Optimizing the Connection Diagram and Turns Number for the Three-Phase to Multiphase Transformer Converter Secondary Winding Coils
DOI:
https://doi.org/10.24160/1993-6982-2023-1-17-24Keywords:
phase number converter, transformer, multiphase winding, connection diagram, optimizationAbstract
An approach to determining the optimal connection diagram and the number of turns for secondary winding coils of a three-phase to multiphase transformer-type converter is considered. Each phase of the device’s multiphase winding comprises three coils placed on different core limbs and connected in series with each other. To determine the connection diagram and the number of turns in the multiphase winding coils, it is necessary to solve an optimization problem with taking into account certain constraints that will make it possible to obtain the same number of turns in the series-connected coils of each secondary winding phase, a symmetrical multiphase EMF system, and uniformly distributed symmetrical multiphase load among the three primary winding phases. The formulated optimization problem with constraints is solved using the numerical interior point method. The application of the proposed approach is illustrated by an example of calculating the minimum number of turns in the coils of a three-phase to seven-phase converter, and the converter windings connection diagram is presented. The article gives the calculated apparent power values of the secondary winding coils with a symmetrical resistive-inductive load for a converter with different numbers of coil turns evaluated from solving the optimization problem with various constraints. A prototype three-phase to seven-phase converter has been fabricated on the basis of a three-phase transformer of a standard series. As a result of experimental studies of the prototype, the seven-phase winding instantaneous voltage waveforms, r.m.s. values of currents and voltages, and the primary winding power for no-load and symmetrical load modes have been obtained. The experimental study results have confirmed the calculation results adequacy. By using the proposed approach, it is possible to design a three-phase to multiphase converter with the number of multiphase secondary winding phases more than two. The designed secondary winding coils will have the minimal number of turns, which will make it possible to manufacture a device with smaller mass and dimension indicators and decrease the consumption of expensive electrical materials.
References
1. Копылов И.П. Электрические машины. М.: Юрайт, 2014.
2. Yusoff N., Karim K., Ghani S., Sutikno T., Jidin A. Multiphase Transformer Modeling Using Finite Element Method // Intern. J. Power Electronics and Drive System. 2015. V. 6. No. 1. Pp. 56—64.
3. Singh A., Marti J., Srivastava K. Circuit Reduction Techniques in Multiphase Modeling of Power Transformers // IEEE Trans. Power Delivery. 2010. V. 25. Iss. 3. Pp. 1573—1579.
4. Karekar S. Modeling and Simulation of Three Phases to Seven Phases Transformer Connection // Intern. J. Research in Appl. Sci. and Eng. Technol. 2016. V. 4. No. 3. Pp. 273—280.
5. Kamarposhti M., Hosseyni A. Modified Approach for Harmonic Reduction in Three-phase to Seven-phase Using Transformer Winding Connections // Intern. J. Electrical and Computer Eng. 2019. V. 9. No. 4. Pp. 1496—1505.
6. Tabrez M., Sadhu P., Iqbal A. A Novel Three Phase to Seven Phase Conversion Technique Using Transformer Winding Connections // Technol. and Appl. Sci. Research. 2017. V. 7. No. 5. Pp. 1953—1961.
7. Jyothi B., Pandian A., Bhavana P. Fabrication and Experimental Analysis of Multiple-winding Transformers for Multiphase Supply // Measurement and Control. 2020. V. 53. Iss. 3. Pp. 1—17.
8. Рогинская Л.Э., Латыпов А.Р., Меднов А.А. Выбор параметров многофункционального трансформатора // Вестник МЭИ. 2019. № 1. С. 61—68.
9. Пат. № 2487455 РФ. Девятифазный преобразователь числа фаз / Григорьев С.Н. и др. // Бюл. изобрет. 2013. № 19.
10. Щуров Н.И., Мятеж С.В. Синтез и анализ многофазных вентильных преобразователей. Новосибирск: Изд-во НГТУ, 2020.
