wind-Power Converters on Subsynchronous Damping. – IEEE Systems Journal, 2013, vol. 7, No. 4, pp. 700–712, DOI: 10.1109/JSYST.2012.2226615.
20. Liu H. et al. Subsynchronous Interaction Between Direct-Drive PMSG Based Wind Farms and Weak AC Networks. – IEEE Transactions on Power Systems, 2017, 32(6), pp. 4708–4720, DOI: 10.1109/TPWRS.2017.2682197.
21. Li Y. et al. Wind in Weak Grids: Low-Frequency Oscillations, Subsynchronous Oscillations, and Torsional Interactions. – IEEE Transactions on Power Systems, 2020, vol. 35, No. 1, pp. 109–118, DOI: 10.1109/TPWRS.2019.2924412.
22. Dong D. et al. Analysis of Phase-Locked Loop Low-Frequency Stability in Three-Phase Grid-Connected Power Converters Considering Impedance Interactions. – IEEE Transactions on Industrial Electronics, 2015, vol. 62, No. 1, pp. 310–321, DOI: 10.1109/TIE.2014.2334665.
23. Li G. et al. PLL Phase Margin Design and Analysis for Mitigating Sub/Super-Synchronous Oscillation of Grid-Connected Inverter Under Weak Grid. – International Journal of Electrical Power & Energy Systems, 2023, vol. 151, DOI: 10.1016/j.ijepes.2023.109124.
24. Li G. et al. A Double-Loop Inertia Phase-Locked Loop with Antidisturbance Ability. – IEEE Transactions on Industrial Informatics, 2023, vol. 19, No. 4, pp. 5585–5592. DOI: 10.1109/TII.2022.3189014.
25. Liu H. et al. Stability Analysis of SSR in Multiple Wind Farms Connected to Series-Compensated Systems Using Impedance Network Model. – IEEE Transactions on Power Systems, 2018, vol. 33, No. 3, pp. 3118–3128, DOI: 10.1109/TPWRS.2017.2764159.
26. Liu H., Xie X. Comparative Studies on the Impedance Models of VSC-Based Renewable Generators for SSI Stability Analysis. – IEEE Transactions on Energy Conversion, 2019, vol. 34, No. 3, pp. 1442–1453, DOI: 10.1109/TEC.2019.2913778.
27. Fan L., Miao Z. Admittance-Based Stability Analysis: Bode Plots, Nyquist Diagrams or Eigenvalue Analysis. – IEEE Transactions on Power Systems, 2020, vol. 35, No. 4, pp. 3312–3315, DOI: 10.1109/TPWRS.2020.2996014.
28. Bi T. et al. Study on Response Characteristics of Grid-Side Inverter Controller of PMSG to Sub-Synchronous Frequency Component. – IET Renewable Power Generation, 2017, vol. 11, No. 7, pp. 966–972, DOI: 10.1049/iet-rpg.2016.0994.
29. Суворов А.А. и др. Синтез и тестирование типовых структур систем автоматического управления на основе виртуального синхронного генератора для генерирующих установок с силовым преобразователем. – Электрические станции, 2022, № 3 (1088), c. 43–57.
30. Wu B. et al. Power Conversion and Control of Wind Energy Systems. Hoboken, U.S.A.: John Wiley & Sons, 2011, 480 p.
31. Blaabjerg F. et al. Overview of Control and Grid Synchronization for Distributed Power Generation Systems. – IEEE Transactions on Industrial Electronics, 2006, vol. 53, No. 5, pp. 1398–1409, DOI: 10.1109/TIE.2006.881997.
32. Ali Z. et al. Three-Phase Phase-Locked Loop Synchronization Algorithms for Grid-Connected Renewable Energy Systems: A Review. – Renewable and Sustainable Energy Reviews, 2018, vol. 90, 434–452, DOI: 10.1016/j.rser.2018.03.086.
33. Симонов А.В., Илюшин П.В. О совершенствовании методических подходов к математическому моделированию ветроэнергетических установок в отечественных программных комплексах АРМ СРЗА и RASTRKZ. – Релейная защита и автоматизация, 2024, № 1 (54), с. 60–65.
