Оптимизация режима электроэнергетической системы в условиях аварийных отказов ЛЭП и при пиковых нагрузках с использованием FACTS и программ реагирования на спрос
Ключевые слова:
аварийные отказы, пиковая нагрузка, многоцелевая функция, нагрузочная способность системы, параллельные и последовательные устройства FACTS, программа реагирования на спрос, статическая устойчивость, потери мощности
Аннотация
Особенностью современных электроэнергетических систем являются частые изменения параметров режима и схем, вызванные случайными факторами, которые могут сопровождаться аварийными отказами её главных элементов – генераторов и линий электропередачи. В этих условиях в энергосистеме с ограниченным резервом мощности генерации для покрытия спроса, например в периоды пиковой нагрузки, возникнет необходимость в дополнительных технических мерах, позволяющих одновременно максимизировать передачу мощности и увеличить предел статической устойчивости энергосистемы. В статье предлагается многоцелевой подход к оптимизации режима системы в условиях отказа линий электропередачи и изменения спроса в периоды пиковой нагрузки. Техническая реализация задачи оптимизации проводится с помощью современных компенсирующих средств, включая последовательные и параллельные устройства FACTS, и программы реагирования на спрос. Решение задачи многоцелевой оптимизации позволяет исследовать влияние возможных отказов линий электропередачи на мощность компенсирующих устройств и выбор степени реагирования на спрос, а также связанные с этим затраты при различных изменениях нагрузки в периоды пика. Разработка и применение различных стратегий выбора подходящих многоцелевых функций обеспечивает одновременное улучшение технических и экономических показателей энергосистемы в условиях конкурентного рынка. Применение эволюционных методов для решения задач многоцелевой оптимизации позволяет повысить гибкость управления устройствами компенсации и программной реализацией реагирования на спрос в энергосистеме. Имитационные программы выполнены в средах MATLAB и PSAT с использованием тестовой системы IEEE 30-bus.
Литература
1. Althowibi F.A., Mustafa M.W. Maximum Power System Loadability to Detect Voltage Collapse. – 4th International Power Engineering and Optimization Conference, 2010, pp. 49–52, DOI:10.1109/PEOCO.2010.5559231.
2. Bazmi A.A., Zahedi G. Sustainable Energy Systems: Role of Optimization Modeling Techniques in Power Generation and Supply – A Review. – Renewable and Sustainable Energy Review, 2011, 15(8), pp. 3480–3500, DOI:10.1016/j.rser.2011.05.003.
3. Рахманов Н.Р., Гулиев Г.Б. Применение модели нейронной сети для оценки текущего значения предела устойчивости электрической системы по напряжению. – Электричество, 2015, № 4, с. 4–11.
4. Gao H. et al. Real-Time Long-Term Voltage Stability Assessment Based on eGBDT for Large-Scale Power System with High Renewables Penetration. – Electric Power Systems Research, 2023, vol. 214(6), DOI:10.1016/j.epsr.2022.108915.
5. Rahmanov N.R. et al. Method for Assessing the Voltage Stability Limit During Emergency Outages of the Line and Generators in the Power System. – Rudenko International Conference on Methodological Problems in Reliability Study of Large Energy Systems, 2019, vol. 139, DOI: 10.1051/e3sconf/201913901020.
6. Khazali A.H., Kalantar M. Reactive /Voltage control by A Multi-Agent based PSO approach considering voltage stability. – 24th International Power System Conference, Tehran, 2009, pp. 1–8.
7. Hosseini H., Banaei M.R. Performance of Active Power Line Conditioner for Loss Reduction in the Power Distribution System. – IEEE Region 10 Conference TENCON, 2004, pp. 97–100, DOI:10.1109/TENCON.2004.1414877.
8. Гашимов A.M., Гулиев Г.Б., Рахманов Н.Р. Улучшенный алгоритм нечеткой логики для управления реактивной мощностью и напряжением в распределительных сетях. – Энергетика. Известия высших учебных заведений и энергетических объединений СНГ, 2014, № 2, c. 29–39.
9. Devi S., Geethajali M. Optimal Location and Sizing Determination of Distributed Generation and DSTATCOM using Particle Swarm Optimization Algorithm. – Elsevier International Journal of Electrical Power and Energy Systems, 2014, vol. 62. pp. 562–570, DOI:10.1016/j.ijepes.2014.05.015.