11. Рогинская Л.Э., Горбунов А.С., Ялалова З.И. Улучшение электромагнитной совместимости преобразовательных устройств с сетью и нагрузкой с помощью многофазных трансформаторов // Электротехнические и информационные комплексы и системы. 2014. Т. 10. № 3. С. 21—29.
12. Kant P., Singh B. A New Three-phase to five-phase Transformer with Power Quality Improvement in Hybrid-multilevel Inverter Based VCIMD // IEEE Trans. Power Delivery. 2020. V. 35. No. 2. Pp. 871—880.
13. Закарюкин В.П., Крюков А.В. Моделирование многофазных линий электропередачи. Иркутск: Изд-во ИрГУПС, 2014.
14. Гершенгорн А.И. Многофазные линии электропередачи высокого и сверхвысокого напряжения // Электрические станции. 1994. № 8. С. 67—70.
15. Kettner A., Paolone M. On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems // IEEE Trans. Power Systems. 2019. V. 34. Iss. 1. Pp. 444—453.
16. Levi E., Barrero F., Duran M. Multiphase Machines and Drives – Revisited // IEEE Trans. Industrial Electronics. 2016. V. 63. Iss. 1. Pp. 429—432.
17. Rockhill A., Lipo T. A Generalized Transformation Methodology for Polyphase Electric Machines and Networks // Proc. IEEE Int. Electric Mach. and Drives Conf. 2015. Pp. 27—34.
18. Nanoty A. Chudasama A. Control of Designed Developed Six Phase Induction Motor // Intern. J. Electromagnetics and Appl. 2012. No. 2(5). Pp. 77—84.
19. Логачева А.Г., Вафин Ш.И. О потенциальной возможности асинхронного двигателя с короткозамкнутым ротором // Известия высших учебных заведений. Серия «Проблемы энергетики». 2010. № 3—4. С. 63—67.
20. Терешкин В.М. Теоретическое обоснование возможности снижения вибрации электромагнитного происхождения в пятифазной машине переменного тока по сравнению с трехфазной машиной // Вестник Московского авиационного института. 2018. Т. 25. № 4. С. 229— 239.
21. Терешкин В.М., Гришин Д.А., Баландин С.П., Терешкин В.В. Варианты формирования симметричного семифазного выходного напряжения вентильного преобразователя // Вестник Московского энергетического института. 2022. № 1. С. 85—93.
22. Parsa L. An Advantages of Multi-phase machines // Proc. 31st Annual Conf. IEEE Industrial Electronics Soc. 2005. Pp. 1574—1579.
23. Москалев Ю.В. Определение минимального числа витков катушек вторичной обмотки трансформаторного трехфазно-многофазного преобразователя числа фаз // Омский научный вестник. 2022. № 1(181). С. 61—66.
24. Rao S. Engineering Optimization Theory and Practice. Hoboken: John Wiley & Sons, 2020.
25. Borne P., Popescu D., Filip F., Stefanoiu D. Optimization in Engineering Sciences. London: John Wiley & Sons, 2013.
---
Для цитирования: Москалев Ю.В. Оптимизация схемы соединения и количества витков катушек вторичной обмотки трехфазно-многофазного трансформаторного преобразователя числа фаз // Вестник МЭИ. 2023. № 1. С. 17—24. DOI: 10.24160/1993-6982-2023-1-17-24
#
1. Kopylov I.P. Elektricheskie Mashiny. M.: Yurayt, 2014. (in Russian).
2. Yusoff N., Karim K., Ghani S., Sutikno T., Jidin A. Multiphase Transformer Modeling Using Finite Element Method. Intern. J. Power Electronics and Drive System. 2015;6;1:56—64.
3. Singh A., Marti J., Srivastava K. Circuit Reduction Techniques in Multiphase Modeling of Power Transformers. IEEE Trans. Power Delivery. 2010;25;3:1573—1579.
4. Karekar S. Modeling and Simulation of Three Phases to Seven Phases Transformer Connection. Intern. J. Research in Appl. Sci. and Eng. Technol. 2016;4;3:273—280.
5. Kamarposhti M., Hosseyni A. Modified Approach for Harmonic Reduction in Three-phase to Seven-phase Using Transformer Winding Connections. Intern. J. Electrical and Computer Eng. 2019;9;4:1496—1505.