34. Yazdani A., Iravani R. Voltage-Sourced Converters in Power Systems: Modeling, Control, and Applications. Hoboken, U.S.A.: John Wiley & Sons, 2010, 541 p.
35. Попов Е.П. Теория линейных систем автоматического регулирования и управления. М.: Наука, 1989, с. 304.
36. Fan L. Control and Dynamics in Power Systems and Microgrids. Boca Raton, U.S.A.: CRC Press, 2017, 230 p.
37. Wen B. et al. Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters. – IEEE Transactions on Power Electronics, 2016, vol. 31, No. 1, pp. 675–687, DOI: 10.1109/TPEL.2015.2398192.
---
Исследование выполнено за счет гранта Российского научного фонда № 24-29-00004.
#
1. Ilyushin P.V., Georgievskiy I.D. Energetik – in Russ. (Power Engineer), 2023, No. 5, pp. 13–18.
2. Ruban N.Yu. et al. Vestnik PNIPU. Elektrotehnika, informatsionnye tehnologii, sistemy upravleniya – in Russ. (Bulletin of PNRPU. Electrical Engineering, Information Technology, Control Systems), 2020, No. 36, pp. 7–30.
3. Cheng Y. et al. Real-World Subsynchronous Oscillation Events in Power Grids with High Penetrations of Inverter-Based Resources. – IEEE Transactions on Power Systems, 2023, 38(1), pp. 316–30, DOI: 10.1109/TPWRS.2022.3161418.
4. Xie X., Shair J. Introduction to Power System Oscillatory Stability. – Oscillatory Stability of Converter-Dominated Power Systems. Power Systems. Springer, Cham, 2024, DOI: 10.1007/978-3-031-53357-0_1.
5. Shair J. et al. Overview of Emerging Subsynchronous Oscillations in Practical Wind Power Systems. – Renewable and Sustainable Energy Reviews, 2019, vol. 99, pp. 159–168, DOI: 10.1016/j.rser.2018.09.047.
6. Xie X. et al. Guest Editorial: Control Interactions in Power Electronic Converter Dominated Power Systems. – International Journal of Electrical Power & Energy Systems, 2024, vol. 155, DOI: 10.1016/j.ijepes.2023.109553
7. Suvorov A.A. et al. Elektrichestvo – in Russ. (Electricity), 2023, No. 3, pp. 35–51.
8. Fan L. et al. Real-World 20-Hz IBR Subsynchronous Oscillations: Signatures and Mechanism Analysis. – IEEE Transactions on Energy Conversion, 2022, vol. 37(4), pp. 2863–2873, DOI: 10.1109/TEC.2022.3206795.
9. Zhou J.Z. et al. Impact of Short-Circuit Ratio and Phase-Locked-Loop Parameters on the Small-Signal Behavior of a VSC-HVDC Converter. – IEEE Transactions on Power Delivery, 2014, vol. 29, No. 5, pp. 2287–2296, DOI: 10.1109/TPWRD.2014.2330518.
10. Zhao M. et al. Voltage Dynamics of Current Control Time-Scale in A VSC-Connected Weak Grid. – IEEE Transactions on Power Systems, 2016, vol. 31, No. 4, pp. 2925–2937, DOI: 10.1109/TPWRS.2015.2482605.
11. Strachan N.P., Jovcic D. Stability of a Variable-Speed Permanent Magnet Wind Generator with Weak AC Grids. – IEEE Transactions on Power Delivery, 2010, vol. 25, No. 4, pp. 2779–2788, DOI: 10.1109/TPWRD.2010.2053723.
12. Zhou Y. et al. Connecting Wind Power Plant with Weak Grid-Challenges and Solutions. – 2013 IEEE Power & Energy Society General Meeting, 2013, DOI: 10.1109/PESMG.2013.6672755.
13. Hu J. et al. Small Signal Instability of PLL-Synchronized Type-4 Wind Turbines Connected to High-Impedance AC Grid During LVRT. – IEEE Transactions on Energy Conversion, 2016, vol. 31, No. 4, pp. 1676–1687, DOI: 10.1109/TEC.2016.2577606.
