Poynting’s Vector and the New Theory of a Transformer. Part 7: Disk Windings
Keywords:
transformer, disk winding, magnetic flux, vector diagram, equivalent circuit, short-circuit fault, magnetic field strength, electric field intensity, Poynting’s vector, vector potential
Abstract
A new theory of a two-winding transformer with disk windings is proposed. The principle of its operation is outlined based on analyzing the specifics of Poynting’s vector distribution pattern between the disk windings. The transformers equivalence notion is introduced, the use of which made it possible to avoid cumbersome mathematical manipulations in deriving the equivalent circuit with indication of all key magnetic fluxes in the disk transformer iron and in the core aperture. The families of vector potential distribution and flux function curves obtained proceeding from this notion have made it possible to show that there exists an invariant surface within the primary disk winding boundaries, i.e., a surface on which the values of the above-mentioned quantities no not depend on the load. It is shown, with taking these curves into consideration, that unlike a cylindrical transformer, the overflux that takes place in a disk transformer (with respect to the no-load flux) in the case of a short-circuit fault occurs not in the leg but in the butt yoke closest to the primary winding. As regards the antiflux (directed oppositely to the no-load flux) that takes place in this mode, it flows in the butt yoke closest to the short-circuited secondary winding. The obtained results should be regarded as an important stage of constructing a correct theory of transformers with alternating disk windings.
References
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Cherry E.C. The duality between interlinkend electric and magnetic circuits and the formulation of transformer equivalent circuits. — Proc. of the Physical Society, vol. (B) 62, pp. 101—111, Feb. 1949.
Blume L.F., Boyajian A., Gamilly G., Lenox T.C. Minnec S. Montsinger M.V. Transformer Engineering: A treatise on the Theory, Operation and Application of Transformer. New York: Wiley, 1951.
Вольдек А.И. Схемы замещения индуктивно связанных цепей и их параметры. Таллин: Эстонское государственное издательство, 1952, 36 с.
Slemon G.R. Equivalent Circuits for Transformers and machines including nonlinear effects. — Proc. Inst. Elect. Eng., IV, 1953, vol. 100, pp. 129-143.
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Leon F., Gomez P., Martinez-Velasco, Rioual M. Transformers in Power System ransients: Parameter Determination. Ed. Boca Raton, FL: CRC, 2009, ch. 4, pp.177-250.
Leon F., Farazmand A., Joseph. Comparing the T and Equivalent Circuits for the Calculation of Transformer Inrush Currents. - IEEE Trans. Power Delivery, vol.27, No. 4, pp. 2390-2397, October 2012.
Электродинамическая стойкость трансформаторов и реакторов при коротких замыканиях/Под ред. А.И. Лурье. М.: Знак, 2005, 520 с.
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Туровский Я. Техническая электродинамика. М.: Энергия, 1974, 488 с.
Практикум по ТОЭ. Часть 3/Под ред. М.А. Шакирова. СПб.: Изд-во Политехнического университета, 2017, 300 с.
Шакиров М.А., Варламов Ю.В. Картины магнитных свер- и антипотоков в короткозамкнутом двухобмоточном трансформаторе. Ч. 1. Броневой трансформатор. — Электричество, 2015, № 8, с. 9—19.
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Vasyutinskij S.V. Voprosy teorii i rascheta transformatorov (Questions of theory and calculation of transformaters). Moscow, Energiya (Leningrad branch), 1970, 432 p.
Sergeyenkov B.N., Kiselev V.M., Akimova N.A. Elektricheskiye mashiny. Transformatory/Pod red. I.P. Kopylova (Electrical machines. Transformaters/Edit. by I.P. Kopylov). Moscow, Vysshaya shkola, 1989, 352 p.
Rys’kova Z.A., Fedorov P.D., Zhimerova V.I. Transformatory dlya elektricheskoi kontaktnoi svarki (Transformaters for electrical contact welding). Leningrad, Energoatomizdat, 1990, 424 p.
Boyajian A. Resolution of transformer reactances into primary and secondary reactances. — AIEE Trans., pp. 805—810, Jun 1925.