6. Tabrez M., Sadhu P., Iqbal A. A Novel Three Phase to Seven Phase Conversion Technique Using Transformer Winding Connections. Technol. and Appl. Sci. Research. 2017;7;5:1953—1961.
7. Jyothi B., Pandian A., Bhavana P. Fabrication and Experimental Analysis of Multiple-winding Transformers for Multiphase Supply. Measurement and Control. 2020;53;3:1—17.
8. Roginskaya L.E., Latypov A.R., Mednov A.A. Vybor Parametrov Mnogofunktsional'nogo Transformatora. Vestnik MEI. 2019;1:61—68. (in Russian).
9. Pat. № 2487455 RF. Devyatifaznyy Preobrazovatel' Chisla Faz / Grigor'ev S.N. i dr.. Byul. Izobret. 2013;19. (in Russian).
10. Shchurov N.I., Myatezh S.V. Sintez i Analiz Mnogofaznykh Ventil'nykh Preobrazovateley. Novosibirsk: Izd-vo NGTU, 2020. (in Russian).
11. Roginskaya L.E., Gorbunov A.S., Yalalova Z.I. Uluchshenie Elektromagnitnoy Sovmestimosti Preobrazovatel'nykh Ustroystv s Set'yu i Nagruzkoy s Pomoshch'yu Mnogofaznykh Transformatorov. Elektrotekhnicheskie i Informatsionnye Kompleksy i Sistemy. 2014;10;3:21—29. (in Russian).
12. Kant P., Singh B. A New Three-phase to five-phase Transformer with Power Quality Improvement in Hybrid-multilevel Inverter Based VCIMD. IEEE Trans. Power Delivery. 2020;35;2:871—880.
13. Zakaryukin V.P., Kryukov A.V. Modelirovanie Mnogofaznykh Liniy Elektroperedachi. Irkutsk: Izd-vo IrGUPS, 2014. (in Russian).
14. Gershengorn A.I. Mnogofaznye Linii Elektroperedachi Vysokogo i Sverkhvysokogo Napryazheniya. Elektricheskie Stantsii. 1994;8:67—70. (in Russian).
15. Kettner A., Paolone M. On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems. IEEE Trans. Power Systems. 2019;34;1:444—453.
16. Levi E., Barrero F., Duran M. Multiphase Machines and Drives – Revisited. IEEE Trans. Industrial Electronics. 2016;63;1:429—432.
17. Rockhill A., Lipo T. A Generalized Transformation Methodology for Polyphase Electric Machines and Networks. Proc. IEEE Int. Electric Mach. and Drives Conf. 2015:27—34.
18. Nanoty A. Chudasama A. Control of Designed Developed Six Phase Induction Motor. Intern. J. Electromagnetics and Appl. 2012;2(5):77—84.
19. Logacheva A.G., Vafin Sh.I. O Potentsial'noy Vozmozhnosti Asinkhronnogo Dvigatelya s Korotkozamknutym Rotorom. Izvestiya Vysshikh Uchebnykh Zavedeniy. Seriya «Problemy Energetiki». 2010;3—4:63—67. (in Russian).
20. Tereshkin V.M. Teoreticheskoe Obosnovanie Vozmozhnosti Snizheniya Vibratsii Elektromagnitnogo Proiskhozhdeniya v Pyatifaznoy Mashine Peremennogo Toka po Sravneniyu s Trekhfaznoy Mashinoy. Vestnik Moskovskogo Aviatsionnogo Instituta. 2018;25;4:229— 239. (in Russian).
21. Tereshkin V.M., Grishin D.A., Balandin S.P., Tereshkin V.V. Varianty Formirovaniya Simmetrichnogo Semifaznogo Vykhodnogo Napryazheniya Ventil'nogo Preobrazovatelya. Vestnik Moskovskogo Energeticheskogo Instituta.2022;1:85—93. (in Russian).
22. Parsa L. An Advantages of Multi-phase machines. Proc. 31st Annual Conf. IEEE Industrial Electronics Soc. 2005:1574—1579.