14. Bulatov Yu.N. et al. Intellektual’naya elektrotehnika – in Russ. (Smart Electrical Engineering), 2023, No. 1 (21), pp. 62–84.
15. Huang S.-H. et al. Voltage Control Challenges on Weak Grids with High Penetration of Wind Generation: ERCOT Experience. – 2012 IEEE Power and Energy Society General Meeting, 2012, DOI: 10.1109/PESGM.2012.6344713.
16. Bao L. et al. Hardware Demonstration of Weak Grid Oscillations in Grid-Following Converters. – 2021 North American Power Symposium (NAPS), 2021, DOI: 10.1109/NAPS52732.2021.9654557.
17. Papangelis L. et al. Stability of a Voltage Source Converter Subject to Decrease of Short-Circuit Capacity: A Case Study. – Power Systems Computation Conference (PSCC), 2018, DOI: 10.23919/PSCC.2018.8442773.
18. Fan L. Modeling Type-4 Wind in Weak Grids. – IEEE Transactions on Sustainable Energy, 2019, vol. 10, No. 2, pp. 853–864, DOI: 10.1109/TSTE.2018.2849849.
19. Alawasa K.M. et al. Modeling, Analysis, and Suppression of The Impact of Full-Scale Wind-Power Converters on Subsynchronous Damping. – IEEE Systems Journal, 2013, vol. 7, No. 4, pp. 700–712, DOI: 10.1109/JSYST.2012.2226615.
20. Liu H. et al. Subsynchronous Interaction Between Direct-Drive PMSG Based Wind Farms and Weak AC Networks. – IEEE Transactions on Power Systems, 2017, vol. 32, No. 6, pp. 4708–4720, DOI: 10.1109/TPWRS.2017.2682197.
21. Li Y. et al. Wind in Weak Grids: Low-Frequency Oscillations, Subsynchronous Oscillations, and Torsional Interactions. – IEEE Transactions on Power Systems, 2020, vol. 35, No. 1, pp. 109–118, DOI: 10.1109/TPWRS.2019.2924412.
22. Dong D. et al. Analysis of Phase-Locked Loop Low-Frequency Stability in Three-Phase Grid-Connected Power Converters Considering Impedance Interactions. – IEEE Transactions on Industrial Electronics, 2015, vol. 62, No. 1, pp. 310–321, DOI: 10.1109/TIE.2014.2334665.
23. Li G. et al. PLL Phase Margin Design and Analysis for Mitigating Sub/Super-Synchronous Oscillation of Grid-Connected Inverter Under Weak Grid. – International Journal of Electrical Power & Energy Systems, 2023, vol. 151, DOI: 10.1016/j.ijepes.2023.109124.
24. Li G. et al. A Double-Loop Inertia Phase-Locked Loop with Antidisturbance Ability. – IEEE Transactions on Industrial Informatics, 2023, vol. 19, No. 4, pp. 5585–5592. DOI: 10.1109/TII.2022.3189014.
25. Liu H. et al. Stability Analysis of SSR in Multiple Wind Farms Connected to Series-Compensated Systems Using Impedance Network Model. – IEEE Transactions on Power Systems, 2018, vol. 33, No. 3, pp. 3118–3128, DOI: 10.1109/TPWRS.2017.2764159.
26. Liu H., Xie X. Comparative Studies on the Impedance Models of VSC-Based Renewable Generators for SSI Stability Analysis. – IEEE Transactions on Energy Conversion, 2019, vol. 34, No. 3, pp. 1442–1453, DOI: 10.1109/TEC.2019.2913778.
27. Fan L., Miao Z. Admittance-Based Stability Analysis: Bode Plots, Nyquist Diagrams or Eigenvalue Analysis. – IEEE Transactions on Power Systems, 2020, vol. 35, No. 4, pp. 3312–3315, DOI: 10.1109/TPWRS.2020.2996014.
28. Bi T. et al. Study on Response Characteristics of Grid-Side Inverter Controller of PMSG to Sub-Synchronous Frequency Component. – IET Renewable Power Generation, 2017, vol. 11, No. 7, pp. 966–972, DOI: 10.1049/iet-rpg.2016.0994.
