Методы оценки низкочастотных колебаний в энергосистеме
Ключевые слова:
электроэнергетическая система, низкочастотные колебания, цифровая обработка сигнала
Аннотация
Задача выявления и демпфирования низкочастотных колебаний электрического режима становится особо актуальной для современных электроэнергетических систем с наличием возобновляемых источников энергии, гибких устройств управления на основе силовой электроники и сниженными значениями запаса пропускной способности электрической сети. Проведен обзор и анализ современных исследований, направленных на разработку методов оценки параметров низкочастотных колебаний. Выявлена недостаточная эффективность существующих методов, обусловленная значительной задержкой оценки и низкой адаптивностью. В статье предложен метод ускоренной оценки параметров низкочастотных колебаний с задержкой, равной четверти цикла колебаний. Апробация метода выполнена на синтетических и физических сигналах. В качестве источника синтетических данных использована цифровая модель энергосистемы, состоящей из четырёх синхронных генераторов. Физические данные представляют собой записи переходных процессов, протекающих в реальной энергосистеме. Определение точности оценки низкочастотных колебаний параметров электрического режима основано на анализе разности исходного и восстановленного по вычисленным параметрам сигналов. В результате получены значения ошибки оценки низкочастотных колебаний, подтверждающие точность и эффективность метода при анализе как синтетических, так и данных из реальных энергосистем
Литература
1. Климова Т.Г., Ревякин В.А. Субсинхронные и суперсинхронные колебания в электроэнергетической системе: возникновение и идентификация, обзор. – Энергетик, 2022, № 5, с. 27–32.
2. Климова Т.Г., Савватин М.В. Анализ влияния периодических возмущений на возникновение низкочастотных колебаний в энергосистеме. – Вестник МЭИ, 2015, № 6, с. 56–62.
3. Gupta D.P.S., Sen I. Low Frequency Oscillations in Power Systems: A Physical Account and Adaptive Stabilizers. – Sadhana, 1993, vol. 18, pp. 843–868.
4. Бердин А.С. и др. Оценка участия синхронного генератора в демпфировании низкочастотных колебаний по данным синхронизированных векторных измерений. – Вестник ЮУрГУ. Серия: Энергетика, 2013, т. 13, № 2, с. 62–68.
5. Maity S., Ramya R. A Comprehensive Review of Damping of Low Frequency Oscillations in Power Systems. – The International Journal of Innovative Technology and Exploring Engineering, 2019, vol. 8, No. 6, pp. 133–138.
6. Nocoń A., Paszek S. A Comprehensive Review of Power System Stabilizers. – Energies, 2023, vol. 16, No. 4, DOI:10.3390/en16041945.
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11. Paternina M.R.A. et al. Identification of Electromechanical Oscillatory Modes Based on Variational Mode Decomposition. – Electric Power Systems Research, 2019, vol. 167, pp. 71–85, DOI:10.1016/j.epsr.2018.10.014.
12. Wang Z.C. et al. Hilbert Low-Pass Filter of Non-Stationary Time Sequence Using Analytical Mode Decomposition. – Journal of Vibration and Control, 2017, vol. 23, No. 15, pp. 2444–2469, DOI: 10.1177/10775463156174.
13. Zhao Y., Zhang J., Zhao Q. Online Monitoring of Low-Frequency Oscillation Based on the Improved Analytical Modal Decomposition Method. – IEEE Access, 2020, vol. 8, pp. 215256–215266, DOI: 10.1109/ACCESS.2020.3040848.
14. Zuhaib M., Rihan M. Identification of Low-Frequency Oscillation Modes Using PMU Based Data-Driven Dynamic Mode Decomposition Algorithm. – IEEE Access, 2021, vol. 9, pp. 49434–49447, DOI: 10.1109/ACCESS.2021.3068227.
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19. Sanchez-Gasca J.J., Chow J.H. Performance Comparison of Three Identification Methods for the Analysis of Electromechanical Oscillations. – IEEE Transactions on Power Systems, 1999, vol. 14, No. 3, pp. 995–1002, DOI:10.1109/59.780912.
