Once again about the indivisibility of the scattered inductance of the transformer

Authors

  • S.E. Zіrka Dnipro National University, Ukraine
  • Y.I. Moroz Dnipro National University, Ukraine
  • C.M. Arturi Politecnico di Milano, Italy

DOI:

https://doi.org/10.15588/1607-6761-2021-1-1

Keywords:

transformer, equivalent circuits, leakage inductances, inrush currents

Abstract

Purpose. The purpose of the article is to show the inadequacy of the traditional T-shaped equivalent circuit for modeling transformer operations with saturated core. The aim is to point out the unreasonableness of the separation of the transformer leakage inductance into components. The aim is also to explain the need to apply the П-shaped transformer equivalent circuits to transformers with two and three windings with finite radial thickness.

Methodology. Analysis of magnetic fields in the transformer window and simulation of transient processes in equivalent circuits of the transformer using a preprocessor ATPDraw to the program ATP.

Findings. The unfoundedness of the well-known T-shaped transformer equivalent circuit is shown. Differences in the processes in the core legs and yokes when transformer is connected to the network and during short circuits of the windings are noted. Equivalent circuits of a transformer with two and three windings of finite thickness are proposed, reproducing these differences.

Originality. The absence of physical meaning in dividing the transformer leakage inductance into components is stated. The advantages of the П-shaped equivalent circuit are shown when calculating inrush currents accompanying the transformer switching to the network on its inner and outer windings.

Practical value. We show theoretical insolvency and practical unsuitability of the Т-shaped equivalent circuit for studying transformer operations accompanied by saturation of the magnetic circuit. Advantages of the П-shaped equivalent circuit are clarified.

Author Biographies

S.E. Zіrka, Dnipro National University

Professor of the Department of physics and technology of the Dnipro National University, Dnipro

Y.I. Moroz, Dnipro National University

Ph.D., Associate professor of the Department of physics and technology of the Dnipro National University, Dnipro

C.M. Arturi, Politecnico di Milano

Professor of the Department of electronics, information and bioengineering of the Politecnico di Milano, Milan

References

Boyajian, A. (1925). Resolution of transformer reac-tances into primary and secondary reactances, AIEE Transactions, 805–810. DOI: 10.1109/JAIEE.1925.6535234.

Correggiari, F. (1954) On the splitting of short-circuit reactance of transformers, L’Elettrotecnica, XLI, 1, P. 2–13 (in Italian).

Leites, L.V., Pintsov, A.M. (1974). Skhemy za-meshcheniia mnogoobmotochnykh transformatorov. M. Energiia (in Russian).

Zikherman, M.Kh. (1972). Kharakteristiki namag-nichivaniya moshchnykh transformatorov [Magneti-zation characteristics of large transformers], El-ektrichestvo, 3, 79-82 (in Russian).

Zikherman, M.Kh. (2014). O rasseyanii v transforma-torakh [On the transformer leakage]. Energoekspert, 6, 30-33 (in Russian).

Markvardt, E.G. (1936). Induktivnosti rasseyaniya obmotok transformatora [Leakage inductances of transformer windings]. Elektrichestvo, 23, 26-31 (in Russian).

Petrov, G.N. (1936). Ob induktivnostyakh rasseyaniya obmotok transformatora [On the leakage inductances of transformer windings]. Elektrichestvo, 23, 31-32 (in Russian).

Bessonov, L.A. (1996). Teoreticheskie osnovy el-ektrotekhniki. Elektricheskie tsepi, M. Vysshaya shko-la, 638 (in Russian).

Kalantarov, P.L., Tseitlin, L.A. (1986). Raschet in-duktivnostei. Spravochnaya kniga. Leningrad, Ener-goatomizdat, 488 (in Russian).

Fawzi, T.H., Burke, P.E. (1978). The accurate com-putation of self and mutual inductances of circular coils, IEEE Transactions on Power Apparatus and Systems, 97, 2, 464–468. DOI: 10.1109/TPAS.1978.354506.

Bunin, A.G., Kontorovich, L.N. (1975). Raschet impulsnykh perenapryazhenii v obmotkakh transformatorov s uchetom vliyaniya magnitoprovoda [Calculation of impulse overvoltages in transformer windings taking into account the influence of the mag-netic circuit]. Elektrichestvo, 7, 50-54 (in Russian).

Martinez-Velasco J.A., Mork, B.A. (2003). Trans-former modeling for low frequency transients – The state of the art. International Conf. Power Systems Transients – IPST 2003 in New Orleans, USA.

Lur'e, A.I. (2008). Protsess vklyucheniya transforma-tora na kholostoi khod i korotkoe zamykanie [Pro-cesses at turning on the transformer at idle and short circuit]. Elektrotekhnika, 2, 2-18 (in Russian).

Kulkarni, S.V., Khaparde, S.A. (2004). Transformer engineering: Design and practice. New York: Marcel Dekker.

Chiesa, N, Mork, B.A., Høidalen, H.K. (2010). Trans-former model for inrush current calculations: Simula-tions, measurements and sensitivity analysis. IEEE Transactions on Power Delivery, 25, 4, 2599–608. DOI: doi.org/10.1109/TPWRD.2010.2045518.

