Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода
The algorithm for determining equivalent circuit parameters and a model of three-phase five-legged transformer are proposed. The model takes account the hysteretic and dynamic properties of the core material and reproduces magnetic fluxes in the nonmagnetic medium. The applicability of the model in...
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| Cite this: | Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода / С.Е. Зирка, Ю.И. Мороз, Е.Ю. Мороз, А.Л. Тарчуткин // Технічна електродинаміка. — 2011. — № 5. — С. 25-35. — Бібліогр.: 12 назв. — pос. |
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nasplib_isofts_kiev_ua-123456789-620062025-02-09T14:10:10Z Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода The modeling of transient processes in three-phase transformer taking into account topology and hysteretic properties of the core Зирка, С.Е. Мороз, Ю.И. Мороз, Е.Ю. Тарчуткин, А.Л. Теоретична електротехніка та електрофізика The algorithm for determining equivalent circuit parameters and a model of three-phase five-legged transformer are proposed. The model takes account the hysteretic and dynamic properties of the core material and reproduces magnetic fluxes in the nonmagnetic medium. The applicability of the model in studying main transformer regimes is shown. 2011 Article Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода / С.Е. Зирка, Ю.И. Мороз, Е.Ю. Мороз, А.Л. Тарчуткин // Технічна електродинаміка. — 2011. — № 5. — С. 25-35. — Бібліогр.: 12 назв. — pос. 0204-3599 https://nasplib.isofts.kiev.ua/handle/123456789/62006 621.318.001.4 ru Технічна електродинаміка application/pdf Інститут електродинаміки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
Russian |
| topic |
Теоретична електротехніка та електрофізика Теоретична електротехніка та електрофізика |
| spellingShingle |
Теоретична електротехніка та електрофізика Теоретична електротехніка та електрофізика Зирка, С.Е. Мороз, Ю.И. Мороз, Е.Ю. Тарчуткин, А.Л. Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода Технічна електродинаміка |
| description |
The algorithm for determining equivalent circuit parameters and a model of three-phase five-legged transformer are proposed. The model takes account the hysteretic and dynamic properties of the core material and reproduces magnetic fluxes in the nonmagnetic medium. The applicability of the model in studying main transformer regimes is shown. |
| format |
Article |
| author |
Зирка, С.Е. Мороз, Ю.И. Мороз, Е.Ю. Тарчуткин, А.Л. |
| author_facet |
Зирка, С.Е. Мороз, Ю.И. Мороз, Е.Ю. Тарчуткин, А.Л. |
| author_sort |
Зирка, С.Е. |
| title |
Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода |
| title_short |
Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода |
| title_full |
Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода |
| title_fullStr |
Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода |
| title_full_unstemmed |
Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода |
| title_sort |
моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода |
| publisher |
Інститут електродинаміки НАН України |
| publishDate |
2011 |
| topic_facet |
Теоретична електротехніка та електрофізика |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/62006 |
| citation_txt |
Моделирование переходных процессов в трехфазном трансформаторе с учетом топологии и гистерезисных свойств магнитопровода / С.Е. Зирка, Ю.И. Мороз, Е.Ю. Мороз, А.Л. Тарчуткин // Технічна електродинаміка. — 2011. — № 5. — С. 25-35. — Бібліогр.: 12 назв. — pос. |
| series |
Технічна електродинаміка |
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2025-11-26T17:25:24Z |
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, , , .
.
1. ., . // .
. 2002. 5. . 7 13.
2. ., ., ., . -
// . . – 2010. – 2. – . 11 20.
3. . . – .: , 1981. – 392 .
4. . // -
. – 2008. – 2. – . 2–18.
5. ., ., ., ., ., ., -
., . //
. – 2009. – 4. – . 26 36.
6. Arturi C.M. Transient simulation of a three phase five limb step-up transformer following an out-of-phase
synchronization // IEEE Transactions on Power Delivery. – 1991. – Vol. 6. – 1. – P. 196 207.
7. Chandrasena W., McLaren P.G., Annakkage U.D., Jayasinghe R.P. An improved low-frequency trans-
former model for use in GIC studies // IEEE Transactions on Power Delivery. – 2004. – Vol.19. – 2. – P. 643 651.
8. Fawzi T.H., Burke P.E. The accurate computation of self and mutual inductances of circular coils // IEEE
Transactions on Power Apparatus and Systems. – 1978. – Vol. PAS-97. – 2. – P. 464 468.
9. Jiles D.C., Atherton D.L. Theory of ferromagnetic hysteresis // Journal of Applied Physics. – 1984. –
Vol. 55. – P. 2115 2120.