Markvardt Ye.G. Elektromagnitnye raschety transformatorov (Electromagnetic calculations of transformaters). Moscow, ONTI, Editing of the energy literature, 1938.
Cherry E.C. The duality between interlinkend electric and magnetic circuits and the formulation of transformer equivalent circuits. — Proc. of the Physical Society, vol. (B) 62, pp. 101 — 111, Feb. 1949.
Blume L.F., Boyajian A., Gamilly G., Lenox T.C. Minnec S. Montsinger M.V. Transformer Engineering: A treatise on the Theory, Operation and Application of Transformer. New York: Wiley, 1951.
Vol'dek A.I. Skhemy zameshcheniya induktivno svyazannykh tsepei i ikh parametry (Equivalent circuits of inductively coupled circuits and their parameters). Tallin, Estonskoe gos. izdatel’stvo, 1952, 36 p.
Slemon G.R. Equivalent Circuits for Transformers and machines including nonlinear effects. — Proc. Inst. Elect. Eng., IV, 1953, vol. 100, pp. 129-143.
Penchev P.R. V’’erkhu razseivaneto v transformatore. Sofiya, Tekhnika, 1969.
Leites L.V. Trudy VEI — in Russ. (Proseedings of All-Russian Electrotechnical Institute). Moscow, Energiya, 1969, pp. 277-297.
Leon F., Gomez P., Martinez-Velasco, Rioual M. Transformers in Power System ransients: Parameter Determination. Ed. Boca Raton, FL: CRC, 2009, ch. 4, pp.177-250.
Leon F., Farazmand A., Joseph. Comparing the T and Equivalent Circuits for the Calculation of Transformer Inrush Currents. — IEEE Trans. Power Delivery, vol. 27, No. 4, pp. 2390-2397, October 2012.
Elektrodinamicheskaya stoikost’ transformatorov i reartorov pri korotkikh zamykaniyakh (Electrodynamic withstand of transformers and reactors during short-circuit faults)/Edit. by A.I. Lur’ye. Moscow, Publ. «Znak», 2005, 520 p.
Shakirov M.A. Elektrichestvo — in Russ. (Electricity), 2014, No. 9, pp. 52-59.
Shakirov M.A. Elektrichestvo — in Russ. (Electricity), 2014, No. 10, pp. 53—65.
Shakirov M.A. Elektrichestvo — in Russ. (Electricity), 2017, No. 3, pp. 37—49.
Malygin V.M. Elektrichestvo — in Russ. (Electricity), 2015, No. 4, pp. 60—65.
Bron O.B. Elektromagnitnoe pole kak vid materii (Electromagnetic field asa king of a matter). Moscow, Gos. Energet. Izdatel’stvo, 1962, 260 p.
Edwards J. and Saha T.K. Power flow in transformers via the Poynting vector. Proceedings of the Australasian Universities Power Engineering Conference: AUPEC 2000, pp. 86—91, 24—27 September 2000, Brisbane, Australia: Queensland University of Technology.
Todeschini G., Emanuel A.E. Poynting vector approuch to the study of power flow through a transformer. — Power Quality and Utilization, Journal, 2007, vol. XIII, No.1, pp. 129—137.
Turovskii Ya. Tekhnicheskaya elektrodinamika (Technical electrodynamics). Moscow, Energiya, 1974, 488 p.
Praktikum po teoreticheskim osnovam elektrotekhniki (Practical course on theoretical principles of electrical engineering). Part 3/Edit by M.A. Shakirov. St. Petersburg, Publ. of Politechnical University, 2017, 300 p.
Shakirov M.A., Varlamov Yu.V. Elektrichestvo — in Russ. (Electricity), 2015, No. 8, pp. 9—19.
Сергеенков Б.Н., Киселев В.М., Акимова Н.А. Электрические машины. Трансформаторы/Под ред. И.П. Копылова. М.: Высшая школа, 1989, 352 с.
Рыськова З.А., Федоров П.Д., Жимерова В.И. Трансформаторы для электрической контактной сварки. Л.: Энергоаом- издат, 1990, 424 с.