20. Yang D.C., Rehtanz C., Li Y. Analysis of Low Frequency Oscillations Using Improved Hilbert-Huang Transform. – International Conference on Power System Technology, 2010, DOI:10.1109/POWERCON.2010.5666567.
21. Wies R.W., Pierre J.W., Trudnowski D.J. Use of ARMA Block Processing for Estimating Stationary Low-Frequency Electromechanical Modes of Power Systems. – IEEE Transactions on Power Systems, 2003, vol. 18, No. 1, pp. 167–173, DOI:10.1109/TPWRS.2002.807116.
22. Doraiswami R., Liu W. Real-Time Estimation of the Parameters of Power System Small Signal Oscillations. – IEEE Transactions on Power Systems, 1993, vol. 8, No. 1, pp. 74–83, DOI:10.1109/59.221251.
23. Chen J. et al. An Adaptive Matrix Pencil Algorithm Based-Wavelet Soft-Threshold Denoising for Analysis of Low Frequency Oscillation in Power Systems. – IEEE Access, 2020, vol. 8, pp. 7244–7255, DOI:10.1109/ACCESS.2020.2963953.
24. Chen J. et al. An Adaptive TLS-ESPRIT Algorithm Based on an S-G Filter for Analysis of Low Frequency Oscillation in Wide Area Measurement Systems. – IEEE Access, 2019, vol. 7, pp. 47644-47654, DOI:10.1109/ACCESS.2019.2908629.
25. Román-Messina A. et al. Distributed Monitoring of Power System Oscillations Using Multiblock Principal Component Analysis and Higher-Order Singular Value Decomposition. – Journal of Modern Power Systems and Clean Energy, 2021, vol. 10, No. 4, pp. 818–828, DOI:10.35833/MPCE.2021.000534.
26. Xia Y. et al. Application of Underdetermined Blind Source Separation Algorithm on the Low-Frequency Oscillation in Power Systems. – Energies, 2023, vol. 16, No. 8, DOI:10.3390/en16083571.
27. Senyuk M. et al. Statistical Method of Low Frequency Oscillations Analysis in Power Systems Based on Phasor Measurements. – Mathematics, 2023, vol. 11, No. 2, DOI:10.3390/math11020393.
28. Satheesh R. et al. Identification of Oscillatory Modes in Power System Using Deep Learning Approach. – IEEE Access, 2022, vol. 10, pp. 16556–16565, DOI:10.1109/ACCESS.2022.3149472.
29. Мокеев А.В. Особенности разработки, испытаний и внедрения устройств синхронизированных векторных измерений. – Современные подходы к обеспечению надежности электроэнергетических систем, 2014, с. 56–62.
30. Senyuk M. et al. Fast Algorithms for Estimating the Disturbance Inception Time in Power Systems Based on Time Series of Instantaneous Values of Current and Voltage with a High Sampling Rate. – Mathematics, 2022, vol. 10, No. 21, DOI:10.3390/math10213949.
31. Сенюк М.Д., Дмитриева А.А., Дмитриев С.А. Исследование характеристик метода экспресс-оценки параметров электрического режима в стационарных и динамических процессах. – Электротехнические системы и комплексы, 2021, № 4(53), c. 4–12.
32. Sharma A., Srivastava S.C., Chakrabarti S. Testing and Validation of Power System Dynamic State Estimators Using Real Time Digital Simulator (RTDS). – IEEE Transactions on Power Systems, 2015, vol. 31, No. 3, pp. 2338–2347, DOI:10.1109/TPWRS.2015.2453482.
33. Поляков И.Д., Паздерин А.В., Бартоломей П.И. Способы использования синхронизированных векторных измерений в задаче оценивания состояния электрической сети. – Электричество, 2023, № 5, с. 14–23.
34. Аскаров А.Б. и др. Улучшение демпфирующих свойств виртуального синхронного генератора с помощью корректирующего согласно-параллельного регулятора. – Электричество, 2024, № 1, с. 18–36.
