Оперативный расчет потокораспределения несбалансированной распределительной сети среднего напряжения
Ключевые слова:
несбалансированная распределительная сеть, интеллектуальные счетчики, распределительные трансформаторы, несимметричная нагрузка
Аннотация
В статье рассмотрен новый метод определения нагрузок и напряжений, позволяющий получать надежную оперативную информацию о состоянии распределительной сети среднего напряжения. Предложено использовать значения мощности и напряжения, измеряемые балансовыми интеллектуальными счетчиками на стороне низкого напряжения распределительных трансформаторов. Подход особенно актуален, когда измерений в распределительной сети недостаточно для обеспечения полной наблюдаемости. Использование балансовых счетчиков экономически выгодно, так как стоимость пунктов учета электроэнергии в низковольтной сети значительно ниже, чем в сети среднего напряжения. Анализ математических моделей распределительных трансформаторов в отечественных распределительных сетях со схемами соединения обмоток «звезда–звезда с нулем» и «треугольник–звезда с нулем» позволил разработать простой алгоритм расчета нагрузок и напряжений на первичной стороне трансформаторов в сети среднего напряжения. В результате проведенного исследования определены факторы, влияющие на перераспределение суммарных нагрузок между фазами, симметрирование фазных нагрузок, независимость суммарных мощностей нагрузок и их потерь от составляющей нулевой последовательности напряжения, расчет потокораспределения в несбалансированной сети, реконфигурацию сети для минимизации потерь мощности. Эффективность предложенного метода подтверждена расчетами с использованием измерений, выполненных в реальных распределительных сетях, а полученные выводы проверены на физической модели.
Литература
1. Lei J. et al. Network Reconfiguration in Unbalanced Distribution Systems for Service Restoration and Loss Reduction. – IEEE Power Engineering Society Winter Meeting, 2000, vol. 4, pp. 2345–2350, DOI: 10.1109/PESW.2000.847175.
2. Hu S. et al. Research on Three-Phase Unbalanced Distribution Network Reconfiguration Strategy. – IOP Conference Series: Earth and Environmental Science, 2017, 52(1), DOI:10.1088/1755-1315/52/ 1/012037.
3. Wang Z., Chen F., Li J. Implementing Transformer Nodal Admittance Matrices into Backward/Forward Sweep-Based Power Flow Analysis for Unbalanced Radial Distribution Systems. – IEEE Transactions on Power Systems, 2004, vol. 19 (4), pp. 1831–1836, DOI:10.1109/TPWRS.2004.835659.
4. Xiao P., Yu D.C., Yan W. A Unified Three-Phase Transformer Model for Distribution Load Flow Calculations. – IEEE Transactions on Power Systems, 2006, 21(1), pp. 153–159, DOI:10.1109/TPWRS.2005.857847.
5. Luo G.X., Semlyen A. Efficient Load Flow for Large Weakly Meshed Networks. – IEEE Transactions on Power Systems, 1990, vol. 5, No. 4, pp. 1309–1316, DOI:10.1109/59.99382.
6. Zimmerman R.D., Chiang H.-D. Fast Decoupled Power Flow for Unbalanced Radial Distribution Systems. – IEEE Transactions on Power Systems, 1995, vol. 10, No. 4, pp. 2045–2052, DOI:10.1109/59.476074.
7. Zhang F., Cheng C.S. A Modified Newton Method for Radial Distribution System Power Flow Analysis. – IEEE Transactions on Power Systems, 1997, vol. 12, No. 1, pp. 389–397, DOI:10.1109/59.575728.
8. Chen T.-H. et al. Three-Phase Cogenerator and Transformer Models for Distribution System Analysis. – IEEE Transactions on Power Delivery, 1991, vol. 6, No. 4, pp. 1671–1681, DOI:10.1109/61.97706.
9. Lu C.N., Teng J.H., Liu W.-H.E. Distribution System State Estimation. – IEEE Transactions on Power Systems, 1995, vol. 10, No. 1, pp. 229–240, DOI:10.1109/59.373946.