29. Suvorov A.A. et al. Elektricheskie stantsii – in Russ. (Electrical Power Plants), 2022, No. 3 (1088), pp. 43–57.
30. Wu B. et al. Power Conversion and Control of Wind Energy Systems. Hoboken, U.S.A.: John Wiley & Sons, 2011, 480 p.
31. Blaabjerg F. et al. Overview of Control and Grid Synchronization for Distributed Power Generation Systems. – IEEE Transactions on Industrial Electronics, 2006, vol. 53, No. 5, pp. 1398–1409, DOI: 10.1109/TIE.2006.881997.
32. Ali Z. et al. Three-Phase Phase-Locked Loop Synchronization Algorithms for Grid-Connected Renewable Energy Systems: A Review. – Renewable and Sustainable Energy Reviews, 2018, vol. 90, 434–452, DOI: 10.1016/j.rser.2018.03.086.
33. Simonov A.V., Ilyushin P.V. Releynaya zashchita i avtomatizatsiya – in Russ. (Relay Protection and Automation), 2024, No. 1 (54), pp. 60–65.
34. Yazdani A., Iravani R. Voltage-Sourced Converters in Power Systems: Modeling, Control, and Applications. Hoboken, U.S.A.: John Wiley & Sons, 2010, 541 p.
35. Popov E.P. Teoriya lineynykh sistem avtomaticheskogo regulirovaniya i upravleniya (Theory of Linear Systems of Automatic Regulation and Control). M.: Nauka, 1989, 304 p.
36. Fan L. Control and Dynamics in Power Systems and Microgrids. Boca Raton, U.S.A.: CRC Press, 2017, 230 p.
37. Wen B. et al. Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters. – IEEE Transactions on Power Electronics, 2016, vol. 31, No. 1, pp. 675–687, DOI: 10.1109/TPEL.2015.2398192
---
The study was financially supported by the Russian Science Foundation, grant no. 24-29-00004
2. Рубан Н.Ю. и др. Анализ влияния возобновляемых источников энергии с силовыми преобразователями на процессы в современных энергосистемах. – Вестник ПНИПУ. Электротехника, информационные технологии, системы управления, 2020, № 36, с. 7–30.
3. Cheng Y. et al. Real-World Subsynchronous Oscillation Events in Power Grids With High Penetrations of Inverter-Based Resources. – IEEE Transactions on Power Systems, 2023, 38(1), pp. 316–30, DOI: 10.1109/TPWRS.2022.3161418.
4. Xie X., Shair J. Introduction to Power System Oscillatory Stability. – Oscillatory Stability of Converter-Dominated Power Systems. Power Systems. Springer, Cham, 2024, DOI: 10.1007/978-3-031-53357-0_1.
5. Shair J. et al. Overview of Emerging Subsynchronous Oscillations in Practical Wind Power Systems. – Renewable and Sustainable Energy Reviews, 2019, vol. 99, pp. 159–168, DOI: 10.1016/j.rser.2018.09.047.
6. Xie X. et al. Guest Editorial: Control Interactions in Power Electronic Converter Dominated Power Systems. – International Journal of Electrical Power & Energy Systems, 2024, vol. 155, DOI: 10.1016/j.ijepes.2023.109553.
7. Суворов А.А. и др. Управление сетевым инвертором на основе виртуального синхронного генератора при изменении плотности электрической сети. – Электричество, 2023, № 3, с. 35–51.
8. Fan L. et al. Real-World 20-Hz IBR Subsynchronous Oscillations: Signatures and Mechanism Analysis. – IEEE Transactions on Energy Conversion, 2022, vol. 37(4), pp. 2863–2873, DOI: 10.1109/TEC.2022.3206795.
9. Zhou J.Z. et al. Impact of Short-Circuit Ratio and Phase-Locked-Loop Parameters on the Small-Signal Behavior of a VSC-HVDC Converter. – IEEE Transactions on Power Delivery, 2014, vol. 29, No. 5, pp. 2287–2296, DOI: 10.1109/TPWRD.2014.2330518.
10. Zhao M. et al. Voltage Dynamics of Current Control Time-Scale in A VSC-Connected Weak Grid. – IEEE Transactions on Power Systems, 2016, vol. 31, No. 4, pp. 2925–2937, DOI: 10.1109/TPWRS.2015.2482605.