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Исследование выполнено за счет гранта Российского научного фонда № 23-79-01024, https://rscf.ru/project/23-79-01024/
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24. Chen J. et al. An Adaptive TLS-ESPRIT Algorithm Based on an S-G Filter for Analysis of Low Frequency Oscillation in Wide Area Measurement Systems. – IEEE Access, 2019, vol. 7, pp. 47644–47654, DOI:10.1109/ACCESS.2019.2908629.
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The research was financially supported by the Russian Science Foundation, grant no. 23-79-01024, https://rscf.ru/project/23-79-01024/
2. Климова Т.Г., Савватин М.В. Анализ влияния периодических возмущений на возникновение низкочастотных колебаний в энергосистеме. – Вестник МЭИ, 2015, № 6, с. 56–62.
3. Gupta D.P.S., Sen I. Low Frequency Oscillations in Power Systems: A Physical Account and Adaptive Stabilizers. – Sadhana, 1993, vol. 18, pp. 843–868.
4. Бердин А.С. и др. Оценка участия синхронного генератора в демпфировании низкочастотных колебаний по данным синхронизированных векторных измерений. – Вестник ЮУрГУ. Серия: Энергетика, 2013, т. 13, № 2, с. 62–68.
5. Maity S., Ramya R. A Comprehensive Review of Damping of Low Frequency Oscillations in Power Systems. – The International Journal of Innovative Technology and Exploring Engineering, 2019, vol. 8, No. 6, pp. 133–138.
6. Nocoń A., Paszek S. A Comprehensive Review of Power System Stabilizers. – Energies, 2023, vol. 16, No. 4, DOI:10.3390/en16041945.
7. Попов А.И., Бутин К.П., Родионов А.В. Разработка способов визуального представления параметров низкочастотных колебаний в энергосистеме. – Методические вопросы исследования надежности больших систем энергетики, 2023, с. 526–535.
8. Бердин А.С. и др. Сравнение методов определения синхронизирующей мощности синхронной машины по результатам экспериментальных исследований на электродинамической модели. – Известия НТЦ Единой энергетической системы, 2015, № 2 (73), с. 72–82.
9. Chen G., Wang Z. A Signal Decomposition Theorem with Hilbert Transform and Its Application to Narrowband Time Series with Closely Spaced Frequency Components. – Mechanical Systems and Signal Processing, 2012, vol. 28, pp. 258–279, DOI: 10.1016/j.ymssp.2011.02.002.
10. Liu L. et al. Modal Identification of Low-Frequency Oscillations in Power Systems Based on Improved Variational Modal Decomposition and Sparse Time-Domain Method. – Sustainability, 2022, vol. 14, No. 24, DOI: 10.3390/su142416867.
11. Paternina M.R.A. et al. Identification of Electromechanical Oscillatory Modes Based on Variational Mode Decomposition. – Electric Power Systems Research, 2019, vol. 167, pp. 71–85, DOI:10.1016/j.epsr.2018.10.014.
12. Wang Z.C. et al. Hilbert Low-Pass Filter of Non-Stationary Time Sequence Using Analytical Mode Decomposition. – Journal of Vibration and Control, 2017, vol. 23, No. 15, pp. 2444–2469, DOI: 10.1177/10775463156174.
13. Zhao Y., Zhang J., Zhao Q. Online Monitoring of Low-Frequency Oscillation Based on the Improved Analytical Modal Decomposition Method. – IEEE Access, 2020, vol. 8, pp. 215256–215266, DOI: 10.1109/ACCESS.2020.3040848.
14. Zuhaib M., Rihan M. Identification of Low-Frequency Oscillation Modes Using PMU Based Data-Driven Dynamic Mode Decomposition Algorithm. – IEEE Access, 2021, vol. 9, pp. 49434–49447, DOI: 10.1109/ACCESS.2021.3068227.
15. Senyuk M. et al. Power System Transient Stability Assessment Based on Machine Learning Algorithms and Grid Topology. – Mathematics, 2023, vol. 11, No. 3, DOI:10.3390/math11030525.