10. Kothari D.P., Nagrath I.J. Modern Power System Analysis. Tata McGraw-Hill Publishing Company, 2003, 694 p.
11. Golub I. et al. Reconfiguration of a Primary Three-Phase Three-Wire Distribution Network with Unbalanced Loads. – ENERGY-21. E3S Web of Conferences, 2020, DOI:10.1051/e3sconf/202020902013.
12. Ni F. et al. Three-Phase State Estimation in the Medium-Voltage Network with Aggregated Smart Meter Data. – International Journal of Electrical Power and Energy Systems, 2018, 98, pp. 463–473, DOI:10.1016/j.ijepes.2017.12.033.
13. Golub I., Boloev E. Determination of Losses in Distribution Networks by Smart Meter Measurements. –International Conference on Electrical, Communication, and Computer Engineering (ICECCE), 2021, DOI: 10.1109/ICECCE52056.2021.9514102.
14. Chen T.-H., Chang Y.-L. Integrated Models of Distribution Transformers and Their Loads for Three-Phase Power Flow Analyses. – IEEE Transactions on Power Delivery, 1996, 11(1), pp. 507–513, DOI:10.1109/61.484135.
15. Dugan R.C. A Perspective on Transformer Modeling for Distribution System Analysis. – IEEE Power Engineering Society General Meeting, 2003, vol. 1, pp. 114–119, DOI:10.1109/PES.2003.1267146.
16. Костенко М.П., Пиотровский Л.М. Электрические машины. Ч. 2. Машины переменного тока. Трансформаторы. Л.: Энергия, 1972. 648 с.
17. Петров Г.Н. Электрические машины. Ч. 1. Введение. Трансформаторы. М.: Энергия, 1974, 240 с.
18. Косоухов Ф.Д. и др. Энергосбережение в низковольтных электрических сетях при несимметричной нагрузке. СПб.: Лань, 2016, 280 с.
19. Косоухов Ф.Д. и др. Критерий потерь мощности от несимметричных токов в трехфазных трансформаторах и четырехпроводных линиях. – Электроэнергия. Передача и распределение, 2023, № 6(81), с. 64-72.
20. Arrillaga J., Bradley D.A., Bodger P.S. Power System Harmonics. Chichester etc.: Wiley, 1985, 336 p.
21. Bazrafshan M., Gatsis N. Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix. – IEEE Transactions on Power Systems, 2018, 33(2), pp. 2015–2029, DOI:10.1109/TPWRS.2017.2728618.
22. Gorman M.J., Grainger J.J. Transformer Modelling for Distribution System Studies. II. Addition of models to Y/sub BUS/ and Z/sub BUS. – IEEE Transactions on Power Delivery, 1992, 7(2), pp. 575–580. DOI:10.1109/61.127051.
23. Голуб И.И. и др. Алгоритм реконфигурации городской распределительной сети. – Известия РАН. Энергетика, 2020, №5, с. 3-12.
24. Голуб И.И. и др. Отказоустойчивость распределительной сети среднего напряжения. – Энергетик, 2023, № 5, с. 3–12.
25. Найфельд М.Р. Заземления, защитные меры электробезопасности. М.: Энергия, 1971, 311 с.
26. Padilha-Feltrin A., Ochoa L. Distribution Transformers Modeling with Angular Displacement – Actual Values and per Unit Analysis. – Sba Controle & Automação, 2007, vol. 18, No. 4, pp. 490–500, DOI:10.1590/S0103-17592007000400009.
#
1. Lei J. et al. Network Reconfiguration in Unbalanced Distribution Systems for Service Restoration and Loss Reduction. – IEEE Power Engineering Society Winter Meeting, 2000, vol. 4, pp. 2345–2350, DOI: 10.1109/PESW.2000.847175.
2. Hu S. et al. Research on Three-Phase Unbalanced Distribution Network Reconfiguration Strategy. – IOP Conference Series: Earth and Environmental Science, 2017, 52(1), DOI:10.1088/1755-1315/52/ 1/012037.
3. Wang Z., Chen F., Li J. Implementing Transformer Nodal Admittance Matrices into Backward/Forward Sweep-Based Power Flow Analysis for Unbalanced Radial Distribution Systems. – IEEE Transactions on Power Systems, 2004, vol. 19 (4), pp. 1831–1836, DOI:10.1109/TPWRS.2004.835659.
