Online Load Flow Analysis of an Unbalanced Medium Voltage Distribution Network
Keywords:
elunbalanced distribution network, smart meters, distribution transformers, unbalanced loads
Abstract
The article discusses a new method for determining loads and voltages, using which it is possible to obtain reliable operational information about the state of a medium voltage distribution network. It is proposed to use the power and voltage values measured by balanced smart meters on the low voltage side of distribution transformers. This approach is especially relevant when the measurements available in the distribution network are not sufficient to ensure full observability. The use of balance meters is economically advantageous, since the cost of electricity metering points in a low voltage network is significantly lower than it is in a medium voltage network. An analysis of the mathematical models of power transformers used in Russian distribution networks with the “wye-wye with neutral” and “delta-wye with neutral” winding connection diagrams made it possible to develop a simple algorithm for calculating the loads and voltages on the primary side of transformers in a medium voltage network. As a result of the study, the factors influencing the redistribution of total loads between phases, the symmetry of phase loads, the independence of total load capacities and their losses from the zero-sequence voltage component, the load flow calculation in an unbalanced network, and network reconfiguration to minimize power losses have been determined. The effectiveness of the proposed method is confirmed by calculations using measurements performed in real distribution networks, and the conclusions derived have been verified on a physical model.
References
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
Published
2025-04-24
Issue
Section
Article
