Topological Algorithms for Analyzing and Synthesizing Electric Power System Load Flow Modes
Keywords:
electric power system, topology, graph theory, matrix of current distribution coefficients, compensating devices, OLTC operating taps
Abstract
The article addresses the development of the topological method for producing the load flow mode parameters of a complex electric power system grid proceeding from the theory of directed graphs. The obtained exact solution from zero iteration of the equations of nodal voltages with using the matrix of distribution coefficients is the basis for the development of algorithms for analyzing and synthesizing the electric power system load flow modes. The topological algorithms for determining the load flow parameters are developed proceeding from analytical expressions for the distribution coefficients obtained on the basis of all possible and specific trees of the complex power system grid’s directional graph. The load flow topological algorithms make it possible to determine the necessary capacities of modern FACTS devices and OLTC tap positions at which the desired voltage level is ensured on the transformer secondary winding busbars from the viewpoint of synthesizing load flow modes in terms of voltage.
References
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9. Ахметбаев Д.С. Топологический метод формирования узловых уравнений в обращенной форме для электроэнергетических систем. – Электричество, 2018, № 5, с. 18–27.
10. Kirchhoff G. Poggendorfs Annalen, 1845, Bd 64, 512 р.; 1847, 497 p.
11. Maxwell J.C. Electricity and Magnetism, 1892, v.1, 403 p.
12. Гераскин О.Т. Методы определения 2 деревьев графа в топологии электрических сетей. – Известия АН СССР. Энергетика и транспорт, 1967, № 5, с. 106–112.
13. Akhmetbaev D.S., Dzhandigulov A.R. Development of Algorithms for the Formation of Steady–State Modes Based on the Topology of Electric Power Systems. – Journal of Physics: Conference Series, 2019, 1392(1), 012079, DOI:10.1088/1742–6596/1392/1/012079.
14. Akhmetbayev D.S., Dzhandigulov A.R., Bystrova S.V. Topological System Method of Formation of Transformer Transformation Coefficients. – E3S Web of Conferences, 2020, 216(3), DOI:10. 1051/e3sconf/202021601087.
15. Кристофидес Н. Теория графов. Алгоритмический подход. М.: Мир, 1978, 432 с.
16. Kesavan H.K., Pai M.A., Bhat M.V. Piecewise Solution of the Load–Flow Problem. – IEEE Transactions on Power Apparatus and Systems, 1972, PAS–91 (4), pp. 1382–1386, DOI:10.1109/TPAS.1972. 293269.
17. Percival W.S. The Solution of Passive Electrical Networks by Means of Mathematical Trees. – Journal of the Institution of Electrical Engineers, 1953, vol. 100, Part III, 1492R, pр. 143–150, DOI:10.1049/PI–3.1953.0033.
18. Массель Л., Гальперов В. Анализ надежности работы многоагентных систем с использованием графовой модели. – Вестник ИрГТУ, 2017, т. 21, № 1(120), с. 77–80.
19. Bakry O.M. et al. Improvement of Distribution Networks Performance Using Renewable Energy Sources–Based Hybrid Optimization Techniques. – Ain Shams Engineering Journa, 2022, 13(6):101786, DOI: 10.1016/j.asej.2022.101786.
20. Hemeida M.G. et al. Optimal Probabilistic Location of DGs Using Monte Carlo Simulation Based Different Bio–Inspired Algorithms. – Ain Shams Engineering Journal, 2021, 12(3), DOI: 10.1016/j.asej.2021.02.007.
21. Yang H. et al. Nonlinear Active Distribution Network Optimization for Improving the Renewable Energy Power Quality and Economic Efficiency: a Multi–Objective Bald Eagle Search Algorithm. – Soft Computing, 2023, 27(22), DOI: 10.1007/s00500–023–08913–3.
#
1. Venikov V.А. Elektrichestvo – in Russ. (Electricity), 1978, No. 5, pp. 64–67.
2. Manusov B.Z., Lykin A.V., Sidorkin Yu.М. Izvestiya vuzov SSSR. Energetika – in Russ. (News of Universities of the USSR. Energy Industry), 1974, No. 9, pp. 3–7.