10. Martinez J.A., Mork B.A. Transformer modeling for low- and mid-frequency transients – A review // IEEE
Transactions on Power Delivery. – 2005. – Vol. 20. – 2. – . 1625–1632.
11. Theocharis A.D., Milias-Argitis J., Zacharias Th. Three-phase transformer model including magnetic
hysteresis and eddy currents effects // IEEE Transactions on Power Delivery. – 2009. – Vol. 24. – 3. – . 1284–1294.
12. Zirka S.E., Moroz Yu.I., Marketos P., Moses A.J., Jiles D.C., Matsuo T. Generalization of the classical
method for calculating dynamic hysteresis loops in grain-oriented electrical steels // IEEE Transactions on Magnetics. –
2008. – Vol. 44. – 9. – . 2113–2126.
621.318.001.4
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ISSN 1607-7970. .e . 2011. 5 35
The modeling of transient processes in three-phase transformer taking into account topology and hysteretic
properties of the core
S.E.Zirka1, Yu.I.Moroz2, E.Yu.Moroz3, A.L.Tarchutkin4,
1,2,3 Dnipropetrovskyi Natsionalnyi Universytet,
Gagarina pr., 72, Dnipropetrovsk, 40010, Ukrain ,
4 Vidkryte Aktsionerne Tovarystvo “VIT”,
Ukrain , Zaporizhzhia
The algorithm for determining equivalent circuit parameters and a model of three-phase five-legged transformer are
proposed. The model takes account the hysteretic and dynamic properties of the core material and reproduces magnetic
fluxes in the nonmagnetic medium. The applicability of the model in studying main transformer regimes is shown.
References 12, tables 3, figures 8.
Key words: three-phase five-legged transformer, equivalent circuit, hysteretic, core material.
1. Zirka S.E., Moroz Yu.I. Algorithms of the hysteresis modeling in the magnetodynamic problems //
Tekhnichna elektrodynamika. – 2002. 5. P. 7 13. (Rus)
2. Zirka S.E., Moroz Yu.I., Moroz E.Yu., Tarchutkin O.L. The modeling of transformer transients taking into
account hysteresis properties of the core // Tekhnichna elektrodynamika. – 2010. – 2. – P. 11 20. (Rus)
3. Leites L.V. Electromagnetic calculations of transformers and reactors. – Moskva: Energiia, 1981. – 392 p. (Rus)
4. Lurie A.I. Transformer energization under no-load and short-circuit events // Elektrotechnika. – 2008. – 2.
– P. 2–18. (Rus)
5. Pauk Yu.I., Dorogokuplia V.A., Zhelonin V.A., Kravchenko S.V., Lazarev V.I., Ostrenko M.V., Tarchutkin O.L.,
Chornogotskii V.M. The software for design of transformers and reactors // Electro. – 2009. – 4. – P. 26 36. (Rus)
6. Arturi C.M. Transient simulation of a three phase five limb step-up transformer following an out-of-phase
synchronization // IEEE Transactions on Power Delivery. – 1991. – Vol. 6. – 1. – P. 196 207.
7. Chandrasena W., McLaren P.G., Annakkage U.D., Jayasinghe R.P. An improved low-frequency transformer
model for use in GIC studies // IEEE Transactions on Power Delivery. – 2004. – Vol.19. – 2. – P. 643 651.
8. Fawzi T.H., Burke P.E. The accurate computation of self and mutual inductances of circular coils // IEEE
Transactions on Power Apparatus and Systems. – 1978. – Vol. PAS-97. – 2. – P. 464 468.
9. Jiles D.C., Atherton D.L. Theory of ferromagnetic hysteresis // Journal of Applied Physics. – 1984. –
Vol. 55. – P. 2115 2120.
10. Martinez J.A., Mork B.A. Transformer modeling for low- and mid-frequency transients – A review // IEEE
Transactions on Power Delivery. – 2005. – Vol. 20. – 2. – . 1625–1632.
11. Theocharis A.D., Milias-Argitis J., Zacharias Th. Three-phase transformer model including magnetic hys-
teresis and eddy currents effects // IEEE Transactions on Power Delivery. – 2009. – Vol. 24. – 3. – . 1284–1294.
12. Zirka S.E., Moroz Yu.I., Marketos P., Moses A.J., Jiles D.C., Matsuo T. Generalization of the classical
method for calculating dynamic hysteresis loops in grain-oriented electrical steels // IEEE Transactions on Magnetics. –
2008. – Vol. 44. – 9. – . 2113–2126.
25.03.2011
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