Optimization Studies of an Electric Power System with Hydroelectric and Thermal Power Plants
DOI:
https://doi.org/10.24160/0013-5380-2026-5-74-85Keywords:
electric power systems, thermal power plant, hydroelectric power plant, mathematical modeling, optimization of electric power system operation modesAbstract
The article presents a methodological approach to modeling and optimizing the operating modes of an electric power system comprising energy sources of various types. To address the general problem of optimizing power system operation modes, a two-level approach is proposed: at the lower level, hourly fuel costs are minimized taking into account the composition of operating equipment, and at the upper level, the power system annual operation cycle is optimized through balancing the generation at hydroelectric and thermal power plants. The main results of solving the general problem are the determination of annual fuel costs, the optimal distribution of thermal and hydroelectric power plant capacities by months, and the composition of power equipment switched in operation. To achieve acceptable accuracy in determining the minimum fuel costs with taking into account the operation of hydroelectric power plants, an iterative process has been implemented, which continues until a small change in hydroelectric power capacity is achieved by months at adjacent iterations. The testing was performed on a power system model including hydroelectric power plants with reservoirs of long-term and seasonal regulation, as well as gas- and coal-fired thermal power plants. The methodological approach can be used in planning the development of power systems, evaluating investment projects, and elaborating adaptive control algorithms under the conditions of varying loads and climatic factors.
References
1. Веселов Ф. и др. Развитие электроэнергетики – на распутье стратегических решений. – Энергетическая политика, 2024, № 2 (193), с. 90–105.
2. Подковальников С.В. и др. Технологические и интеллектуально-цифровые инновации – основа трансформации электроэнергетических систем. – Электричество, 2025, № 9, с. 4–21.
3. Подковальников С.В., Хамисов О.В., Семёнов К.А. Концептуально-методологические и прикладные вопросы обоснования развития электроэнергетических систем в современных условиях. – Известия РАН. Энергетика, 2022, № 5, с. 3–21.
4. Weinand J.M., Scheller F., McKenna R. Reviewing Energy System Modelling of Decentralized Energy Autonomy. – Energy, 2020, vol. 203, DOI: 10.1016/j.energy.2020.117817.
5. Петров Н.А. и др. Присоединение изолированных энергорайонов Центральной и Западной Якутии к ЕЭС России: предпосылки, этапы, эффекты. – Электроэнергия. Передача и распределение, 2021, № 5 (68), с. 28–35.
6. Белей В.Ф., Коцарь Г.В. Энергетика Калининградской области: переход к изолированному режиму работы и оценка перспектив развития. – Электричество, 2025, № 5, с. 16–27.
7. Wanxing Zh. et al. Ultra High Voltage Direct Current Line Application for Energy Systems with High Share of Renewable Energy Sources – Current Trends in Multidisciplinary Research–2025: Materials of V Int. Student Scientific and Practical Conf., 2025, pp. 169–173.
8. Иерархическое моделирование систем энергетики / под ред. Н.И. Воропая, В.А. Стенникова. Новосибирск: Академическое изд-во «Гео», 2020, 314 с.
9. Wiebrow E. The Effects of Shutting Down the Last Nuclear Power Plants in Germany: A Model-Based Analysis of Network Flows and Redispatch. – Energy Strategy Reviews, 2026, vol. 64, DOI: 10.1016/j.esr.2026.102068.
10. Sivakumar S. et al. Multi-Objective Hybrid Grasshopper Optimization and Differential Evolution Algorithm for Wind-Integrated Power System Expansion with Energy Storage Solutions. – Results in Engineering, 2026, vol. 29, DOI: 10.1016/j.rineng.2026.109392.
11. Гашимов А.М., Рахманов Н.Р. Оптимизация режима электроэнергетической системы в условиях аварийных отказов ЛЭП и при пиковых нагрузках с использованием FACTS и программ реагирования на спрос. – Электричество, 2024, № 6, с. 4–15.
12. Беляев Н.А., Коровкин Н.В. Оптимизация перспективной структуры энергосистемы на основе алгоритма роя частиц. – Электричество, 2026, № 2, с. 40–50.