11. Strachan N.P., Jovcic D. Stability of a Variable-Speed Permanent Magnet Wind Generator with Weak AC Grids. – IEEE Transactions on Power Delivery, 2010, 25(4), pp. 2779–2788, DOI: 10.1109/TPWRD.2010.2053723.
12. Zhou Y. et al. Connecting Wind Power Plant with Weak Grid-Challenges and Solutions. – 2013 IEEE Power & Energy Society General Meeting, 2013, DOI: 10.1109/PESMG.2013.6672755.
13. Hu J. et al. Small Signal Instability of PLL-Synchronized Type-4 Wind Turbines Connected to High-Impedance AC Grid During LVRT. – IEEE Transactions on Energy Conversion, 2016, vol. 31, No. 4, pp. 1676–1687, DOI: 10.1109/TEC.2016.2577606.
14. Булатов Ю.Н. и др. Регулирование напряжения в микросети постоянного и переменного тока на базе энергороутеров и накопителей электроэнергии. – Интеллектуальная электротехника, 2023, № 1 (21), c. 62–84.
15. Huang S.-H. et al. Voltage Control Challenges on Weak Grids with High Penetration of Wind Generation: ERCOT Experience. – 2012 IEEE Power and Energy Society General Meeting, 2012, DOI: 10.1109/PESGM.2012.6344713.
16. Bao L. et al. Hardware Demonstration of Weak Grid Oscillations in Grid-Following Converters. – 2021 North American Power Symposium (NAPS), 2021, DOI: 10.1109/NAPS52732.2021.9654557.
17. Papangelis L. et al. Stability of a Voltage Source Converter Subject to Decrease of Short-Circuit Capacity: A Case Study. – Power Systems Computation Conference (PSCC), 2018, DOI: 10.23919/PSCC.2018.8442773.
18. Fan L. Modeling Type-4 Wind in Weak Grids. – IEEE Transactions on Sustainable Energy, 2019, vol. 10, No. 2, pp. 853–864, DOI: 10.1109/TSTE.2018.2849849.
19. Alawasa K.M. et al. Modeling, Analysis, and Suppression of The Impact of Full-Scale Wind-Power Converters on Subsynchronous Damping. – IEEE Systems Journal, 2013, vol. 7, No. 4, pp. 700–712, DOI: 10.1109/JSYST.2012.2226615.
20. Liu H. et al. Subsynchronous Interaction Between Direct-Drive PMSG Based Wind Farms and Weak AC Networks. – IEEE Transactions on Power Systems, 2017, 32(6), pp. 4708–4720, DOI: 10.1109/TPWRS.2017.2682197.
21. Li Y. et al. Wind in Weak Grids: Low-Frequency Oscillations, Subsynchronous Oscillations, and Torsional Interactions. – IEEE Transactions on Power Systems, 2020, vol. 35, No. 1, pp. 109–118, DOI: 10.1109/TPWRS.2019.2924412.
22. Dong D. et al. Analysis of Phase-Locked Loop Low-Frequency Stability in Three-Phase Grid-Connected Power Converters Considering Impedance Interactions. – IEEE Transactions on Industrial Electronics, 2015, vol. 62, No. 1, pp. 310–321, DOI: 10.1109/TIE.2014.2334665.
23. Li G. et al. PLL Phase Margin Design and Analysis for Mitigating Sub/Super-Synchronous Oscillation of Grid-Connected Inverter Under Weak Grid. – International Journal of Electrical Power & Energy Systems, 2023, vol. 151, DOI: 10.1016/j.ijepes.2023.109124.
24. Li G. et al. A Double-Loop Inertia Phase-Locked Loop with Antidisturbance Ability. – IEEE Transactions on Industrial Informatics, 2023, vol. 19, No. 4, pp. 5585–5592. DOI: 10.1109/TII.2022.3189014.
25. Liu H. et al. Stability Analysis of SSR in Multiple Wind Farms Connected to Series-Compensated Systems Using Impedance Network Model. – IEEE Transactions on Power Systems, 2018, vol. 33, No. 3, pp. 3118–3128, DOI: 10.1109/TPWRS.2017.2764159.