23. Moskalev Yu.V. Opredelenie Minimal'nogo Chisla Vitkov Katushek Vtorichnoy Obmotki Transformatornogo Trekhfazno-mnogofaznogo Preobrazovatelya Chisla Faz. Omskiy Nauchnyy Vestnik. 2022;1(181):61—66. (in Russian).
24. Rao S. Engineering Optimization Theory and Practice. Hoboken: John Wiley & Sons, 2020.
25. Borne P., Popescu D., Filip F., Stefanoiu D. Optimization in Engineering Sciences. London: John Wiley & Sons, 2013.
---
For citation: Moskalev Yu.V. Optimization Scheme Connection and Coils Turns Number of the Secondary Winding of the Three-Phase-Multiphase Transformer Converter. Bulletin of MPEI. 2023;1:17—24. (in Russian). DOI: 10.24160/1993-6982-2023-1-17-24.
2. Yusoff N., Karim K., Ghani S., Sutikno T., Jidin A. Multiphase Transformer Modeling Using Finite Element Method // Intern. J. Power Electronics and Drive System. 2015. V. 6. No. 1. Pp. 56—64.
3. Singh A., Marti J., Srivastava K. Circuit Reduction Techniques in Multiphase Modeling of Power Transformers // IEEE Trans. Power Delivery. 2010. V. 25. Iss. 3. Pp. 1573—1579.
4. Karekar S. Modeling and Simulation of Three Phases to Seven Phases Transformer Connection // Intern. J. Research in Appl. Sci. and Eng. Technol. 2016. V. 4. No. 3. Pp. 273—280.
5. Kamarposhti M., Hosseyni A. Modified Approach for Harmonic Reduction in Three-phase to Seven-phase Using Transformer Winding Connections // Intern. J. Electrical and Computer Eng. 2019. V. 9. No. 4. Pp. 1496—1505.
6. Tabrez M., Sadhu P., Iqbal A. A Novel Three Phase to Seven Phase Conversion Technique Using Transformer Winding Connections // Technol. and Appl. Sci. Research. 2017. V. 7. No. 5. Pp. 1953—1961.
7. Jyothi B., Pandian A., Bhavana P. Fabrication and Experimental Analysis of Multiple-winding Transformers for Multiphase Supply // Measurement and Control. 2020. V. 53. Iss. 3. Pp. 1—17.
8. Рогинская Л.Э., Латыпов А.Р., Меднов А.А. Выбор параметров многофункционального трансформатора // Вестник МЭИ. 2019. № 1. С. 61—68.
9. Пат. № 2487455 РФ. Девятифазный преобразователь числа фаз / Григорьев С.Н. и др. // Бюл. изобрет. 2013. № 19.
10. Щуров Н.И., Мятеж С.В. Синтез и анализ многофазных вентильных преобразователей. Новосибирск: Изд-во НГТУ, 2020.
11. Рогинская Л.Э., Горбунов А.С., Ялалова З.И. Улучшение электромагнитной совместимости преобразовательных устройств с сетью и нагрузкой с помощью многофазных трансформаторов // Электротехнические и информационные комплексы и системы. 2014. Т. 10. № 3. С. 21—29.
12. Kant P., Singh B. A New Three-phase to five-phase Transformer with Power Quality Improvement in Hybrid-multilevel Inverter Based VCIMD // IEEE Trans. Power Delivery. 2020. V. 35. No. 2. Pp. 871—880.
13. Закарюкин В.П., Крюков А.В. Моделирование многофазных линий электропередачи. Иркутск: Изд-во ИрГУПС, 2014.
14. Гершенгорн А.И. Многофазные линии электропередачи высокого и сверхвысокого напряжения // Электрические станции. 1994. № 8. С. 67—70.
15. Kettner A., Paolone M. On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems // IEEE Trans. Power Systems. 2019. V. 34. Iss. 1. Pp. 444—453.
16. Levi E., Barrero F., Duran M. Multiphase Machines and Drives – Revisited // IEEE Trans. Industrial Electronics. 2016. V. 63. Iss. 1. Pp. 429—432.