3. Fazylov Kh.F., Nasyrov T.Kh. Ustanovivshiesya rezhimy elektroenergeticheskikh sistem i ikh optimizatsiya (The Steady–State Modes of Electric Power Systems and Their Optimization). Tashkent: Molniya, 1999, 370 p.
4. Mel'nikov N.А. Elektrichestvo – in Russ. (Electricity), 1961, No. 2, pp. 9–13.
5. Geraskin О.Т. Izvestiya vuzov. Energetika – in Russ. (News of Universities. Energy Industry), 1967, No. 5, pp. 20–24.
6. Akhmetbayev D.S. et al. Development of Topological Method for Calculating Current Distribution Coefficients in Complex Power Networks. – Results in Physics, 2017, 7(2), pp. 1644–1649, DOI:10.1016/j.rinp.2017.03.010.
7. Mel'nikov N.А. Matrichnyy metod analiza elektricheskikh tsepey (Matrix Method of Analysis of Electric Circuits). M.: Energiya, 1972, 232 p.
8. Ahmetbaev D.S. Elektrichestvo – in Russ. (Electricity), 2010, No. 11, pp. 23–27.
9. Ahmetbaev D.S. Elektrichestvo – in Russ. (Electricity), 2018, No. 5, pp. 18–27.
10. Kirchhoff G. Poggendorfs Annalen, 1845, Bd 64, 512 р.; 1847, 497 p.
11. Maxwell J.C. Electricity and Magnetism, 1892, v.1, 403 p.
12. Geraskin O.T. Izvestiya AN SSSR. Energetika i transport – in Russ. (Izvestia of the USSR Academy of Sciences. Energy and Transport), 1967, No. 5, pp. 106–112.
13. Akhmetbaev D.S., Dzhandigulov A.R. Development of Algorithms for the Formation of Steady–State Modes Based on the Topology of Electric Power Systems. – Journal of Physics: Conference Series, 2019, 1392(1), 012079, DOI:10.1088/1742–6596/1392/1/012079.
14. Akhmetbayev D.S., Dzhandigulov A.R., Bystrova S.V. Topological System Method of Formation of Transformer Transformation Coefficients. – E3S Web of Conferences, 2020, 216(3), DOI:10.1051/e3sconf/202021601087.
15. Kristofides N. Teoriya grafov. Algoritmicheskiy podkhod (Graph Theory. Algorithmic Approach). М.: Mir, 1978, 432 p.
16. Kesavan H.K., Pai M.A., Bhat M.V. Piecewise Solution of the Load–Flow Problem. – IEEE Transactions on Power Apparatus and Systems, 1972, PAS–91 (4), pp. 1382–1386, DOI:10.1109/TPAS.1972.293269.
17. Percival W.S. The Solution of Passive Electrical Networks by Means of Mathematical Trees. – Journal of the Institution of Electrical Engineers, 1953, vol. 100, Part III, 1492R, pр. 143–150, DOI:10.1049/PI–3.1953.0033.
18. Massel' L., Gal'perov V. Vestnik IRGTU – in Russ. (Bulletin of the IrSTU), 2017, vol. 21, No. 1(120), pp. 77–80.
19. Bakry O.M. et al. Improvement of Distribution Networks Performance Using Renewable Energy Sources–Based Hybrid Optimization Techniques. – Ain Shams Engineering Journa, 2022, 13(6):101786, DOI: 10.1016/j.asej.2022.101786.
20. Hemeida M.G. et al. Optimal Probabilistic Location of DGs Using Monte Carlo Simulation Based Different Bio–Inspired Algorithms. – Ain Shams Engineering Journal, 2021, 12(3), DOI: 10.1016/j.asej.2021.02.007.
21. Yang H. et al. Nonlinear Active Distribution Network Optimization for Improving the Renewable Energy Power Quality and Economic Efficiency: a Multi–Objective Bald Eagle Search Algorithm. – Soft Computing, 2023, 27(22), DOI: 10.1007/s00500–023–08913–3.
2. Манусов Б.З., Лыкин А.В., Сидоркин Ю.М. Алгоритмы метода Ньютона–Рафсона для решения узловых уравнений в обращенной форме. – Известия вузов СССР. Энергетика, 1974, № 9, с. 3–7.