26. Liu H., Xie X. Comparative Studies on the Impedance Models of VSC-Based Renewable Generators for SSI Stability Analysis. – IEEE Transactions on Energy Conversion, 2019, vol. 34, No. 3, pp. 1442–1453, DOI: 10.1109/TEC.2019.2913778.
27. Fan L., Miao Z. Admittance-Based Stability Analysis: Bode Plots, Nyquist Diagrams or Eigenvalue Analysis. – IEEE Transactions on Power Systems, 2020, vol. 35, No. 4, pp. 3312–3315, DOI: 10.1109/TPWRS.2020.2996014.
28. Bi T. et al. Study on Response Characteristics of Grid-Side Inverter Controller of PMSG to Sub-Synchronous Frequency Component. – IET Renewable Power Generation, 2017, vol. 11, No. 7, pp. 966–972, DOI: 10.1049/iet-rpg.2016.0994.
29. Суворов А.А. и др. Синтез и тестирование типовых структур систем автоматического управления на основе виртуального синхронного генератора для генерирующих установок с силовым преобразователем. – Электрические станции, 2022, № 3 (1088), c. 43–57.
30. Wu B. et al. Power Conversion and Control of Wind Energy Systems. Hoboken, U.S.A.: John Wiley & Sons, 2011, 480 p.
31. Blaabjerg F. et al. Overview of Control and Grid Synchronization for Distributed Power Generation Systems. – IEEE Transactions on Industrial Electronics, 2006, vol. 53, No. 5, pp. 1398–1409, DOI: 10.1109/TIE.2006.881997.
32. Ali Z. et al. Three-Phase Phase-Locked Loop Synchronization Algorithms for Grid-Connected Renewable Energy Systems: A Review. – Renewable and Sustainable Energy Reviews, 2018, vol. 90, 434–452, DOI: 10.1016/j.rser.2018.03.086.
33. Симонов А.В., Илюшин П.В. О совершенствовании методических подходов к математическому моделированию ветроэнергетических установок в отечественных программных комплексах АРМ СРЗА и RASTRKZ. – Релейная защита и автоматизация, 2024, № 1 (54), с. 60–65.
34. Yazdani A., Iravani R. Voltage-Sourced Converters in Power Systems: Modeling, Control, and Applications. Hoboken, U.S.A.: John Wiley & Sons, 2010, 541 p.
35. Попов Е.П. Теория линейных систем автоматического регулирования и управления. М.: Наука, 1989, с. 304.
36. Fan L. Control and Dynamics in Power Systems and Microgrids. Boca Raton, U.S.A.: CRC Press, 2017, 230 p.
37. Wen B. et al. Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters. – IEEE Transactions on Power Electronics, 2016, vol. 31, No. 1, pp. 675–687, DOI: 10.1109/TPEL.2015.2398192.
---
Исследование выполнено за счет гранта Российского научного фонда № 24-29-00004.
#
1. Ilyushin P.V., Georgievskiy I.D. Energetik – in Russ. (Power Engineer), 2023, No. 5, pp. 13–18.
2. Ruban N.Yu. et al. Vestnik PNIPU. Elektrotehnika, informatsionnye tehnologii, sistemy upravleniya – in Russ. (Bulletin of PNRPU. Electrical Engineering, Information Technology, Control Systems), 2020, No. 36, pp. 7–30.
3. Cheng Y. et al. Real-World Subsynchronous Oscillation Events in Power Grids with High Penetrations of Inverter-Based Resources. – IEEE Transactions on Power Systems, 2023, 38(1), pp. 316–30, DOI: 10.1109/TPWRS.2022.3161418.
4. Xie X., Shair J. Introduction to Power System Oscillatory Stability. – Oscillatory Stability of Converter-Dominated Power Systems. Power Systems. Springer, Cham, 2024, DOI: 10.1007/978-3-031-53357-0_1.
5. Shair J. et al. Overview of Emerging Subsynchronous Oscillations in Practical Wind Power Systems. – Renewable and Sustainable Energy Reviews, 2019, vol. 99, pp. 159–168, DOI: 10.1016/j.rser.2018.09.047.