4. Xiao P., Yu D.C., Yan W. A Unified Three-Phase Transformer Model for Distribution Load Flow Calculations. – IEEE Transactions on Power Systems, 2006, 21(1), pp. 153–159, DOI:10.1109/TPWRS.2005.857847.
5. Luo G.X., Semlyen A. Efficient Load Flow for Large Weakly Meshed Networks. – IEEE Transactions on Power Systems, 1990, vol. 5, No. 4, pp. 1309–1316, DOI:10.1109/59.99382.
6. Zimmerman R.D., Chiang H.-D. Fast Decoupled Power Flow for Unbalanced Radial Distribution Systems. – IEEE Transactions on Power Systems, 1995, vol. 10, No. 4, pp. 2045–2052, DOI:10.1109/59.476074.
7. Zhang F., Cheng C.S. A Modified Newton Method for Radial Distribution System Power Flow Analysis. – IEEE Transactions on Power Systems, 1997, vol. 12, No. 1, pp. 389–397, DOI:10.1109/59.575728.
8. Chen T.-H. et al. Three-Phase Cogenerator and Transformer Models for Distribution System Analysis. – IEEE Transactions on Power Delivery, 1991, vol. 6, No. 4, pp. 1671–1681, DOI:10.1109/61.97706.
9. Lu C.N., Teng J.H., Liu W.-H.E. Distribution System State Estimation. – IEEE Transactions on Power Systems, 1995, vol. 10, No. 1, pp. 229–240, DOI:10.1109/59.373946.
10. Kothari D.P., Nagrath I.J. Modern Power System Analysis. Tata McGraw-Hill Publishing Company, 2003, 694 p.
11. Golub I. et al. Reconfiguration of a Primary Three-Phase Three-Wire Distribution Network with Unbalanced Loads. – ENERGY-21. E3S Web of Conferences, 2020, DOI:10.1051/e3sconf/202020902013.
12. Ni F. et al. Three-Phase State Estimation in the Medium-Voltage Network with Aggregated Smart Meter Data. – International Journal of Electrical Power and Energy Systems, 2018, 98, pp. 463–473, DOI:10.1016/j.ijepes.2017.12.033.
13. Golub I., Boloev E. Determination of Losses in Distribution Networks by Smart Meter Measurements. – International Conference on Electrical, Communication, and Computer Engineering (ICECCE), 2021, DOI: 10.1109/ICECCE52056.2021.9514102.
14. Chen T.-H., Chang Y.-L. Integrated Models of Distribution Transformers and Their Loads for Three-Phase Power Flow Analy-ses. – IEEE Transactions on Power Delivery, 1996, 11(1), pp. 507–513, DOI:10.1109/61.484135.
15. Dugan R.C. A Perspective on Transformer Modeling for Distribution System Analysis. – IEEE Power Engineering Soci-ety General Meeting, 2003, vol. 1, pp. 114–119, DOI:10.1109/PES.2003. 1267146.
16. Kostenko M.P., Piotrovskiy L.M. Elektricheskiye mashiny. Ch. 2. Mashiny peremennogo toka. Transformatory (Electric Machines. Part 2. AC Machines. Transformers). L.: Energiya, 1972, 648 p.
17. Petrov G.N. Elektricheskiye mashiny. Ch. 1. Vvedeniye. Transformatory (Electric Machines. Part 1. Introduction. Transformers). M.: Energiya, 1974, 240 p.
18. Kosoukhov F.D. et al. Energosberezheniye v nizkovoltnyh elektricheskih setyah pri nesimmetrichnoy nagruzke (Energy Saving in Low-Voltage Electrical Networks with Asymmetrical Load). SPb.: Lan’, 2016, 280 p.
19. Kosoukhov F.D. et al. Elektroenergiya. Peredacha i raspre-delenie – in Russ. (Electricity. Transmission and Distribution), 2023, No. 6(81), pp. 64–72.
20. Arrillaga J., Bradley D.A., Bodger P.S. Power System Harmonics. Chichester etc.: Wiley, 1985, 336 p.
21. Bazrafshan M., Gatsis N. Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix. – IEEE Transactions on Power Systems, 2018, 33(2), pp. 2015–2029, DOI:10.1109/TPWRS.2017.2728618.