10. Elsheikh A.M.F. et al. Optimal Capacitor Placement and Sizing in Radial Electric Power Systems. – Alexandria Engineering Journal, 2014, vol 53(4), pp. 809–816, DOI:10.1016/j.aej.2014.09.012.
11. Mohamad Imran A., Kowsalya M. Optimal Distributed Generation and Capacitor Placement in Power Distribution Network for Power Loss Minimization. – International Conference on Advances in Electrical Engineering (ICAEE), 2014, DOI:10.1109/ICAEE.2014.6838519.
12. Гашимов А.М. и др. Вероятностное потокораспределение как реакция на стохастичность нагрузки в энергосистеме. – Энергетика. Известия высших учебных заведений и энергетических объединений СНГ, 2016, № 6. с. 519–528
13. Maronani I. et al. Optimized FACTS Devices for Power System Enhancement: Applications and Solving Methods. – Sustainability, 2023, vol. 15(12), DOI:10.3390/su15129348.
14. Rashed G.I., Shaheen H.I., Cheng S.J. Optimal Location and Parameter Settings of Multiple TESC for Increasing Power System Loadability Based on GA and PSO Techniques. – The 3rd International Conference on Natural Computation (ICNC), 2007, DOI:10.1109/ICNC.2007.521.
15. Hashimov A.M. et al. Probabilistic Evaluation of Voltage Stability Limit of Power System under the Conditions of Accidental Emergency Outages of Lines and Generators. – International Journal on Technical and Physical Problems of Engineering, 2020, iss. 43, vol. 12, No. 2, pp. 40–45.
16. Song Y., Hill D.J., Liu T. Static Voltage Stability Analysis of Distribution Systems Based on Network – Load Admittance Ratio. – IEEE Transactions on Power Systems, 2019, 34(3), pp. 2270–2280, DOI:10.1109/TPWRS.2018.2886636.
17. Sun X. et al. Sustainable Energy Transition in China: Renewable Options and Impacts on the Electricity System. – Energies, 2016, 9(12), DOI:10.3390/en9120980.
18. Renedek J., Tihamer S., Bartok B. Evaluation of Renewable Energy Sources in Peripheral Areas and Renewable Energy – Based Rural Development. – Renewable and Sustainable Energy Reviews, 2018, 90(7), pp. 516–535, DOI:10.1016/j.rser.2018.03.020.
19. Spiegel T. Impact of Renewable Energy Expansion to the Balancing Energy Demand of Differential Balancing Groups. – Journal of Sustainable Development of Energy, Water and Environmental Systems, 2018, vol.6(4), pp. 784–799, DOI:10.13044/j.sdewes.d6.0215.
20. Gaete-Morales C. et al. A Novel Framework for Development and Optimization of Future Electricity Scenarios with High Penetration of Renewables and Storage. – Applied Energy, 2019, vol. 250, pp. 1657–1672, DOI:10.1016/j.apenergy.2019.05.006.
21. Mladenov V., Chobanov V., Georgiev A. Impact of Renewable Energy Sources on Power System Flexibility Requirements. – Energies, 2021, 14(10), DOI:10.3390 /en 14102813.
22. Shadmesgaran M.R., Hashimov A.M., Rahmanov N.R. A Glance of the Optimal Control Effects on Technical and Economic Operation in GRID. – International Journal on Technical and Physical Problems of Engineering, 2020, iss. 45, vol. 12, No. 4, pp. 1–10.
23. Salami Y., Ieyasurya B. A Comprehensive Evaluation of DC Power Flow Models and their Application to Power Systems Security Analysis. – CIGRE Canada Conference, Vancouver, BC, 2016, 753, pp. 1-8. Methods to mitigate or avoid power outages.
24. Power Systems Test Case Archive [Электрон. ресурс], URL: https://labs.ece.uw.edu/pstca (дата обращения 15.02.2024)
#
1. Althowibi F.A., Mustafa M.W. Maximum Power System Loadability to Detect Voltage Collapse. – 4th International Power Engineering and Optimization Conference, 2010, pp. 49–52, DOI:10.1109/PEOCO.2010.5559231.
2. Bazmi A.A., Zahedi G. Sustainable Energy Systems: Role of Optimization Modeling Techniques in Power Generation and Supply – A Review. – Renewable and Sustainable Energy Review, 2011, 15(8), pp. 3480–3500, DOI:10.1016/j.rser.2011.05.003.