Boyajian A. Resolution of transformer reactances into primary and secondary reactances. — AIEE Trans., pp. 805—810, Jun 1925.
Марквардт Е.Г. Электромагнитные расчеты трансформаторов. М.: ОНТИ, Редакция энергетической литературы, 1938.
Cherry E.C. The duality between interlinkend electric and magnetic circuits and the formulation of transformer equivalent circuits. — Proc. of the Physical Society, vol. (B) 62, pp. 101—111, Feb. 1949.
Blume L.F., Boyajian A., Gamilly G., Lenox T.C. Minnec S. Montsinger M.V. Transformer Engineering: A treatise on the Theory, Operation and Application of Transformer. New York: Wiley, 1951.
Вольдек А.И. Схемы замещения индуктивно связанных цепей и их параметры. Таллин: Эстонское государственное издательство, 1952, 36 с.
Slemon G.R. Equivalent Circuits for Transformers and machines including nonlinear effects. — Proc. Inst. Elect. Eng., IV, 1953, vol. 100, pp. 129-143.
Пенчев П.Р. Въерху разсейването в трансформаторите. София: Техника, 1969.
Лейтес Л.В. Эквивалентная схема двухобмоточного трансформатора, опыты х.х. и к.з. М.: Труды ВЭИ, 1969, с. 277-297.
Leon F., Gomez P., Martinez-Velasco, Rioual M. Transformers in Power System ransients: Parameter Determination. Ed. Boca Raton, FL: CRC, 2009, ch. 4, pp.177-250.
Leon F., Farazmand A., Joseph. Comparing the T and Equivalent Circuits for the Calculation of Transformer Inrush Currents. - IEEE Trans. Power Delivery, vol.27, No. 4, pp. 2390-2397, October 2012.
Электродинамическая стойкость трансформаторов и реакторов при коротких замыканиях/Под ред. А.И. Лурье. М.: Знак, 2005, 520 с.
Шакиров М.А. Вектор Пойнтинга и новая теория трансформаторов. Ч. 1. — Электричество, 2014, № 9, с. 52-59.
Шакиров М.А. Вектор Пойнтинга и новая теория трансформаторов. Ч. 2. — Электричество, 2014, № 10, с. 53—65.
Шакиров М.А. Вектор Пойнтинга и новая теория трансформаторов. Ч. 4. «Анатомия» трансформатора. — Электричество, 2017, № 3, с. 37—49.
Малыгин В.М. Локализация потока энергии в трансформаторе (по поводу статьи М.А. Шакирова, Электричество, 2014, № 9 и 10). — Электричество, 2015, № 4, с. 60—65.
Брон О.Б. Электромагнитное поле как вид материи. М.: ГЭИ, 1962, 260 с.
Edwards J. and Saha T.K. Power flow in transformers via the Poynting vector. Proceedings of the Australasian Universities Power Engineering Conference: AUPEC 2000, pp. 86—91, 24—27 September 2000, Brisbane, Australia: Queensland University of Technology.
Todeschini G., Emanuel A.E. Poynting vector approuch to the study of power flow through a transformer. — Power Quality and Utilization, Journal, 2007, vol. XIII, No.1, pp. 129—137.
Туровский Я. Техническая электродинамика. М.: Энергия, 1974, 488 с.
Практикум по ТОЭ. Часть 3/Под ред. М.А. Шакирова. СПб.: Изд-во Политехнического университета, 2017, 300 с.
Шакиров М.А., Варламов Ю.В. Картины магнитных свер- и антипотоков в короткозамкнутом двухобмоточном трансформаторе. Ч. 1. Броневой трансформатор. — Электричество, 2015, № 8, с. 9—19.
#
Vasyutinskij S.V. Voprosy teorii i rascheta transformatorov (Questions of theory and calculation of transformaters). Moscow, Energiya (Leningrad branch), 1970, 432 p.
Sergeyenkov B.N., Kiselev V.M., Akimova N.A. Elektricheskiye mashiny. Transformatory/Pod red. I.P. Kopylova (Electrical machines. Transformaters/Edit. by I.P. Kopylov). Moscow, Vysshaya shkola, 1989, 352 p.