6. Xie X. et al. Guest Editorial: Control Interactions in Power Electronic Converter Dominated Power Systems. – International Journal of Electrical Power & Energy Systems, 2024, vol. 155, DOI: 10.1016/j.ijepes.2023.109553
7. Suvorov A.A. et al. Elektrichestvo – in Russ. (Electricity), 2023, No. 3, pp. 35–51.
8. Fan L. et al. Real-World 20-Hz IBR Subsynchronous Oscillations: Signatures and Mechanism Analysis. – IEEE Transactions on Energy Conversion, 2022, vol. 37(4), pp. 2863–2873, DOI: 10.1109/TEC.2022.3206795.
9. Zhou J.Z. et al. Impact of Short-Circuit Ratio and Phase-Locked-Loop Parameters on the Small-Signal Behavior of a VSC-HVDC Converter. – IEEE Transactions on Power Delivery, 2014, vol. 29, No. 5, pp. 2287–2296, DOI: 10.1109/TPWRD.2014.2330518.
10. Zhao M. et al. Voltage Dynamics of Current Control Time-Scale in A VSC-Connected Weak Grid. – IEEE Transactions on Power Systems, 2016, vol. 31, No. 4, pp. 2925–2937, DOI: 10.1109/TPWRS.2015.2482605.
11. Strachan N.P., Jovcic D. Stability of a Variable-Speed Permanent Magnet Wind Generator with Weak AC Grids. – IEEE Transactions on Power Delivery, 2010, vol. 25, No. 4, pp. 2779–2788, DOI: 10.1109/TPWRD.2010.2053723.
12. Zhou Y. et al. Connecting Wind Power Plant with Weak Grid-Challenges and Solutions. – 2013 IEEE Power & Energy Society General Meeting, 2013, DOI: 10.1109/PESMG.2013.6672755.
13. Hu J. et al. Small Signal Instability of PLL-Synchronized Type-4 Wind Turbines Connected to High-Impedance AC Grid During LVRT. – IEEE Transactions on Energy Conversion, 2016, vol. 31, No. 4, pp. 1676–1687, DOI: 10.1109/TEC.2016.2577606.
14. Bulatov Yu.N. et al. Intellektual’naya elektrotehnika – in Russ. (Smart Electrical Engineering), 2023, No. 1 (21), pp. 62–84.
15. Huang S.-H. et al. Voltage Control Challenges on Weak Grids with High Penetration of Wind Generation: ERCOT Experience. – 2012 IEEE Power and Energy Society General Meeting, 2012, DOI: 10.1109/PESGM.2012.6344713.
16. Bao L. et al. Hardware Demonstration of Weak Grid Oscillations in Grid-Following Converters. – 2021 North American Power Symposium (NAPS), 2021, DOI: 10.1109/NAPS52732.2021.9654557.
17. Papangelis L. et al. Stability of a Voltage Source Converter Subject to Decrease of Short-Circuit Capacity: A Case Study. – Power Systems Computation Conference (PSCC), 2018, DOI: 10.23919/PSCC.2018.8442773.
18. Fan L. Modeling Type-4 Wind in Weak Grids. – IEEE Transactions on Sustainable Energy, 2019, vol. 10, No. 2, pp. 853–864, DOI: 10.1109/TSTE.2018.2849849.
19. Alawasa K.M. et al. Modeling, Analysis, and Suppression of The Impact of Full-Scale Wind-Power Converters on Subsynchronous Damping. – IEEE Systems Journal, 2013, vol. 7, No. 4, pp. 700–712, DOI: 10.1109/JSYST.2012.2226615.
20. Liu H. et al. Subsynchronous Interaction Between Direct-Drive PMSG Based Wind Farms and Weak AC Networks. – IEEE Transactions on Power Systems, 2017, vol. 32, No. 6, pp. 4708–4720, DOI: 10.1109/TPWRS.2017.2682197.
21. Li Y. et al. Wind in Weak Grids: Low-Frequency Oscillations, Subsynchronous Oscillations, and Torsional Interactions. – IEEE Transactions on Power Systems, 2020, vol. 35, No. 1, pp. 109–118, DOI: 10.1109/TPWRS.2019.2924412.
