V.V Zinovkin, O.V. Blyzniakov


Purpose. To derive the relationships for calculating determination of equivalent quantities for electromagnetic field in massive ferrous bodies at strongly varying loads.

Methodology. We have applied methodological fundamentals of skin-effect theory for massive ferrous bodies combined with methods of mathematical physics as well as physical and computer simulation.

Findings. We have found the mathematical expressions for the equivalence ratios allowing calculate basic electromagnetic field quantities, such as magnetic flux and losses, in massive ferrous bodies under strongly varying loads. Their adequacy is confirmed by research on physical and computer models, as well as existing computational procedures of the additional losses in the massive units of energy-intensive electrical equipment for special purposes.

Originality. For the first time, we have established mathematical dependencies between skin losses and magnetic flux in massive ferrous body and total and individual harmonic distortion of periodically varying magnetic and electric fields. Found dependences are the basis for the development of refined computational procedures for determining the parameters of the electromagnetic field in massive ferromagnetic elements of electrical equipment under strongly-varying loads.

Practical value. The use of derived expressions for the equivalence ratios enable successfully solve the problems aimed to optimize constructive components when designing electrical equipment for supplying consumers with strongly-varying behavior of the load.


electromagnetic field; strongly-varying load; massive ferrous body; skin-effect; skin magnetic flux; skin losses; equivalence ratio; composition of high harmonics.

Full Text:



[1] Nejman, L.R. (1949). Skin-effect in ferromagnetic bodies. Moskow–Leningrad: Gosenergoizdat, 190 (Rus).

[2] Andreeva, T.A., Berezovskij, A.A., Zinovkin, V.V., Kravchenko A.N., Sisunenko O.I. (1975). Skin losses in massive ferrous bodies under simultaneous magnetization by direct and alternating magnetic fields. Boundary problems of electrodynamics for non-conductive mediums. Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev, 5–36. (Rus.).

[3] Zinovkin, V.V., Zozulia, D.V., Kravchenko, A.N., Feshchenko P.P. (1993). Research of transformer losses under strongly varying loads. Technical Electrodynamics, 6, 11–16. (Rus.).

[4] Gzarmeski, L. (1996). Comments on Active Power Flow and Energy Accounts in Electrical Systems With Non-sinusoidal Waveforms and Asymmetry. IEEE Transactions on Power Delivery, 11, 3, 1244-1250.

[5] Zinovkin, V.V., Rassalskij, A.N. (1998). Special features of electrical-and-technological operating duties of metallurgic complexes. New Materials and Technologies in Metallurgy and Machine Building, 2, 151–154. (Rus.).

[6] Zinovkin, V.V. (1999). Research of the losses in ferrous power transformer tank on the physical models under sine and non-sine currents. New materials and technologies in metallurgy and machine building, 2, 78–83 (Rus.).

[7] Zinovkin, V.V. (1999). Research of skin-effect in massive ferrous body under strongly-varying electromagnetic field. Electronics and Electricity, 1, 14–21. (Rus.).

[8] Zinovkin, V.V., Rassalskij, A.N. (1999). Normalization of equivalent magnetic permeability for ferromagnetic materials applying in electric machine engineering. Electronics and Electricity, 2, 11–16. (Rus.).

[9] Zinovkin, V.V. (2000). Research of superficial losses in massive structural steels to be magnetized by strongly varying and dc magnetic fields, Works of the Institute of Electrodynamics of the National Academy of Sciences of Ukraine. Power Engineering 2000, 17–30. (Rus.).

[10] Zinovkin, V.V., Zaluzhnyj, M.Y. (2002). Research of non-stationary electromagnetic processes in power-intensive electrical equipment using physical models. Electronics and Electricity, 1, 77–83. (Rus.).

[11] Zinovkin, V.V., Zaluzhnyj, M.Y. (2003). Simulation of non-stationary electromagnetic processes and their special features with use of ТООL BOX POWER SYSTEM of software MATLAB. Trudy Mehzdun. nauch.-techn. konf. "Problemy povyshenia effektivnosti elektromekhanicheskih preobrazovatelej v elekroenergeticheskih sistemah" [Proceedings of Int. Sci.-Technical Conf. “Problems of enhancement of electromechanical converters efficiency in power systems”], Sevastopol, SNTU, 75–80. (Rus.).

[12] V.V. Zinovkin, V.V. Kusch, M.Y. Zaluzhnyj (2004). Procedure of Experimental Researches of Physical Processes Using Models of Power Electric Equipment Under Strongly-Varying Currents, Papers of 4-th Scientific-and-Technical Conference: “Metrology of Electrical Measurements in Electrical Engineering”. RAO UES, VNIIE, 264–268. (Rus.).

[13] Zinovkin, V.V. (2005). Probabilistic parameters of strongly varying loads of power-intensive electrotechnological complexes, Works of the Institute of Electrodynamics of the National Academy of Sciences of Ukraine, 1, 136–144. (Rus.).

[14] Zinovkin, V.V. (2005). Non-stationary electromagnetic processes in electric equipment for power-intensive electric technological complexes with strongly-varying behavior of the load. Radio Electronics, Computer Science, Control, 2, 142–148. (Rus.).

[15] D.S. Yarymbash, (2015). On specific features of modeling electromagnetic field in the connection area of side busbar packages to graphitization furnace current leads, Russian Electrical Engineering, 86, 2, 86–92.

[16] Yarymbash, D., Kotsur, M., Yarymbash, S., & Kotsur, I. (2017). Features of parameter determination of the induction motor substitution circuit for short-circuit mode. Electrical Engineering And Power Engineering, 1, 24-30. doi:10.15588/1607-6761-2017-1-4.

[17] Divchuk, T., Yarymbash, D., Yarymbash, S., Kylymnyk, I., Kotsur, M., & Bezverkhnia, Y. (2018). Approach to determination of no load current of three-phase power transformers with plane rods magnetic systems. Electrical Engineering And Power Engineering, 2, 56-66. doi:10.15588/1607-6761-2017-2-6.

[18] Yarymbash, D., Kotsur, M., Yarymbash, S., & Kotsur, I. (2016). Features of three-dimensional simulation of the electromagnetic fields of the asynchronous motors. Electrical Engineering And Power Engineering, 2, 43-50. doi:10.15588/1607-6761-2016-2-5.

[19] Divchuk, T., Yarymbash, D., Yarymbash, S., Kylymnyk, I., Kotsur, M., & Bezverkhnia, Y. (2018). An Adjusting approach to the determination of the permeability functional dependencies of anisotropic cold-rolled electrotechnical steels. Electrical Engineering And Power Engineering, 2, 6-15. doi:10.15588/1607-6761-2018-2-1.

[20] Yarymbash, D., Yarymbash, S., Divchuk, T., & Kylymnik, I. (2016). The features of magnetic flux distribution of the idling mode of the power transformers. Electrical Engineering And Power Engineering, 2, 5-12. doi:10.15588/1607-6761-2016-2-1.

GOST Style Citations

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Copyright (c) 2019 V.V Zinovkin, O.V. Blyzniakov

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Address of the journal editorial office: Editorial office of the the scientific journal "Electrical Engineering and Power Engineering", Zaporizhzhia Polytechnic National University, Zhukovskiy street, 64, Zaporizhzhia, 69063, Ukraine. phone: +38-061-769-82-96 – the Editing and Publishing Department. E-mail:;