3. Rahmanov N.R., Guliev G.B. Elektrichestvo – in Russ. (Electricity), 2015, No. 4, pp. 4–11.
4. Gao H. et al. Real-Time Long-Term Voltage Stability Assessment Based on eGBDT for Large-Scale Power System with High Renewables Penetration. – Electric Power Systems Research, 2023, vol. 214(6), DOI:10.1016/j.epsr.2022.108915.
5. Rahmanov N.R. et al. Method for Assessing the Voltage Stability Limit During Emergency Outages of the Line and Generators in the Power System. – Rudenko International Conference on Methodological Problems in Reliability Study of Large Energy Systems, 2019, vol. 139, DOI: 10.1051/e3sconf/201913901020.
6. Khazali A.H., Kalantar M. Reactive /Voltage control by A Multi-Agent based PSO approach considering voltage stability. – 24th International Power System Conference, Tehran, 2009, pp. 1–8.
7. Hosseini H., Banaei M.R. Performance of Active Power Line Conditioner for Loss Reduction in the Power Distribution System. – IEEE Region 10 Conference TENCON, 2004, pp. 97–100, DOI:10.1109/TENCON.2004.1414877.
8. Hashimov A.M., Guliev G.B., Rahmanov N.R. Energetika. Izvestiya vysshih uchebnyh zavedeniy i energeticheskih ob"edineniy SNG – in Russ. (Power Industry. News of Higher Educational Institutions and Energy Associations of the CIS), 2014, No. 2, pp. 29–39.
9. Devi S., Geethajali M. Optimal Location and Sizing Determination of Distributed Generation and DSTATCOM using Particle Swarm Optimization Algorithm. – Elsevier International Journal of Electrical Power and Energy Systems, 2014, vol. 62. pp. 562–570, DOI:10.1016/j.ijepes.2014.05.015.
10. Elsheikh A.M.F. et al. Optimal Capacitor Placement and Sizing in Radial Electric Power Systems. – Alexandria Engineering Journal, 2014, vol 53(4), pp. 809–816, DOI:10.1016/j.aej.2014.09.012.
11. Mohamad Imran A., Kowsalya M. Optimal Distributed Generation and Capacitor Placement in Power Distribution Network for Power Loss Minimization. – International Conference on Advances in Electrical Engineering (ICAEE), 2014, DOI:10.1109/ICAEE.2014.6838519.
12. Hashimov А.М. et al. Energetika. Izvestiya vysshih uchebnyh zavedeniy i energeticheskih ob"edineniy SNG – in Russ. (Power Industry. News of Higher Educational Institutions and Energy Associations of the CIS), 2016, No. 6. pp. 519–528.
13. Maronani I. et al. Optimized FACTS Devices for Power System Enhancement: Applications and Solving Methods. – Sustainability, 2023, vol. 15(12), DOI:10.3390/su15129348.
14. Rashed G.I., Shaheen H.I., Cheng S.J. Optimal Location and Parameter Settings of Multiple TESC for Increasing Power System Loadability Based on GA and PSO Techniques. – The 3rd International Conference on Natural Computation (ICNC), 2007, DOI:10.1109/ICNC.2007.521.
15. Hashimov A.M. et al. Probabilistic Evaluation of Voltage Stability Limit of Power System under the Conditions of Accidental Emergency Outages of Lines and Generators. – International Journal on Technical and Physical Problems of Engineering, 2020, iss. 43, vol. 12, No. 2, pp. 40–45.
16. Song Y., Hill D.J., Liu T. Static Voltage Stability Analysis of Distribution Systems Based on Network – Load Admittance Ratio. – IEEE Transactions on Power Systems, 2019, 34(3), pp. 2270–2280, DOI:10.1109/TPWRS.2018.2886636.
17. Sun X. et al. Sustainable Energy Transition in China: Renewable Options and Impacts on the Electricity System. – Energies, 2016, 9(12), DOI:10.3390/en9120980.
18. Renedek J., Tihamer S., Bartok B. Evaluation of Renewable Energy Sources in Peripheral Areas and Renewable Energy – Based Rural Development. – Renewable and Sustainable Energy Reviews, 2018, 90(7), pp. 516–535, DOI:10.1016/j.rser.2018.03.020.
19. Spiegel T. Impact of Renewable Energy Expansion to the Balancing Energy Demand of Differential Balancing Groups. – Journal of Sustainable Development of Energy, Water and Environmental Systems, 2018, vol.6(4), pp. 784–799, DOI:10.13044/j.sdewes.d6.0215.