22. Gorman M.J., Grainger J.J. Transformer modelling for distribution system studies. II. Addition of models to Y/sub BUS/ and Z/sub BUS. – IEEE Transactions on Power Delivery, 1992, 7(2), pp. 575–580. DOI:10.1109/61.127051.
23. Golub I.I. et al. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Energy Industry), 2020, No. 5, pp. 3–12.
24. Golub I.I. et al. Energetik – in Russ. (Power Engineer), 2023, No. 5, pp. 3–12.
25. Nayfeld M.R. Zazemleniya. zashchitnyye mery elektrobezo-pasnosti (Grounding, Protective Measures Electrical Safety). M.: Energiya, 1971, 311 p.
26. Padilha-Feltrin A., Ochoa L. Distribution Transformers Modeling with Angular Displacement – Actual Values and per Unit Analysis. – Sba Controle & Automação, 2007, vol. 18, No. 4, pp. 490–500, DOI:10.1590/S0103-17592007000400009
2. Hu S. et al. Research on Three-Phase Unbalanced Distribution Network Reconfiguration Strategy. – IOP Conference Series: Earth and Environmental Science, 2017, 52(1), DOI:10.1088/1755-1315/52/ 1/012037.
3. Wang Z., Chen F., Li J. Implementing Transformer Nodal Admittance Matrices into Backward/Forward Sweep-Based Power Flow Analysis for Unbalanced Radial Distribution Systems. – IEEE Transactions on Power Systems, 2004, vol. 19 (4), pp. 1831–1836, DOI:10.1109/TPWRS.2004.835659.
4. Xiao P., Yu D.C., Yan W. A Unified Three-Phase Transformer Model for Distribution Load Flow Calculations. – IEEE Transactions on Power Systems, 2006, 21(1), pp. 153–159, DOI:10.1109/TPWRS.2005.857847.
5. Luo G.X., Semlyen A. Efficient Load Flow for Large Weakly Meshed Networks. – IEEE Transactions on Power Systems, 1990, vol. 5, No. 4, pp. 1309–1316, DOI:10.1109/59.99382.
6. Zimmerman R.D., Chiang H.-D. Fast Decoupled Power Flow for Unbalanced Radial Distribution Systems. – IEEE Transactions on Power Systems, 1995, vol. 10, No. 4, pp. 2045–2052, DOI:10.1109/59.476074.
7. Zhang F., Cheng C.S. A Modified Newton Method for Radial Distribution System Power Flow Analysis. – IEEE Transactions on Power Systems, 1997, vol. 12, No. 1, pp. 389–397, DOI:10.1109/59.575728.
8. Chen T.-H. et al. Three-Phase Cogenerator and Transformer Models for Distribution System Analysis. – IEEE Transactions on Power Delivery, 1991, vol. 6, No. 4, pp. 1671–1681, DOI:10.1109/61.97706.
9. Lu C.N., Teng J.H., Liu W.-H.E. Distribution System State Estimation. – IEEE Transactions on Power Systems, 1995, vol. 10, No. 1, pp. 229–240, DOI:10.1109/59.373946.
10. Kothari D.P., Nagrath I.J. Modern Power System Analysis. Tata McGraw-Hill Publishing Company, 2003, 694 p.
11. Golub I. et al. Reconfiguration of a Primary Three-Phase Three-Wire Distribution Network with Unbalanced Loads. – ENERGY-21. E3S Web of Conferences, 2020, DOI:10.1051/e3sconf/202020902013.
12. Ni F. et al. Three-Phase State Estimation in the Medium-Voltage Network with Aggregated Smart Meter Data. – International Journal of Electrical Power and Energy Systems, 2018, 98, pp. 463–473, DOI:10.1016/j.ijepes.2017.12.033.
13. Golub I., Boloev E. Determination of Losses in Distribution Networks by Smart Meter Measurements. –International Conference on Electrical, Communication, and Computer Engineering (ICECCE), 2021, DOI: 10.1109/ICECCE52056.2021.9514102.
14. Chen T.-H., Chang Y.-L. Integrated Models of Distribution Transformers and Their Loads for Three-Phase Power Flow Analyses. – IEEE Transactions on Power Delivery, 1996, 11(1), pp. 507–513, DOI:10.1109/61.484135.