17. Rockhill A., Lipo T. A Generalized Transformation Methodology for Polyphase Electric Machines and Networks // Proc. IEEE Int. Electric Mach. and Drives Conf. 2015. Pp. 27—34.
18. Nanoty A. Chudasama A. Control of Designed Developed Six Phase Induction Motor // Intern. J. Electromagnetics and Appl. 2012. No. 2(5). Pp. 77—84.
19. Логачева А.Г., Вафин Ш.И. О потенциальной возможности асинхронного двигателя с короткозамкнутым ротором // Известия высших учебных заведений. Серия «Проблемы энергетики». 2010. № 3—4. С. 63—67.
20. Терешкин В.М. Теоретическое обоснование возможности снижения вибрации электромагнитного происхождения в пятифазной машине переменного тока по сравнению с трехфазной машиной // Вестник Московского авиационного института. 2018. Т. 25. № 4. С. 229— 239.
21. Терешкин В.М., Гришин Д.А., Баландин С.П., Терешкин В.В. Варианты формирования симметричного семифазного выходного напряжения вентильного преобразователя // Вестник Московского энергетического института. 2022. № 1. С. 85—93.
22. Parsa L. An Advantages of Multi-phase machines // Proc. 31st Annual Conf. IEEE Industrial Electronics Soc. 2005. Pp. 1574—1579.
23. Москалев Ю.В. Определение минимального числа витков катушек вторичной обмотки трансформаторного трехфазно-многофазного преобразователя числа фаз // Омский научный вестник. 2022. № 1(181). С. 61—66.
24. Rao S. Engineering Optimization Theory and Practice. Hoboken: John Wiley & Sons, 2020.
25. Borne P., Popescu D., Filip F., Stefanoiu D. Optimization in Engineering Sciences. London: John Wiley & Sons, 2013.
---
Для цитирования: Москалев Ю.В. Оптимизация схемы соединения и количества витков катушек вторичной обмотки трехфазно-многофазного трансформаторного преобразователя числа фаз // Вестник МЭИ. 2023. № 1. С. 17—24. DOI: 10.24160/1993-6982-2023-1-17-24
#
1. Kopylov I.P. Elektricheskie Mashiny. M.: Yurayt, 2014. (in Russian).
2. Yusoff N., Karim K., Ghani S., Sutikno T., Jidin A. Multiphase Transformer Modeling Using Finite Element Method. Intern. J. Power Electronics and Drive System. 2015;6;1:56—64.
3. Singh A., Marti J., Srivastava K. Circuit Reduction Techniques in Multiphase Modeling of Power Transformers. IEEE Trans. Power Delivery. 2010;25;3:1573—1579.
4. Karekar S. Modeling and Simulation of Three Phases to Seven Phases Transformer Connection. Intern. J. Research in Appl. Sci. and Eng. Technol. 2016;4;3:273—280.
5. Kamarposhti M., Hosseyni A. Modified Approach for Harmonic Reduction in Three-phase to Seven-phase Using Transformer Winding Connections. Intern. J. Electrical and Computer Eng. 2019;9;4:1496—1505.
6. Tabrez M., Sadhu P., Iqbal A. A Novel Three Phase to Seven Phase Conversion Technique Using Transformer Winding Connections. Technol. and Appl. Sci. Research. 2017;7;5:1953—1961.
7. Jyothi B., Pandian A., Bhavana P. Fabrication and Experimental Analysis of Multiple-winding Transformers for Multiphase Supply. Measurement and Control. 2020;53;3:1—17.
8. Roginskaya L.E., Latypov A.R., Mednov A.A. Vybor Parametrov Mnogofunktsional'nogo Transformatora. Vestnik MEI. 2019;1:61—68. (in Russian).
9. Pat. № 2487455 RF. Devyatifaznyy Preobrazovatel' Chisla Faz / Grigor'ev S.N. i dr.. Byul. Izobret. 2013;19. (in Russian).
10. Shchurov N.I., Myatezh S.V. Sintez i Analiz Mnogofaznykh Ventil'nykh Preobrazovateley. Novosibirsk: Izd-vo NGTU, 2020. (in Russian).