16. Rueda J.L., Juárez C.A., Erlich I. Wavelet-based Analysis of Power System Low-Frequency Electromechanical Oscillations. – IEEE Transactions on Power Systems, 2011, vol. 26, No. 3, pp. 1733–1743, DOI:10.1109/TPWRS.2010.2104164.
17. Philip J.G., Yang Y., Jung J. Identification of Power System Oscillation Modes Using Empirical Wavelet Transform and Yoshida–Bertecco Algorithm. – IEEE Access, 2022, vol. 10, pp. 48927–48935, DOI:10.1109/ACCESS.2022.3172295.
18. Daubechies I., Lu J., Wu H.T. Synchrosqueezed Wavelet Transforms: An Empirical Mode Decomposition-Like Tool. – Applied and Computational Harmonic Analysis, 2011, vol. 30, No. 2, pp. 243–261, DOI:10.1016/j.acha.2010.08.002.
19. Sanchez-Gasca J.J., Chow J.H. Performance Comparison of Three Identification Methods for the Analysis of Electromechanical Oscillations. – IEEE Transactions on Power Systems, 1999, vol. 14, No. 3, pp. 995–1002, DOI:10.1109/59.780912.
20. Yang D.C., Rehtanz C., Li Y. Analysis of Low Frequency Oscillations Using Improved Hilbert-Huang Transform. – International Conference on Power System Technology, 2010, DOI:10.1109/POWERCON.2010.5666567.
21. Wies R.W., Pierre J.W., Trudnowski D.J. Use of ARMA Block Processing for Estimating Stationary Low-Frequency Electromechanical Modes of Power Systems. – IEEE Transactions on Power Systems, 2003, vol. 18, No. 1, pp. 167–173, DOI:10.1109/TPWRS.2002.807116.
22. Doraiswami R., Liu W. Real-Time Estimation of the Parameters of Power System Small Signal Oscillations. – IEEE Transactions on Power Systems, 1993, vol. 8, No. 1, pp. 74–83, DOI:10.1109/59.221251.
23. Chen J. et al. An Adaptive Matrix Pencil Algorithm Based-Wavelet Soft-Threshold Denoising for Analysis of Low Frequency Oscillation in Power Systems. – IEEE Access, 2020, vol. 8, pp. 7244–7255, DOI:10.1109/ACCESS.2020.2963953.
24. Chen J. et al. An Adaptive TLS-ESPRIT Algorithm Based on an S-G Filter for Analysis of Low Frequency Oscillation in Wide Area Measurement Systems. – IEEE Access, 2019, vol. 7, pp. 47644-47654, DOI:10.1109/ACCESS.2019.2908629.
25. Román-Messina A. et al. Distributed Monitoring of Power System Oscillations Using Multiblock Principal Component Analysis and Higher-Order Singular Value Decomposition. – Journal of Modern Power Systems and Clean Energy, 2021, vol. 10, No. 4, pp. 818–828, DOI:10.35833/MPCE.2021.000534.
26. Xia Y. et al. Application of Underdetermined Blind Source Separation Algorithm on the Low-Frequency Oscillation in Power Systems. – Energies, 2023, vol. 16, No. 8, DOI:10.3390/en16083571.
27. Senyuk M. et al. Statistical Method of Low Frequency Oscillations Analysis in Power Systems Based on Phasor Measurements. – Mathematics, 2023, vol. 11, No. 2, DOI:10.3390/math11020393.
28. Satheesh R. et al. Identification of Oscillatory Modes in Power System Using Deep Learning Approach. – IEEE Access, 2022, vol. 10, pp. 16556–16565, DOI:10.1109/ACCESS.2022.3149472.
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Исследование выполнено за счет гранта Российского научного фонда № 23-79-01024, https://rscf.ru/project/23-79-01024/
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The research was financially supported by the Russian Science Foundation, grant no. 23-79-01024, https://rscf.ru/project/23-79-01024/