Rys’kova Z.A., Fedorov P.D., Zhimerova V.I. Transformatory dlya elektricheskoi kontaktnoi svarki (Transformaters for electrical contact welding). Leningrad, Energoatomizdat, 1990, 424 p.
Boyajian A. Resolution of transformer reactances into primary and secondary reactances. — AIEE Trans., pp. 805—810, Jun 1925.
Markvardt Ye.G. Elektromagnitnye raschety transformatorov (Electromagnetic calculations of transformaters). Moscow, ONTI, Editing of the energy literature, 1938.
Cherry E.C. The duality between interlinkend electric and magnetic circuits and the formulation of transformer equivalent circuits. — Proc. of the Physical Society, vol. (B) 62, pp. 101 — 111, Feb. 1949.
Blume L.F., Boyajian A., Gamilly G., Lenox T.C. Minnec S. Montsinger M.V. Transformer Engineering: A treatise on the Theory, Operation and Application of Transformer. New York: Wiley, 1951.
Vol'dek A.I. Skhemy zameshcheniya induktivno svyazannykh tsepei i ikh parametry (Equivalent circuits of inductively coupled circuits and their parameters). Tallin, Estonskoe gos. izdatel’stvo, 1952, 36 p.
Slemon G.R. Equivalent Circuits for Transformers and machines including nonlinear effects. — Proc. Inst. Elect. Eng., IV, 1953, vol. 100, pp. 129-143.
Penchev P.R. V’’erkhu razseivaneto v transformatore. Sofiya, Tekhnika, 1969.
Leites L.V. Trudy VEI — in Russ. (Proseedings of All-Russian Electrotechnical Institute). Moscow, Energiya, 1969, pp. 277-297.
Leon F., Gomez P., Martinez-Velasco, Rioual M. Transformers in Power System ransients: Parameter Determination. Ed. Boca Raton, FL: CRC, 2009, ch. 4, pp.177-250.
Leon F., Farazmand A., Joseph. Comparing the T and Equivalent Circuits for the Calculation of Transformer Inrush Currents. — IEEE Trans. Power Delivery, vol. 27, No. 4, pp. 2390-2397, October 2012.
Elektrodinamicheskaya stoikost’ transformatorov i reartorov pri korotkikh zamykaniyakh (Electrodynamic withstand of transformers and reactors during short-circuit faults)/Edit. by A.I. Lur’ye. Moscow, Publ. «Znak», 2005, 520 p.
Shakirov M.A. Elektrichestvo — in Russ. (Electricity), 2014, No. 9, pp. 52-59.
Shakirov M.A. Elektrichestvo — in Russ. (Electricity), 2014, No. 10, pp. 53—65.
Shakirov M.A. Elektrichestvo — in Russ. (Electricity), 2017, No. 3, pp. 37—49.
Malygin V.M. Elektrichestvo — in Russ. (Electricity), 2015, No. 4, pp. 60—65.
Bron O.B. Elektromagnitnoe pole kak vid materii (Electromagnetic field asa king of a matter). Moscow, Gos. Energet. Izdatel’stvo, 1962, 260 p.
Edwards J. and Saha T.K. Power flow in transformers via the Poynting vector. Proceedings of the Australasian Universities Power Engineering Conference: AUPEC 2000, pp. 86—91, 24—27 September 2000, Brisbane, Australia: Queensland University of Technology.
Todeschini G., Emanuel A.E. Poynting vector approuch to the study of power flow through a transformer. — Power Quality and Utilization, Journal, 2007, vol. XIII, No.1, pp. 129—137.
Turovskii Ya. Tekhnicheskaya elektrodinamika (Technical electrodynamics). Moscow, Energiya, 1974, 488 p.
Praktikum po teoreticheskim osnovam elektrotekhniki (Practical course on theoretical principles of electrical engineering). Part 3/Edit by M.A. Shakirov. St. Petersburg, Publ. of Politechnical University, 2017, 300 p.
Shakirov M.A., Varlamov Yu.V. Elektrichestvo — in Russ. (Electricity), 2015, No. 8, pp. 9—19.