15. Dugan R.C. A Perspective on Transformer Modeling for Distribution System Analysis. – IEEE Power Engineering Society General Meeting, 2003, vol. 1, pp. 114–119, DOI:10.1109/PES.2003.1267146.
16. Костенко М.П., Пиотровский Л.М. Электрические машины. Ч. 2. Машины переменного тока. Трансформаторы. Л.: Энергия, 1972. 648 с.
17. Петров Г.Н. Электрические машины. Ч. 1. Введение. Трансформаторы. М.: Энергия, 1974, 240 с.
18. Косоухов Ф.Д. и др. Энергосбережение в низковольтных электрических сетях при несимметричной нагрузке. СПб.: Лань, 2016, 280 с.
19. Косоухов Ф.Д. и др. Критерий потерь мощности от несимметричных токов в трехфазных трансформаторах и четырехпроводных линиях. – Электроэнергия. Передача и распределение, 2023, № 6(81), с. 64-72.
20. Arrillaga J., Bradley D.A., Bodger P.S. Power System Harmonics. Chichester etc.: Wiley, 1985, 336 p.
21. Bazrafshan M., Gatsis N. Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix. – IEEE Transactions on Power Systems, 2018, 33(2), pp. 2015–2029, DOI:10.1109/TPWRS.2017.2728618.
22. Gorman M.J., Grainger J.J. Transformer Modelling for Distribution System Studies. II. Addition of models to Y/sub BUS/ and Z/sub BUS. – IEEE Transactions on Power Delivery, 1992, 7(2), pp. 575–580. DOI:10.1109/61.127051.
23. Голуб И.И. и др. Алгоритм реконфигурации городской распределительной сети. – Известия РАН. Энергетика, 2020, №5, с. 3-12.
24. Голуб И.И. и др. Отказоустойчивость распределительной сети среднего напряжения. – Энергетик, 2023, № 5, с. 3–12.
25. Найфельд М.Р. Заземления, защитные меры электробезопасности. М.: Энергия, 1971, 311 с.
26. Padilha-Feltrin A., Ochoa L. Distribution Transformers Modeling with Angular Displacement – Actual Values and per Unit Analysis. – Sba Controle & Automação, 2007, vol. 18, No. 4, pp. 490–500, DOI:10.1590/S0103-17592007000400009.
#
1. Lei J. et al. Network Reconfiguration in Unbalanced Distribution Systems for Service Restoration and Loss Reduction. – IEEE Power Engineering Society Winter Meeting, 2000, vol. 4, pp. 2345–2350, DOI: 10.1109/PESW.2000.847175.
2. Hu S. et al. Research on Three-Phase Unbalanced Distribution Network Reconfiguration Strategy. – IOP Conference Series: Earth and Environmental Science, 2017, 52(1), DOI:10.1088/1755-1315/52/ 1/012037.
3. Wang Z., Chen F., Li J. Implementing Transformer Nodal Admittance Matrices into Backward/Forward Sweep-Based Power Flow Analysis for Unbalanced Radial Distribution Systems. – IEEE Transactions on Power Systems, 2004, vol. 19 (4), pp. 1831–1836, DOI:10.1109/TPWRS.2004.835659.
4. Xiao P., Yu D.C., Yan W. A Unified Three-Phase Transformer Model for Distribution Load Flow Calculations. – IEEE Transactions on Power Systems, 2006, 21(1), pp. 153–159, DOI:10.1109/TPWRS.2005.857847.
5. Luo G.X., Semlyen A. Efficient Load Flow for Large Weakly Meshed Networks. – IEEE Transactions on Power Systems, 1990, vol. 5, No. 4, pp. 1309–1316, DOI:10.1109/59.99382.
6. Zimmerman R.D., Chiang H.-D. Fast Decoupled Power Flow for Unbalanced Radial Distribution Systems. – IEEE Transactions on Power Systems, 1995, vol. 10, No. 4, pp. 2045–2052, DOI:10.1109/59.476074.
7. Zhang F., Cheng C.S. A Modified Newton Method for Radial Distribution System Power Flow Analysis. – IEEE Transactions on Power Systems, 1997, vol. 12, No. 1, pp. 389–397, DOI:10.1109/59.575728.
