field model, three phase transformer, idling, magnetic field, finite element method, harmonic anal-ysis, non-sinusoidal and asymmetrical currents


Purpose. The aim of the work is to define the idle currents harmonic composition of the power transformer using spatial field models, that take into account the structural construction of the active part of the transformer, the hysteresis of nonlinear magnetic properties of the electrical steel, and the electrical asymmetry of the currents in phase windings.

Methodology. The research was carried out using harmonic analysis methods, the theory of magnetic fields, the theory of electrical circuits, the theory of power transformers, finite element methods, and symmetric components.

Findings. Based on the numerical implementation of 3D models of the magnetic field in a three-phase power transformer with the connection of the primary windings according to the “Y” scheme, the harmonic composition of the phase idle currents is determined. An improved approach has been applied to increase the efficiency of field simulation of the research idle mode by setting the conditions of symmetry of the magnetic field on a plane with the axes of the legs of the magnetic system. This made it possible to reduce the volume of the 3D geometric area by 2 times and to ensure a proportional decrease in the time and computational resources, required for the numerical implementation of the mathematical model by the finite element method. The features of non-sinusoidal changes in time of momentary values of idle currents are determined and their uneven distribution in the transformer phases is estimated. It is characterized by an increase in the effective currents to 113.2%, 112.9% in phases A and C and their decrease to 72.4% in phase B. It is shown that the amplitude of the main harmonic decreases for the positive phase-sequence by 5.08% of the amplitude of the transformer idling current and increases to 27.91% for the negative phase-sequence. The prevailing influence of the odd higher harmonic components of the idle phase currents, the amplitudes of which are 24, 21% and 4% of the amplitude of the idle current for its third, fifth and seventh harmonics is established. The use of a compensating winding system, which is connected to the adjusting windings in negative phase-sequence with a phase shift of 120 degrees, reduces the effective value of the idle current of the negative phase-sequence to 5%, approximates the effective value of the first harmonic of the idle current, and also reduce the deviation of the phase shift angles compared to the symmetric idle mode up to 2%.

Originality. Based on theoretical and experimental researches, the prevailing influence of the third harmonic components on the non-sinusoidal phase of the idle phase currents in the primary windings, connected in "Y" is determined. The use of additional symmetry boundary conditions provides a significant increase in the efficiency of numerical implementation due to a two-fold reduction in the volume of the 3D field modeling of a power transformer in idle mode. For the scheme of connecting the windings of the transformer “Y” without a neutral wire, taking into account the interrelated effects of hysteresis and eddy currents on specific losses and magnetization power, due to the high accuracy of describing the interrelation between magnetic flux density and magnetic field strength in ferromagnetic media, the new features of idle current harmonic composition with the advantage of the third harmonic was determined and experimentally confirmed.

Practical value. The proposed approaches and methods allow to reduce the current error and the relative error for idle losses up to 1.41% and 1.2% for a 3D model of a three-phase power transformer. The use of a system with a compensating winding allows to reduce the amplitude of the third harmonic components of idle phase currents up to 2 - 2.5 times and by balancing the current load of the phases reduce the amplitudes of phase idle currents and the effective value of idle current up to 15 - 16 %.

Author Biographies

T.E. Divchuk, Zaporizhzhia National Technical University

Senior Lecturer, Department of Electrical Machines, Zaporizhzhia National Technical University, Zaporizhzhia

D.S. Yarymbash, Zaporizhzhia National Technical University

Dr. Tech. Sci., Professor, Head of the Department of Electrical Machines, Zaporizhzhia National Technical University, Zaporizhzhia

M.I. Kotsur, Zaporizhzhia National Technical University

Ph.D, Associate Professor, Associate Professor of the Department of Electrical and Electronic Apparatuses, Zaporizhzhia National Technical University, Zaporizhzhia

S.T. Yarymbash, Zaporizhzhia National Technical University

Ph.D, Associate Professor, Associate Professor of the Department of Electrical Machines, Zaporizhzhia National Technical University, Zaporizhzhia


[1] Kulkarni, S. (2004). Transformer Engineering: Design and Practice. New York: Marcel Dekker, 478.

[2] Biki, MA (2013). Design of power transformers. Calculation of the main parameters. M.:Znak, 612.