3. Фазылов Х.Ф., Насыров Т.Х. Установившиеся режимы электроэнергетических систем и их оптимизация. Ташкент: Молния, 1999, 370 с.
4. Мельников Н.А. Применение коэффициентов распределения при расчетах сложных схем замещения электрических цепей. – Электричество, 1961, № 2, с. 9–13.
5. Гераскин О.Т. Топологический анализ коэффициентов токораспределения в электрических сетях. – Известия вузов. Энергетика, 1967, № 5, с. 20–24.
6. Akhmetbayev D.S. et al. Development of Topological Method for Calculating Current Distribution Coefficients in Complex Power Networks. – Results in Physics, 2017, 7(2), pp. 1644–1649, DOI:10.1016/j.rinp.2017.03.010.
7. Мельников Н.А. Матричный метод анализа электрических цепей. М.: Энергия, 1972, 232 с.
8. Ахметбаев Д.С. Метод расчета установившихся режимов электрических сетей на основе коэффициентов токораспределения. – Электричество, 2010, № 11, с. 23–27.
9. Ахметбаев Д.С. Топологический метод формирования узловых уравнений в обращенной форме для электроэнергетических систем. – Электричество, 2018, № 5, с. 18–27.
10. Kirchhoff G. Poggendorfs Annalen, 1845, Bd 64, 512 р.; 1847, 497 p.
11. Maxwell J.C. Electricity and Magnetism, 1892, v.1, 403 p.
12. Гераскин О.Т. Методы определения 2 деревьев графа в топологии электрических сетей. – Известия АН СССР. Энергетика и транспорт, 1967, № 5, с. 106–112.
13. Akhmetbaev D.S., Dzhandigulov A.R. Development of Algorithms for the Formation of Steady–State Modes Based on the Topology of Electric Power Systems. – Journal of Physics: Conference Series, 2019, 1392(1), 012079, DOI:10.1088/1742–6596/1392/1/012079.
14. Akhmetbayev D.S., Dzhandigulov A.R., Bystrova S.V. Topological System Method of Formation of Transformer Transformation Coefficients. – E3S Web of Conferences, 2020, 216(3), DOI:10. 1051/e3sconf/202021601087.
15. Кристофидес Н. Теория графов. Алгоритмический подход. М.: Мир, 1978, 432 с.
16. Kesavan H.K., Pai M.A., Bhat M.V. Piecewise Solution of the Load–Flow Problem. – IEEE Transactions on Power Apparatus and Systems, 1972, PAS–91 (4), pp. 1382–1386, DOI:10.1109/TPAS.1972. 293269.
17. Percival W.S. The Solution of Passive Electrical Networks by Means of Mathematical Trees. – Journal of the Institution of Electrical Engineers, 1953, vol. 100, Part III, 1492R, pр. 143–150, DOI:10.1049/PI–3.1953.0033.
18. Массель Л., Гальперов В. Анализ надежности работы многоагентных систем с использованием графовой модели. – Вестник ИрГТУ, 2017, т. 21, № 1(120), с. 77–80.
19. Bakry O.M. et al. Improvement of Distribution Networks Performance Using Renewable Energy Sources–Based Hybrid Optimization Techniques. – Ain Shams Engineering Journa, 2022, 13(6):101786, DOI: 10.1016/j.asej.2022.101786.
20. Hemeida M.G. et al. Optimal Probabilistic Location of DGs Using Monte Carlo Simulation Based Different Bio–Inspired Algorithms. – Ain Shams Engineering Journal, 2021, 12(3), DOI: 10.1016/j.asej.2021.02.007.
21. Yang H. et al. Nonlinear Active Distribution Network Optimization for Improving the Renewable Energy Power Quality and Economic Efficiency: a Multi–Objective Bald Eagle Search Algorithm. – Soft Computing, 2023, 27(22), DOI: 10.1007/s00500–023–08913–3.
#
1. Venikov V.А. Elektrichestvo – in Russ. (Electricity), 1978, No. 5, pp. 64–67.
2. Manusov B.Z., Lykin A.V., Sidorkin Yu.М. Izvestiya vuzov SSSR. Energetika – in Russ. (News of Universities of the USSR. Energy Industry), 1974, No. 9, pp. 3–7.