11. Roginskaya L.E., Gorbunov A.S., Yalalova Z.I. Uluchshenie Elektromagnitnoy Sovmestimosti Preobrazovatel'nykh Ustroystv s Set'yu i Nagruzkoy s Pomoshch'yu Mnogofaznykh Transformatorov. Elektrotekhnicheskie i Informatsionnye Kompleksy i Sistemy. 2014;10;3:21—29. (in Russian).
12. Kant P., Singh B. A New Three-phase to five-phase Transformer with Power Quality Improvement in Hybrid-multilevel Inverter Based VCIMD. IEEE Trans. Power Delivery. 2020;35;2:871—880.
13. Zakaryukin V.P., Kryukov A.V. Modelirovanie Mnogofaznykh Liniy Elektroperedachi. Irkutsk: Izd-vo IrGUPS, 2014. (in Russian).
14. Gershengorn A.I. Mnogofaznye Linii Elektroperedachi Vysokogo i Sverkhvysokogo Napryazheniya. Elektricheskie Stantsii. 1994;8:67—70. (in Russian).
15. Kettner A., Paolone M. On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems. IEEE Trans. Power Systems. 2019;34;1:444—453.
16. Levi E., Barrero F., Duran M. Multiphase Machines and Drives – Revisited. IEEE Trans. Industrial Electronics. 2016;63;1:429—432.
17. Rockhill A., Lipo T. A Generalized Transformation Methodology for Polyphase Electric Machines and Networks. Proc. IEEE Int. Electric Mach. and Drives Conf. 2015:27—34.
18. Nanoty A. Chudasama A. Control of Designed Developed Six Phase Induction Motor. Intern. J. Electromagnetics and Appl. 2012;2(5):77—84.
19. Logacheva A.G., Vafin Sh.I. O Potentsial'noy Vozmozhnosti Asinkhronnogo Dvigatelya s Korotkozamknutym Rotorom. Izvestiya Vysshikh Uchebnykh Zavedeniy. Seriya «Problemy Energetiki». 2010;3—4:63—67. (in Russian).
20. Tereshkin V.M. Teoreticheskoe Obosnovanie Vozmozhnosti Snizheniya Vibratsii Elektromagnitnogo Proiskhozhdeniya v Pyatifaznoy Mashine Peremennogo Toka po Sravneniyu s Trekhfaznoy Mashinoy. Vestnik Moskovskogo Aviatsionnogo Instituta. 2018;25;4:229— 239. (in Russian).
21. Tereshkin V.M., Grishin D.A., Balandin S.P., Tereshkin V.V. Varianty Formirovaniya Simmetrichnogo Semifaznogo Vykhodnogo Napryazheniya Ventil'nogo Preobrazovatelya. Vestnik Moskovskogo Energeticheskogo Instituta.2022;1:85—93. (in Russian).
22. Parsa L. An Advantages of Multi-phase machines. Proc. 31st Annual Conf. IEEE Industrial Electronics Soc. 2005:1574—1579.
23. Moskalev Yu.V. Opredelenie Minimal'nogo Chisla Vitkov Katushek Vtorichnoy Obmotki Transformatornogo Trekhfazno-mnogofaznogo Preobrazovatelya Chisla Faz. Omskiy Nauchnyy Vestnik. 2022;1(181):61—66. (in Russian).
24. Rao S. Engineering Optimization Theory and Practice. Hoboken: John Wiley & Sons, 2020.
25. Borne P., Popescu D., Filip F., Stefanoiu D. Optimization in Engineering Sciences. London: John Wiley & Sons, 2013.
---
For citation: Moskalev Yu.V. Optimization Scheme Connection and Coils Turns Number of the Secondary Winding of the Three-Phase-Multiphase Transformer Converter. Bulletin of MPEI. 2023;1:17—24. (in Russian). DOI: 10.24160/1993-6982-2023-1-17-24.
Downloads
Published
2022-10-24
Issue
Section
Electrical Complexes and Systems (2.4.2)
