M. V. Ostrenko, S. М. Tykhovod


The purpose of the work. This paper offers the well founded mathematical model based on the applying of the finite element method, which allows more effective modeling of the eddy currents and losses in the tank of power transformers, reactors and elements of their constructions, caused by the dispersion fields.

Research methods. Based on assumptions of equality to the zero of normal components of the magnetic and electric fields’ intensities in ferromagnetic half-space, this mathematical model enters the surface eddy current density in FEM equations.

The obtained results. Conclusion that the offered mathematical model allows to calculate eddy currents and losses in the power transformers tank, reactors and elements of their constructions more effectively is done. Reduction in tens of times of the resulting system of equations is also arrived, that results to considerable decreasing of calculation time and computer resources without accuracy losses.

Scientific novelty. The novelty of the offered mathematical model is the form that is comfortable for programmatic realization of the known surface impedance boundary condition describing the electromagnetic field distribution in a tank and construction elements and in addition these elements are represented as ferromagnetic conducting half-space.

Practical importance. Examples of single-phase autotransformer 167MVA 345kV 161kV calculation in a program complex ELMAG - 3d software, created on the basis of the described method and in the program complex ANSYS software with the use of classic approach of solid modeling of transformer, demonstrate applicability and required accuracy of the described method in the context of problems of losses calculation in the tank and construction elements of power transformers.


finite element method; surface current density


Иванков В. Ф. Электротепловые расчетные модели элементов конструкции трансформаторного оборудования / Иванков В. Ф., Басова А. В., Шульга Н. В.// Електротехніка та електроенергетика. – 2014 .– № 2.– С. 41–53.

Kurt P. Thermal-Electromagnetic Coupling in the FiniteElement Simulation of Power Transformers. / Preis Kurt // IEEE Trans. on Magn.– 2006. – vol. 42, No. 4.– Р. 999–1002.

Guйrin C. 3D Eddy Current Losses Calculation in Transformer Tanks Using the Finite Element Method / Christophe Guйrin, Gerard Tanneau, Gerard Meunier // IEEE Trans. on Magn.- 1993.– vol. 29, No. 2.– Р. 1419–1422.

Ostrenko M. V. Power transformers and reactors stray losses and temperatures calculation using coupled IEM and FEM technique / Maxym V. Ostrenko, Olexandr L. Tarchutkin, Bogdan Y. Andriienko // Computational Technologies in Electrical and Electronics Engineering (SIBIRCON).– 2010. – IEEE Region 8 International Conference, p. 717–721.

Яримбаш Д. С. Особливості визначення параметрів короткого замикання силових трансформаторів засобами польового моделювання. / Д. С. Яримбаш, С. Т. Яримбаш, Т. Є. Дівчук, І. М. Килимник // Електротехніка та електроенергетика. – 2016. – № 1. – С. 12–17.

ANSYS software. – [Электронный ресурс] . – режим доступа:

Григорьев А. Д. Методы вычислительной электродинамики / А. Д. Григорьев.– М.: Физматлит, 2012. – 432 с.

Ostrenko M. V. Power Transformers and Reactors Structure Losses and Temperatures Calculation Using Surface Impedance Boundary Conditions / Maxym Ostrenko, Bogdan Andriienko, Sergei Tikhovod and Denys Prychynenko // 1-st IEEE Conference Advances in Magnetics AIM.- 2016.- Р.14-16.

Susnjic L. 3D finite-element determination of stray losses in power transformer / L. Susnjic, Z. Haznadar and Z. Valkovic // Electric Power System Research 78.– 2008.– Р.1814–1818.

Wagner B. Error Evaluation of Surface Impedance Boundary Conditions With Magnetic Vector Potential Formulation on a Cylindrical Test Problem / Bernhard Wagner, Werner Renhart and Christian Magele // IEEE Trans. on Magn.– 2008.– vol. 44, No. 6.– Р. 734–737.

Aymard N. An Improved Modified Surface Impedance for Transverse Electric Problems / N. Aymard, M. Feliachi // IEEE Trans. on Magn.– 1997. vol. 33, No. 2.– Р. 1267–1270.

Ida N. High Order Surface Impedance Boundary Conditions with the A- Formulation / Nathan Ida, Yvonnic Lemenach and Thomas Henneron // FACTA UNIVERSITATIS, Ser.: Elec. Energ. – 2011.– vol. 24 no. 2 .– Р. 147–155.

Бердник С. Л. Использование концепции поверхностного импеданса в задачах электродинамики (75 лет спустя) / С. Л. Бердник // Радиофизика и астрономия .– 2014.– Т.19, №1.– С. 57–80.

Бессонов Л. А Теоретические основы электротехники: Электромагнитное поле, Учебник для студентов вузов. – 7-е изд., перераб. и доп. / Л. А. Бессонов .– М.: Высш. школа.– 1978. – 231с.

Kuczmann M. Nodal and Edge Finite Element Analysis of Eddy Current Field Problems / Miklos Kuczmann // PRZEGLAD ELEKTROTECHNICZNY.- 2008 .– Р. 194–197.

Zienkiewicz O. C. The finite element method. Fifth edition. / Zienkiewicz O. C, Taylor R. L. // Volume 1: The Basis. «Butterworth-Heinemann». – Oxford. – 2000 .

Левин В. И. Методы математической физики. Учебное пособие для физико-математических факультетов педагогических институтов / В. И. Левин. – М. : Высш. школа. – 1956. – 243 с.

Андрієнко Б. Ю. Комп’ютерна програма «Програма розрахунку тривимірного магнітного поля, вихрових струмів, втрат та температур у силових трансформаторах та реакторах ELMAG-3D» СВІДОЦТВО про реєстрацію авторського права на твір № 41639 / Б. Ю Андрієнко, О. Л. Тарчуткін, М. В. Остренко. – Державна служба інтелектуальної власності України, – 2012.

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