20. Gaete-Morales C. et al. A Novel Framework for Development and Optimization of Future Electricity Scenarios with High Penetration of Renewables and Storage. – Applied Energy, 2019, vol. 250, pp. 1657–1672, DOI:10.1016/j.apenergy.2019.05.006.
21. Mladenov V., Chobanov V., Georgiev A. Impact of Renewable Energy Sources on Power System Flexibility Requirements. – Energies, 2021, 14(10), DOI:10.3390 /en 14102813.
22. Shadmesgaran M.R., Hashimov A.M., Rahmanov N.R. A Glance of the Optimal Control Effects on Technical and Economic Operation in GRID. – International Journal on Technical and Physical Problems of Engineering, 2020, iss. 45, vol. 12, No. 4, pp. 1–10.
23. Salami Y., Ieyasurya B. A Comprehensive Evaluation of DC Power Flow Models and their Application to Power Systems Security Analysis. – CIGRE Canada Conference, Vancouver, BC, 2016, 753, pp. 1-8. Methods to mitigate or avoid power outages.
24. Power Systems Test Case Archive [Электрон. ресурс], URL: https://labs.ece.uw.edu/pstca (дата обращения 15.02.2024)
2. Bazmi A.A., Zahedi G. Sustainable Energy Systems: Role of Optimization Modeling Techniques in Power Generation and Supply – A Review. – Renewable and Sustainable Energy Review, 2011, 15(8), pp. 3480–3500, DOI:10.1016/j.rser.2011.05.003.
3. Рахманов Н.Р., Гулиев Г.Б. Применение модели нейронной сети для оценки текущего значения предела устойчивости электрической системы по напряжению. – Электричество, 2015, № 4, с. 4–11.
4. Gao H. et al. Real-Time Long-Term Voltage Stability Assessment Based on eGBDT for Large-Scale Power System with High Renewables Penetration. – Electric Power Systems Research, 2023, vol. 214(6), DOI:10.1016/j.epsr.2022.108915.
5. Rahmanov N.R. et al. Method for Assessing the Voltage Stability Limit During Emergency Outages of the Line and Generators in the Power System. – Rudenko International Conference on Methodological Problems in Reliability Study of Large Energy Systems, 2019, vol. 139, DOI: 10.1051/e3sconf/201913901020.
6. Khazali A.H., Kalantar M. Reactive /Voltage control by A Multi-Agent based PSO approach considering voltage stability. – 24th International Power System Conference, Tehran, 2009, pp. 1–8.
7. Hosseini H., Banaei M.R. Performance of Active Power Line Conditioner for Loss Reduction in the Power Distribution System. – IEEE Region 10 Conference TENCON, 2004, pp. 97–100, DOI:10.1109/TENCON.2004.1414877.
8. Гашимов A.M., Гулиев Г.Б., Рахманов Н.Р. Улучшенный алгоритм нечеткой логики для управления реактивной мощностью и напряжением в распределительных сетях. – Энергетика. Известия высших учебных заведений и энергетических объединений СНГ, 2014, № 2, c. 29–39.
9. Devi S., Geethajali M. Optimal Location and Sizing Determination of Distributed Generation and DSTATCOM using Particle Swarm Optimization Algorithm. – Elsevier International Journal of Electrical Power and Energy Systems, 2014, vol. 62. pp. 562–570, DOI:10.1016/j.ijepes.2014.05.015.
10. Elsheikh A.M.F. et al. Optimal Capacitor Placement and Sizing in Radial Electric Power Systems. – Alexandria Engineering Journal, 2014, vol 53(4), pp. 809–816, DOI:10.1016/j.aej.2014.09.012.
11. Mohamad Imran A., Kowsalya M. Optimal Distributed Generation and Capacitor Placement in Power Distribution Network for Power Loss Minimization. – International Conference on Advances in Electrical Engineering (ICAEE), 2014, DOI:10.1109/ICAEE.2014.6838519.
12. Гашимов А.М. и др. Вероятностное потокораспределение как реакция на стохастичность нагрузки в энергосистеме. – Энергетика. Известия высших учебных заведений и энергетических объединений СНГ, 2016, № 6. с. 519–528
13. Maronani I. et al. Optimized FACTS Devices for Power System Enhancement: Applications and Solving Methods. – Sustainability, 2023, vol. 15(12), DOI:10.3390/su15129348.
14. Rashed G.I., Shaheen H.I., Cheng S.J. Optimal Location and Parameter Settings of Multiple TESC for Increasing Power System Loadability Based on GA and PSO Techniques. – The 3rd International Conference on Natural Computation (ICNC), 2007, DOI:10.1109/ICNC.2007.521.