De Leon, F., Farazmand, A. and Joseph P. (2012). Comparing the T and π equivalent circuits for the cal-culation of transformer inrush currents. IEEE Trans-actions on Power Delivery, 27, 4, 2390-2398. DOI: 10.1109/TPWRD.2012.2208229.

Zirka S.E., Moroz Yu.I., Moroz E.Yu., Tarchutkin A.L. (2012). Topologicheskie modeli transformatora Топологические модели трансформатора. [Topo-logical transformer models] Elektrichestvo, 10, 33-42 (in Russian)

Zirka, S.E., Moroz, Y. I., Arturi, C. M., Chiesa, N. and Høidalen, H.K. (2012). Topology-correct reversible transformer model. IEEE Transactions on Power De-livery, 27, 4, 2037-2045. DOI: 10.1109/TPWRD.2012.2205275.

Cherry, E.C. (1949). The duality between interlinked electric and magnetic circuits and the formation of transformer equivalent circuits. Proceedings of the Physical Society, B, 62, 101–111.

https://www.emtp.org.

Zirka S.E., Moroz Yu.I., Moroz E.Yu. (2010). Inver-snaya model magnitnogo gisterezisa [Inverse model of magnetic hysteresis]. Tehnicheskaya elektro-dinamika, 4, 3-7 (in Russian).

Zirka, S.E., Moroz, Y.I., Harrison, R. G., Chiesa, N. (2014). Inverse hysteresis models for transient simula-tion. IEEE Transactions on Power Delivery, 29, 2, 552-559. DOI: 10.1109/TPWRD.2013.2274530.

Zirka, S.E., Moroz, Y.I., Chiesa, N, Harrison, R.G., Høidalen, H.Kr. (2015). Implementation of inverse hysteresis model into EMTP —Part I: Static model. IEEE Transactions on Power Delivery, 30, 5, 2224-2232. DOI: 10.1109/TPWRD.2015.2416201.

Zirka, S.E., Moroz Y.I., Chiesa N., Harrison R.G., Høidalen H.Kr. (2015). Implementation of inverse hysteresis model into EMTP – Part II: Dynamic mod-el. IEEE Transactions on Power Delivery, 30, 5, 2233–2241. DOI: doi.org/10.1109/TPWRD.2015.2416199.

Jazebi, S., Zirka, S.E., Lambert, M., Rezaei-Zare, A. Chiesa, N., Moroz, Y., Chen, X., Martinez-Duro, M., Arturi, C.M., Dick, E.P., Narang, A., Walling, R.A., Mahseredjian, J., Martinez, J.A., de León, F. (2016). Duality derived transformer models for low-frequency electromagnetic transients—Part I: Topological mod-els, IEEE Transactions on Power Delivery, 31, 5, 2410-2419. DOI: 10.1109/TPWRD.2016.2517327.

Shakirov, M.A. (2016). 2nТ-shaped equivalent cir-cuit of a transformer comprising n windings. St. Pe-tersburg Polytechnic University Journal of Engineering Sciences and Technology. 3(249), 49-63. DOI: 10.5862/JEST.246.6.

Arturi, C.M. (1994). Model of a highly saturated three- phase autotransformer with tertiary winding and five-limb core and analysis of a time-varying short-circuit transient, European Transactions on Elec-trical Power, 4, 6, 513-524. DOI: https://doi.org/10.1002/etep.4450040620.

Edelmann, H. (1959). Descriptive determination of transformer equivalent circuits. Arch. elektr. Ubema-gung 13, 253–261 (in German).

Zhao, J., Zirka, S.E., Moroz, Y.I., Arturi, C.M. (2020). Structure and properties of the hybrid and topological transformer models, International Journal of Electrical Power & Energy Sys-tems, 118, 105785. DOI: doi.org/10.1016/j.ijepes.2019.105785.

Boyajian, A. (1924). Theory of three-circuit trans-formers. Journal AIEE; 43, 4, 345–355. DOI: https://doi.org/10.1109/JAIEE.1924.6535983.

Zirka S.E., Moroz Yu.I., Moroz E.Yu., Tarchutkin A.L. (2010). Modelirovanie perekhodnykh protsessov v transformatore s uchetom gisterezisnykh svoistv magnitoprovoda [Modeling of transformer transients taking into account hysteresis properties of the core. Tehnicheskaya elektrodinamika. 2, 11-20 (in Rus-sian).

Zirka, S.E., Moroz, Y.I., Arturi, C.M., Elovaara, J., Lahtinen, M. (2018). Topological reversible model of three-phase five-limb transformer. Electrical Engineer-ing and Power Engineering. 3, 6–13. DOI: 10.15588/1607-6761-2018-3-1.

Karsai, K, Kerényi, D, Kiss, L. (1987). Large power transformers. New York: Elsevier, 614.

Published

2021-03-31

How to Cite

Zіrka S., Moroz, Y., & Arturi, C. (2021). Once again about the indivisibility of the scattered inductance of the transformer. Electrical Engineering and Power Engineering, (1), 8–17. https://doi.org/10.15588/1607-6761-2021-1-1