8. Chen T.-H. et al. Three-Phase Cogenerator and Transformer Models for Distribution System Analysis. – IEEE Transactions on Power Delivery, 1991, vol. 6, No. 4, pp. 1671–1681, DOI:10.1109/61.97706.
9. Lu C.N., Teng J.H., Liu W.-H.E. Distribution System State Estimation. – IEEE Transactions on Power Systems, 1995, vol. 10, No. 1, pp. 229–240, DOI:10.1109/59.373946.
10. Kothari D.P., Nagrath I.J. Modern Power System Analysis. Tata McGraw-Hill Publishing Company, 2003, 694 p.
11. Golub I. et al. Reconfiguration of a Primary Three-Phase Three-Wire Distribution Network with Unbalanced Loads. – ENERGY-21. E3S Web of Conferences, 2020, DOI:10.1051/e3sconf/202020902013.
12. Ni F. et al. Three-Phase State Estimation in the Medium-Voltage Network with Aggregated Smart Meter Data. – International Journal of Electrical Power and Energy Systems, 2018, 98, pp. 463–473, DOI:10.1016/j.ijepes.2017.12.033.
13. Golub I., Boloev E. Determination of Losses in Distribution Networks by Smart Meter Measurements. – International Conference on Electrical, Communication, and Computer Engineering (ICECCE), 2021, DOI: 10.1109/ICECCE52056.2021.9514102.
14. Chen T.-H., Chang Y.-L. Integrated Models of Distribution Transformers and Their Loads for Three-Phase Power Flow Analy-ses. – IEEE Transactions on Power Delivery, 1996, 11(1), pp. 507–513, DOI:10.1109/61.484135.
15. Dugan R.C. A Perspective on Transformer Modeling for Distribution System Analysis. – IEEE Power Engineering Soci-ety General Meeting, 2003, vol. 1, pp. 114–119, DOI:10.1109/PES.2003. 1267146.
16. Kostenko M.P., Piotrovskiy L.M. Elektricheskiye mashiny. Ch. 2. Mashiny peremennogo toka. Transformatory (Electric Machines. Part 2. AC Machines. Transformers). L.: Energiya, 1972, 648 p.
17. Petrov G.N. Elektricheskiye mashiny. Ch. 1. Vvedeniye. Transformatory (Electric Machines. Part 1. Introduction. Transformers). M.: Energiya, 1974, 240 p.
18. Kosoukhov F.D. et al. Energosberezheniye v nizkovoltnyh elektricheskih setyah pri nesimmetrichnoy nagruzke (Energy Saving in Low-Voltage Electrical Networks with Asymmetrical Load). SPb.: Lan’, 2016, 280 p.
19. Kosoukhov F.D. et al. Elektroenergiya. Peredacha i raspre-delenie – in Russ. (Electricity. Transmission and Distribution), 2023, No. 6(81), pp. 64–72.
20. Arrillaga J., Bradley D.A., Bodger P.S. Power System Harmonics. Chichester etc.: Wiley, 1985, 336 p.
21. Bazrafshan M., Gatsis N. Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix. – IEEE Transactions on Power Systems, 2018, 33(2), pp. 2015–2029, DOI:10.1109/TPWRS.2017.2728618.
22. Gorman M.J., Grainger J.J. Transformer modelling for distribution system studies. II. Addition of models to Y/sub BUS/ and Z/sub BUS. – IEEE Transactions on Power Delivery, 1992, 7(2), pp. 575–580. DOI:10.1109/61.127051.
23. Golub I.I. et al. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Energy Industry), 2020, No. 5, pp. 3–12.
24. Golub I.I. et al. Energetik – in Russ. (Power Engineer), 2023, No. 5, pp. 3–12.
25. Nayfeld M.R. Zazemleniya. zashchitnyye mery elektrobezo-pasnosti (Grounding, Protective Measures Electrical Safety). M.: Energiya, 1971, 311 p.
26. Padilha-Feltrin A., Ochoa L. Distribution Transformers Modeling with Angular Displacement – Actual Values and per Unit Analysis. – Sba Controle & Automação, 2007, vol. 18, No. 4, pp. 490–500, DOI:10.1590/S0103-17592007000400009