15. Hashimov A.M. et al. Probabilistic Evaluation of Voltage Stability Limit of Power System under the Conditions of Accidental Emergency Outages of Lines and Generators. – International Journal on Technical and Physical Problems of Engineering, 2020, iss. 43, vol. 12, No. 2, pp. 40–45.
16. Song Y., Hill D.J., Liu T. Static Voltage Stability Analysis of Distribution Systems Based on Network – Load Admittance Ratio. – IEEE Transactions on Power Systems, 2019, 34(3), pp. 2270–2280, DOI:10.1109/TPWRS.2018.2886636.
17. Sun X. et al. Sustainable Energy Transition in China: Renewable Options and Impacts on the Electricity System. – Energies, 2016, 9(12), DOI:10.3390/en9120980.
18. Renedek J., Tihamer S., Bartok B. Evaluation of Renewable Energy Sources in Peripheral Areas and Renewable Energy – Based Rural Development. – Renewable and Sustainable Energy Reviews, 2018, 90(7), pp. 516–535, DOI:10.1016/j.rser.2018.03.020.
19. Spiegel T. Impact of Renewable Energy Expansion to the Balancing Energy Demand of Differential Balancing Groups. – Journal of Sustainable Development of Energy, Water and Environmental Systems, 2018, vol.6(4), pp. 784–799, DOI:10.13044/j.sdewes.d6.0215.
20. Gaete-Morales C. et al. A Novel Framework for Development and Optimization of Future Electricity Scenarios with High Penetration of Renewables and Storage. – Applied Energy, 2019, vol. 250, pp. 1657–1672, DOI:10.1016/j.apenergy.2019.05.006.
21. Mladenov V., Chobanov V., Georgiev A. Impact of Renewable Energy Sources on Power System Flexibility Requirements. – Energies, 2021, 14(10), DOI:10.3390 /en 14102813.
22. Shadmesgaran M.R., Hashimov A.M., Rahmanov N.R. A Glance of the Optimal Control Effects on Technical and Economic Operation in GRID. – International Journal on Technical and Physical Problems of Engineering, 2020, iss. 45, vol. 12, No. 4, pp. 1–10.
23. Salami Y., Ieyasurya B. A Comprehensive Evaluation of DC Power Flow Models and their Application to Power Systems Security Analysis. – CIGRE Canada Conference, Vancouver, BC, 2016, 753, pp. 1-8. Methods to mitigate or avoid power outages.
24. Power Systems Test Case Archive [Электрон. ресурс], URL: https://labs.ece.uw.edu/pstca (дата обращения 15.02.2024)
#
1. Althowibi F.A., Mustafa M.W. Maximum Power System Loadability to Detect Voltage Collapse. – 4th International Power Engineering and Optimization Conference, 2010, pp. 49–52, DOI:10.1109/PEOCO.2010.5559231.
2. Bazmi A.A., Zahedi G. Sustainable Energy Systems: Role of Optimization Modeling Techniques in Power Generation and Supply – A Review. – Renewable and Sustainable Energy Review, 2011, 15(8), pp. 3480–3500, DOI:10.1016/j.rser.2011.05.003.
3. Rahmanov N.R., Guliev G.B. Elektrichestvo – in Russ. (Electricity), 2015, No. 4, pp. 4–11.
4. Gao H. et al. Real-Time Long-Term Voltage Stability Assessment Based on eGBDT for Large-Scale Power System with High Renewables Penetration. – Electric Power Systems Research, 2023, vol. 214(6), DOI:10.1016/j.epsr.2022.108915.
5. Rahmanov N.R. et al. Method for Assessing the Voltage Stability Limit During Emergency Outages of the Line and Generators in the Power System. – Rudenko International Conference on Methodological Problems in Reliability Study of Large Energy Systems, 2019, vol. 139, DOI: 10.1051/e3sconf/201913901020.
6. Khazali A.H., Kalantar M. Reactive /Voltage control by A Multi-Agent based PSO approach considering voltage stability. – 24th International Power System Conference, Tehran, 2009, pp. 1–8.
7. Hosseini H., Banaei M.R. Performance of Active Power Line Conditioner for Loss Reduction in the Power Distribution System. – IEEE Region 10 Conference TENCON, 2004, pp. 97–100, DOI:10.1109/TENCON.2004.1414877.