22. Dong D. et al. Analysis of Phase-Locked Loop Low-Frequency Stability in Three-Phase Grid-Connected Power Converters Considering Impedance Interactions. – IEEE Transactions on Industrial Electronics, 2015, vol. 62, No. 1, pp. 310–321, DOI: 10.1109/TIE.2014.2334665.
23. Li G. et al. PLL Phase Margin Design and Analysis for Mitigating Sub/Super-Synchronous Oscillation of Grid-Connected Inverter Under Weak Grid. – International Journal of Electrical Power & Energy Systems, 2023, vol. 151, DOI: 10.1016/j.ijepes.2023.109124.
24. Li G. et al. A Double-Loop Inertia Phase-Locked Loop with Antidisturbance Ability. – IEEE Transactions on Industrial Informatics, 2023, vol. 19, No. 4, pp. 5585–5592. DOI: 10.1109/TII.2022.3189014.
25. Liu H. et al. Stability Analysis of SSR in Multiple Wind Farms Connected to Series-Compensated Systems Using Impedance Network Model. – IEEE Transactions on Power Systems, 2018, vol. 33, No. 3, pp. 3118–3128, DOI: 10.1109/TPWRS.2017.2764159.
26. Liu H., Xie X. Comparative Studies on the Impedance Models of VSC-Based Renewable Generators for SSI Stability Analysis. – IEEE Transactions on Energy Conversion, 2019, vol. 34, No. 3, pp. 1442–1453, DOI: 10.1109/TEC.2019.2913778.
27. Fan L., Miao Z. Admittance-Based Stability Analysis: Bode Plots, Nyquist Diagrams or Eigenvalue Analysis. – IEEE Transactions on Power Systems, 2020, vol. 35, No. 4, pp. 3312–3315, DOI: 10.1109/TPWRS.2020.2996014.
28. Bi T. et al. Study on Response Characteristics of Grid-Side Inverter Controller of PMSG to Sub-Synchronous Frequency Component. – IET Renewable Power Generation, 2017, vol. 11, No. 7, pp. 966–972, DOI: 10.1049/iet-rpg.2016.0994.
29. Suvorov A.A. et al. Elektricheskie stantsii – in Russ. (Electrical Power Plants), 2022, No. 3 (1088), pp. 43–57.
30. Wu B. et al. Power Conversion and Control of Wind Energy Systems. Hoboken, U.S.A.: John Wiley & Sons, 2011, 480 p.
31. Blaabjerg F. et al. Overview of Control and Grid Synchronization for Distributed Power Generation Systems. – IEEE Transactions on Industrial Electronics, 2006, vol. 53, No. 5, pp. 1398–1409, DOI: 10.1109/TIE.2006.881997.
32. Ali Z. et al. Three-Phase Phase-Locked Loop Synchronization Algorithms for Grid-Connected Renewable Energy Systems: A Review. – Renewable and Sustainable Energy Reviews, 2018, vol. 90, 434–452, DOI: 10.1016/j.rser.2018.03.086.
33. Simonov A.V., Ilyushin P.V. Releynaya zashchita i avtomatizatsiya – in Russ. (Relay Protection and Automation), 2024, No. 1 (54), pp. 60–65.
34. Yazdani A., Iravani R. Voltage-Sourced Converters in Power Systems: Modeling, Control, and Applications. Hoboken, U.S.A.: John Wiley & Sons, 2010, 541 p.
35. Popov E.P. Teoriya lineynykh sistem avtomaticheskogo regulirovaniya i upravleniya (Theory of Linear Systems of Automatic Regulation and Control). M.: Nauka, 1989, 304 p.
36. Fan L. Control and Dynamics in Power Systems and Microgrids. Boca Raton, U.S.A.: CRC Press, 2017, 230 p.
37. Wen B. et al. Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters. – IEEE Transactions on Power Electronics, 2016, vol. 31, No. 1, pp. 675–687, DOI: 10.1109/TPEL.2015.2398192
---
The study was financially supported by the Russian Science Foundation, grant no. 24-29-00004