3. Fazylov Kh.F., Nasyrov T.Kh. Ustanovivshiesya rezhimy elektroenergeticheskikh sistem i ikh optimizatsiya (The Steady–State Modes of Electric Power Systems and Their Optimization). Tashkent: Molniya, 1999, 370 p.
4. Mel'nikov N.А. Elektrichestvo – in Russ. (Electricity), 1961, No. 2, pp. 9–13.
5. Geraskin О.Т. Izvestiya vuzov. Energetika – in Russ. (News of Universities. Energy Industry), 1967, No. 5, pp. 20–24.
6. Akhmetbayev D.S. et al. Development of Topological Method for Calculating Current Distribution Coefficients in Complex Power Networks. – Results in Physics, 2017, 7(2), pp. 1644–1649, DOI:10.1016/j.rinp.2017.03.010.
7. Mel'nikov N.А. Matrichnyy metod analiza elektricheskikh tsepey (Matrix Method of Analysis of Electric Circuits). M.: Energiya, 1972, 232 p.
8. Ahmetbaev D.S. Elektrichestvo – in Russ. (Electricity), 2010, No. 11, pp. 23–27.
9. Ahmetbaev D.S. Elektrichestvo – in Russ. (Electricity), 2018, No. 5, pp. 18–27.
10. Kirchhoff G. Poggendorfs Annalen, 1845, Bd 64, 512 р.; 1847, 497 p.
11. Maxwell J.C. Electricity and Magnetism, 1892, v.1, 403 p.
12. Geraskin O.T. Izvestiya AN SSSR. Energetika i transport – in Russ. (Izvestia of the USSR Academy of Sciences. Energy and Transport), 1967, No. 5, pp. 106–112.
13. Akhmetbaev D.S., Dzhandigulov A.R. Development of Algorithms for the Formation of Steady–State Modes Based on the Topology of Electric Power Systems. – Journal of Physics: Conference Series, 2019, 1392(1), 012079, DOI:10.1088/1742–6596/1392/1/012079.
14. Akhmetbayev D.S., Dzhandigulov A.R., Bystrova S.V. Topological System Method of Formation of Transformer Transformation Coefficients. – E3S Web of Conferences, 2020, 216(3), DOI:10.1051/e3sconf/202021601087.
15. Kristofides N. Teoriya grafov. Algoritmicheskiy podkhod (Graph Theory. Algorithmic Approach). М.: Mir, 1978, 432 p.
16. Kesavan H.K., Pai M.A., Bhat M.V. Piecewise Solution of the Load–Flow Problem. – IEEE Transactions on Power Apparatus and Systems, 1972, PAS–91 (4), pp. 1382–1386, DOI:10.1109/TPAS.1972.293269.
17. Percival W.S. The Solution of Passive Electrical Networks by Means of Mathematical Trees. – Journal of the Institution of Electrical Engineers, 1953, vol. 100, Part III, 1492R, pр. 143–150, DOI:10.1049/PI–3.1953.0033.
18. Massel' L., Gal'perov V. Vestnik IRGTU – in Russ. (Bulletin of the IrSTU), 2017, vol. 21, No. 1(120), pp. 77–80.
19. Bakry O.M. et al. Improvement of Distribution Networks Performance Using Renewable Energy Sources–Based Hybrid Optimization Techniques. – Ain Shams Engineering Journa, 2022, 13(6):101786, DOI: 10.1016/j.asej.2022.101786.
20. Hemeida M.G. et al. Optimal Probabilistic Location of DGs Using Monte Carlo Simulation Based Different Bio–Inspired Algorithms. – Ain Shams Engineering Journal, 2021, 12(3), DOI: 10.1016/j.asej.2021.02.007.
21. Yang H. et al. Nonlinear Active Distribution Network Optimization for Improving the Renewable Energy Power Quality and Economic Efficiency: a Multi–Objective Bald Eagle Search Algorithm. – Soft Computing, 2023, 27(22), DOI: 10.1007/s00500–023–08913–3.
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2024-02-01
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