8. Hashimov A.M., Guliev G.B., Rahmanov N.R. Energetika. Izvestiya vysshih uchebnyh zavedeniy i energeticheskih ob"edineniy SNG – in Russ. (Power Industry. News of Higher Educational Institutions and Energy Associations of the CIS), 2014, No. 2, pp. 29–39.
9. Devi S., Geethajali M. Optimal Location and Sizing Determination of Distributed Generation and DSTATCOM using Particle Swarm Optimization Algorithm. – Elsevier International Journal of Electrical Power and Energy Systems, 2014, vol. 62. pp. 562–570, DOI:10.1016/j.ijepes.2014.05.015.
10. Elsheikh A.M.F. et al. Optimal Capacitor Placement and Sizing in Radial Electric Power Systems. – Alexandria Engineering Journal, 2014, vol 53(4), pp. 809–816, DOI:10.1016/j.aej.2014.09.012.
11. Mohamad Imran A., Kowsalya M. Optimal Distributed Generation and Capacitor Placement in Power Distribution Network for Power Loss Minimization. – International Conference on Advances in Electrical Engineering (ICAEE), 2014, DOI:10.1109/ICAEE.2014.6838519.
12. Hashimov А.М. et al. Energetika. Izvestiya vysshih uchebnyh zavedeniy i energeticheskih ob"edineniy SNG – in Russ. (Power Industry. News of Higher Educational Institutions and Energy Associations of the CIS), 2016, No. 6. pp. 519–528.
13. Maronani I. et al. Optimized FACTS Devices for Power System Enhancement: Applications and Solving Methods. – Sustainability, 2023, vol. 15(12), DOI:10.3390/su15129348.
14. Rashed G.I., Shaheen H.I., Cheng S.J. Optimal Location and Parameter Settings of Multiple TESC for Increasing Power System Loadability Based on GA and PSO Techniques. – The 3rd International Conference on Natural Computation (ICNC), 2007, DOI:10.1109/ICNC.2007.521.
15. Hashimov A.M. et al. Probabilistic Evaluation of Voltage Stability Limit of Power System under the Conditions of Accidental Emergency Outages of Lines and Generators. – International Journal on Technical and Physical Problems of Engineering, 2020, iss. 43, vol. 12, No. 2, pp. 40–45.
16. Song Y., Hill D.J., Liu T. Static Voltage Stability Analysis of Distribution Systems Based on Network – Load Admittance Ratio. – IEEE Transactions on Power Systems, 2019, 34(3), pp. 2270–2280, DOI:10.1109/TPWRS.2018.2886636.
17. Sun X. et al. Sustainable Energy Transition in China: Renewable Options and Impacts on the Electricity System. – Energies, 2016, 9(12), DOI:10.3390/en9120980.
18. Renedek J., Tihamer S., Bartok B. Evaluation of Renewable Energy Sources in Peripheral Areas and Renewable Energy – Based Rural Development. – Renewable and Sustainable Energy Reviews, 2018, 90(7), pp. 516–535, DOI:10.1016/j.rser.2018.03.020.
19. Spiegel T. Impact of Renewable Energy Expansion to the Balancing Energy Demand of Differential Balancing Groups. – Journal of Sustainable Development of Energy, Water and Environmental Systems, 2018, vol.6(4), pp. 784–799, DOI:10.13044/j.sdewes.d6.0215.
20. Gaete-Morales C. et al. A Novel Framework for Development and Optimization of Future Electricity Scenarios with High Penetration of Renewables and Storage. – Applied Energy, 2019, vol. 250, pp. 1657–1672, DOI:10.1016/j.apenergy.2019.05.006.
21. Mladenov V., Chobanov V., Georgiev A. Impact of Renewable Energy Sources on Power System Flexibility Requirements. – Energies, 2021, 14(10), DOI:10.3390 /en 14102813.
22. Shadmesgaran M.R., Hashimov A.M., Rahmanov N.R. A Glance of the Optimal Control Effects on Technical and Economic Operation in GRID. – International Journal on Technical and Physical Problems of Engineering, 2020, iss. 45, vol. 12, No. 4, pp. 1–10.
23. Salami Y., Ieyasurya B. A Comprehensive Evaluation of DC Power Flow Models and their Application to Power Systems Security Analysis. – CIGRE Canada Conference, Vancouver, BC, 2016, 753, pp. 1-8. Methods to mitigate or avoid power outages.
24. Power Systems Test Case Archive [Электрон. ресурс], URL: https://labs.ece.uw.edu/pstca (дата обращения 15.02.2024)