13. Yin W. et al. Quantifying the Energy Imbalance in Hydrogen Energy Storage-Assisted Power Systems Under Heat Waves. – International Journal of Electrical Power & Energy Systems, 2025, vol. 164, DOI: 10.1016/j.ijepes.2024.110434
14. Wang C. et al. Annual Capacity Analysis and Multi-Objective Optimization of a Nuclear-Renewable Integrated Energy System. – Energy, 2026, vol. 345, DOI: 10.1016/j.energy.2026.140002
15. Ren X. et al. Optimization Design of Nuclear-Renewable Integrated Energy System in Industrial Parks Considering Carbon-Emissions Trading and Green-Certificate Trading. – Energy, 2025, vol. 337, DOI: 10.1016/j.energy.2025.138694.
16. Wang Y., Wang J., Song J. Data-Centric Optimization: An End-to-End Strategy for Power Systems. – Engineering, 2025, DOI: 10.1016/j.eng.2025.09.028.
17. Chen K. et al. Optimization of Multi-Temporal Generation Scheduling in Power System Under Elevated Renewable Penetrations: A Review. – Frontiers in Energy Research, 2023, vol. 11, DOI: 10.3389/fenrg.2022.1054597.
18. Справочник по проектированию электроэнергетических систем / под ред. С.С. Рокотяна, Н.М. Шапиро. М.: Энергоатомиздат, 1985, 352 с.
19. Методические указания по проектированию развития энергосистем (Утв. приказом Минэнерго России от 6.12.2022 № 1286).
20. Клер А.М., Деканова Н.П., Степанова Е.Л. Оптимизация режимных параметров и состава работающего оборудования крупных энергоисточников. – Известия РАН. Энергетика, 2004, № 6, с. 43–52.
21. Степанова Е.Л., Клер А.М., Жарков П.В. Методика создания математических моделей ТЭЦ, предназначенных для проведения оптимизационных исследований режимов работы электроэнергетической системы. – Известия РАН. Энергетика, 2025, № 2, с. 81–94.
22. Kler. A.M., Zharkov P.V., Epishkin N.O. Parametric Optimization of Supercritical Power Plants Using Gradient Methods. – Energy, 2019, vol. 189, DOI: 10.1016/j.energy.2019.116230.
23. Hierarchical Modeling of Energy Systems / Ed. by N.I. Voropai, V.A. Stennikov. – Elsevier, 2023, Chapter 7, pp. 457–502, DOI: 10.1016/C2022-0-02475-2.
24. Клер А.М. и др. Определение наилучших режимов электроэнергетической системы, имеющей в составе ТЭЦ и ГЭС методом ступенчатой оптимизации. – Известия РАН. Энергетика, 2024, № 3, с. 46–63.
---
Работа выполнена в рамках Проекта государственного задания № FWEU-2026-0010 программы фундаментальных исследований РФ на 2026–2030 гг.
#
1. Veselov F. et al. Energeticheskaya politika – in Russ. (Energy Policy), 2024, No. 2 (193), pp. 90–105.
2. Podkoval’nikov S.V. et al. Elektrichestvo – in Russ. (Electrici-ty), 2025, No. 9, pp. 4–21.
3. Podkoval’nikov S.V., Hamisov O.V., Semyonov K.A. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Energy Industry), 2022, No. 5, pp. 3–21.
4. Weinand J.M., Scheller F., McKenna R. Reviewing Energy System Modelling of Decentralized Energy Autonomy. – Energy, 2020, vol. 203, DOI: 10.1016/j.energy.2020.117817.
5. Petrov N.A. et al. Elektroenergiya. Peredacha i raspredelenie – in Russ. (Electricity. Transmission and Distribution), 2021, No. 5 (68), pp. 28–35.
6. Beley V.F., Kotsar’ G.V. Elektrichestvo – in Russ. (Electricity), 2025, No. 5, pp. 16–27.
7. Wanxing Zh. et al. Ultra High Voltage Direct Current Line Application for Energy Systems with High Share of Renewable Energy Sources – Current Trends in Multidisciplinary Research–2025: Materials of V Int. Student Scientific and Practical Conf., 2025, pp. 169–173.
