• Laziz Bazarov Tashkent state transport university
  • Kamila Jurayeva Tashkent state transport university
  • Ivan Bedritskiy Tashkent state transport university
  • Mirkomil Mirasadov Tashkent state transport university


Ключевые слова:

electrical steel, saturated mode, magnetic characteristic, magnetization curve, approximation, incomplete polynomial of odd degree, least squares method, approximation error, ferromagnetic elements


It is made a comparison of functions approximating the main magnetization curve of electrical steels, selected according to two main criteria: obtaining the simplest expressions in an analytical study and achieving a minimum calculation error in quantitative calculations of devices with ferromagnetic components. The cases are considered when ferromagnetic elements in devices operate at alternating current and at high values of magnetic induction, that is, they are in a mode close to saturation, while the phenomena of hysteresis are usually neglected, and the main magnetization curve is used as the magnetic characteristic of the ferromagnetic element, it is shown, that when the devices operate in a saturated mode, an incomplete polynomial of n - degree  can be used for these purposes. It is proved that the errors when approximating by polynomials with degrees 9 and 11 give the smallest errors not exceeding 12 and 8% for components of devices based on cold-rolled steels, and errors not exceeding 13% when approximating by polynomials with degrees 3 and 5 for components of devices based on hot-rolled steels.

Биографии авторов

Laziz Bazarov, Tashkent state transport university

doctoral student, Tashkent, Uzbekistan,

Kamila Jurayeva, Tashkent state transport university


PhD, Associate Professor, Tashkent, Uzbekistan,

Ivan Bedritskiy, Tashkent state transport university

Doctor of Technical Sciences, associate professor, Tashkent, Uzbekistan,

Mirkomil Mirasadov, Tashkent state transport university

assistant teacher, Tashkent, Uzbekistan,

Библиографические ссылки

[1] Mandache, K. Al-Haddad, High Precision Modeling of Nonlinear Lossy Magnetic Devices, IEEE International Symposium of Power Electronics – ISIE 2006, 9–13 July 2006, Montreal, pp. 267–287.

[2] Ivan Bedritsky, Kamila Jurayeva, Zamira Nazirova, and Laziz Bazarov. Amplitude and phase relations in a two-circuit parametric circuit of ferroresonance nature. E3S Web of Conferences 264, 04030 (2021) CONMECHYDRO – 2021,

[3] D. Jiles, D. Atherton. Theory of ferromagnetic hysteresis//Journal of Magnetism and Magnetic Materials. pp.48-60 – 1986

[4] A. Safarov, Kh. Sattarov, S. Jumaboyev. Mathematical modeling of static characteristics of electromagnetic current converter to detect current asymmetry of the traction power supply system// International Conference on “Information Science and Communications Technologies Applications, Trends and Opportunities ICISCT 2019”. Tashkent - 2019. – 3 p. 978-1-7281-2564-0/19/©2019 IEEE

[5] A. Safarov, Kh. Sattarov, S. Jumaboyev. Device for detection of the phase current asymmetry in the three-phase lines of non-traction consumers/ MIST: Aerospace 2019. IOP Conf. Series: Materials Science and Engineering 734 (2020) 012196. doi: 10.1088/1757-899X/734/1/012196. – 4 p.

[6] Bazarov M., Bedritskiy I.M., Boltaev O.Т. Estimation of an error of calculations of ferromagnetic elements from inductance of dispersion// «European Journal of Technical and Natural Sciences» №3, Austria, Vienna: 2017. pp. 47-49

[7] Aliev I.I. Electrotechnical reference book. - 5th edition, stereotyped. - M.: IP RadioSoft, 2010. – 384p.

[8] Bedritskiy I.M. Comparative analysis of analytical expressions for approximating the magnetization curves of electrical steels.– Proceedings of higher educational institutions. Electro mechanics. 2011. №6. С.39-42

[9] Bedritskiy I.M. Comparative analysis of analytical expressions for the approximation of the magnetization curves of electrical steels. // "Electric", LLC "Science and Technology", No. 7. M: 2011. – P. 38-41

[10] Geitenko E.N. Sources of secondary power supply. Circuitry and calculation. Tutorial. - M., 2008. - 448 p.

[11] Gluzman P.L., Milovzorov V.P., Yudin V.V. Devices based on controlled magnetic elements. M.: Radio and communication, 1986. – 160 p.

[12] Gorsky A.N., Rusin Yu.S., Ivanov N.R., Sergeeva L.A. Calculation of electromagnetic elements of secondary power supplies. M.: Radio and communication, 1988. – 176 p.

[13] Dyakonov VP - MATLAB 6.5 SP1 / 7 + Simulink 5/6 In mathematics and modeling / VP Dyakonov. M.: SOLON-Press, 2005.576 p.

[14] Lukichev A.A., Ilyina V.V. A simple mathematical model of the hysteresis loop for nonlinear materials// Bulletin of the Samara Scientific Center of the Russian Academy of Sciences. No. 4 (13) p.39-43. – 2011

[15] Mustafaev R.A., Nabiev M.A., Guliev Z.A., Hajibalaev N.M. On the approximation of the magnetization curve. // Electricity No. 5, 2004.

[16] Myshkis, A.D. Elements of the theory of mathematical models Text. /HELL. Myshkis - M.: KomKniga, 2007. - 192 p.

[17] Pavlovsky, Yu.N. Simulation models and systems Text. / Yu.F. Pavlovsky - M., Computing Center RAS, 2000, 144p.

[18] Rasulov A.N., Melikuziev M.V. Method for calculating electroferromagnetic circuits when approximating the magnetization curve by a generalized power-law function of the nth order// International scientific review №4 (11), pp.23-25. – 2017

[19] Stroyev V.A., Shulzhenko SV. Mathematical modeling of elements of electric power systems. - M.: Publishing house of MEI, 2002 - 56p.

[20] Chernykh, IV. Simulation of electrical devices in MATLAB, SimPowerSystems and Simulink. 2007

[21] Halilov N.A., Bedritsky I.M. To a question on approximation of curves of magnetization of electro technical steels //NEWS OF HIGH SCHOOLS OF REPUBLIC UZBEKISTAN. Engineering in Life Sciences. 2002. № 4. p. 33.

[22] John H. Chan, Andrei Vladimirescu, Xiao-Chun Gao, Peter Liebmann and John Valainis. Nonlinear Transformer Model for Circuit Simulation. TRANSACTIONS ON COMPUTER-AIDED DESIGN. VOL.10.1991. № 4




Как цитировать

Bazarov, L., Jurayeva, K., Bedritskiy, I. ., & Mirasadov, M. (2022). APPROXIMATION OF MAGNETIZATION CURVES OF ELECTRICAL STEEL. Вестник КазАТК, 121(2), 274–281.



Автоматизация, телемеханика, связь, энергетика, информационные системы