8. Ierarhicheskoe modelirovanie sistem energetiki (Hierarchical Modeling of Energy Systems) / Ed. by N.I. Voropay, V.A. Stennikov. Novosibirsk: Akademicheskoe izd-vo «Geo», 2020, 314 p.
9. Wiebrow E. The Effects of Shutting Down the Last Nuclear Power Plants in Germany: A Model-Based Analysis of Network Flows and Redispatch. – Energy Strategy Reviews, 2026, vol. 64, DOI: 10.1016/j.esr.2026.102068.
10. Sivakumar S. et al. Multi-Objective Hybrid Grasshopper Optimization and Differential Evolution Algorithm for Wind-Integrated Power System Expansion with Energy Storage Solutions. – Results in Engineering, 2026, vol. 29, DOI: 10.1016/j.rineng.2026.109392.
11. Gashimov A.M., Rahmanov N.R. Elektrichestvo – in Russ. (Electricity), 2024, No. 6, pp. 4–15.
12. Belyaev N.A., Korovkin N.V. Elektrichestvo – in Russ. (Electricity), 2026, No. 2, pp. 40–50.
13. Yin W. et al. Quantifying the Energy Imbalance in Hydrogen Energy Storage-Assisted Power Systems Under Heat Waves. – International Journal of Electrical Power & Energy Systems, 2025, vol. 164, DOI: 10.1016/j.ijepes.2024.110434
14. Wang C. et al. Annual Capacity Analysis and Multi-Objective Optimization of a Nuclear-Renewable Integrated Energy System. – Energy, 2026, vol. 345, DOI: 10.1016/j.energy.2026.140002
15. Ren X. et al. Optimization Design of Nuclear-Renewable Integrated Energy System in Industrial Parks Considering Carbon-Emissions Trading and Green-Certificate Trading. – Energy, 2025, vol. 337, DOI: 10.1016/j.energy.2025.138694.
16. Wang Y., Wang J., Song J. Data-Centric Optimization: An End-to-End Strategy for Power Systems. – Engineering, 2025, DOI: 10.1016/j.eng.2025.09.028.
17. Chen K. et al. Optimization of Multi-Temporal Generation Scheduling in Power System Under Elevated Renewable Penetrations: A Review. – Frontiers in Energy Research, 2023, vol. 11, DOI: 10.3389/fenrg.2022.1054597.
18. Spravochnik po proektirovaniyu elektroenergeticheskih sistem (Handbook on the Design of Electric Power Systems) / Ed. by S.S. Rokotyan, N.M. Shapiro. M.: Energoatomizdat, 1985, 352 p.
19. Metodicheskie ukazaniya po proektirovaniyu razvitiya energosistem (Utv. prikazom Minenergo Rossii ot 6.12.2022 No. 1286) (Methodological Guidelines for the Design of Energy System Development (Approved by the Order of the Ministry of Energy of the Russian Federation dated 6.12.2022 No. 1286)).
20. Kler A.M., Dekanova N.P., Stepanova E.L. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Energy Industry), 2004, No. 6, pp. 43–52.
21. Stepanova E.L., Kler A.M., Zharkov P.V. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Energy Industry), 2025, No. 2, pp. 81–94.
22. Kler. A.M., Zharkov P.V., Epishkin N.O. Parametric Optimi-zation of Supercritical Power Plants Using Gradient Methods. – Energy, 2019, vol. 189, DOI: 10.1016/j.energy.2019.116230.
23. Hierarchical Modeling of Energy Systems / Ed. by N.I. Voropai, V.A. Stennikov. – Elsevier, 2023, Chapter 7, pp. 457–502, DOI: 10.1016/C2022-0-02475-2.
24. Kler A.M. et al. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Energy Industry), 2024, No. 3, pp. 46–63
---
The work was carried out within the framework of the Project of state assignment no. FWEU-2026-0010 of the Fundamental Research Program of the Russian Federation for 2026–2030.