[3] Novash, V., Rumyantsev, Y. (2015). Calculation of the parameters of the model of a three-phase transformer from the matlab-simulink library taking into account the saturation of the magnetic. Energy. Proceedings of higher educational institutions and energy associations of the CIS, 1, 12–24.

[4] Schiop, A., Popescu, V. (2007). Pspice simulation of power electronics circuit and induction motor drives Revue Roumaine des Sciences Techniques. Serie Electrotechnique and Energetique, 52, 1, 33–42.

[5] Lurye, A. (2008). The process of switching power transfrmator to idle and short circuit. Electrical Engineering, 2, 2, 18.

[6] Leites, L. (1981). Electromagnetic Calculations of Transformers and Reactors. M: Energy, 365.

[7] Tikhomirov, P. (1986). Calculation of transformers. M.: Energoatomizdat, 528.

[8] Jamali, M., Mirzaie, M., Asghar-Gholamian, S. (2011). Calculation and Analysis of Transformer Inrush Current Based on Parameters of Transformer and Operating. Elektronika and Elektrotechnika, 109, 3, 17–20. DOI: 10.5755/j01.eee.109.3.162.

[9] Fedorov, V. (2018). A criterion for determining the number of harmonics of Fourier series approximating voltages and currents of a transformer. Omsk Scientific Herald, 5 (161), 82–89. DOI: 10.25206/1813-8225-2018-161-82-89.

[10] Singh, A., Patel, S. (2015). Mitigation of Inrush Current For Single Phase Transformer by Control Switching Method. International Journal of Electronics, Electrical and Computational System, 4, 146–150.

[11] Taghikhani, M., Sheikholeslami, A., Taghikhani, Z. (2015). Harmonic Modeling of Inrush Current in Core Type Power Transformers Using Hartley Transform. IJEEE, 11, 2, 174–183 URL: http://ijeee.iust.ac.ir/article-1-741-en.pdf.

[12] Chiesa, N. B., Mork, A., Hoidalen, H. K. (2010).Transformer Model for Inrush Current Calculations: Simulations, Measurements and Sensitivity. IEEE Transactions on Power Delivery, 25, 4, 2599–2608. DOI: 10.1109/TPWRD.2010.2045518.

[13] Khederzadeh, M. (2010). Mitigation of the impact of transformer inrush current on voltage sag by TCSC. Electric Power Systems Research, 80, 9, 1049–1055. DOI: https://doi.org/10.1016/j.epsr.2010.01.011" target="_blank">10.1016/j.epsr.2010.01.011.

[14] Tihovod, S. (2014). Simulation of transients in transformers based on magnet-electric equivalent circuits. Electrical engineering and power engineering, 2, 59–68.DOI: 10.15588/1607-6761-2014-2-8.

[15] Lazarev, N. S., Shulga R.N., Shulga A.R. (2010). Current inclusion power transformers. Electrical Engineering, 11, 1–17.

[16] Majumder, R. Ghosh S., Mukherjee R. (2016). Transient Analysis of Single Phase Transformer Using State Model. International Journal of Innovative Research in Science, Engineering and Technology, 5, 3, 3300–3306. DOI: 10.15680/IJIRSET.2016.0503107.

[17] Yarymbash, D. S., Yarymbash, S. T., Kotsur, M. I., Litvinov, D. O. (2018). Computer simulation of electromagnetic field with application the frequency adaptation method. Radio Electronics, Computer Science, Control, 1, 65 – 74. DOI: 10.15588/1607-3274-2018-1-8.

[18] Yarymbash, D. (2014). Influence of the electrodes blanks location on the electric heating power distribution in the acheson furnaces core. Electrical Engineering And Power Engineering, 1, 5-11. doi:http://dx.doi.org/10.15588/1607-6761-2014-1-1

[19] 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:http://dx.doi.org/10.15588/1607-6761-2016-2-5.

[20] 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:http://dx.doi.org/10.15588/1607-6761-2017-1-4.

[21] Ostrenko, M.V., Tihovod, S.M., (2016). Calculation of losses in the design elements of power transformers and reactors using the finite element method with impedance type boundary conditions. Electrical Engineering and Electric Power Engineering, 2, 33–42. DOI: 10.15588 / 1607-6761-2016-2-4

[22] Paikov, I. A., Tikhonov, A. I. (2015). Analysis of models for electromagnetic calculation of power transformers. Vestnik ISEU, 3, 38–43.

[23] Podoltsev, A. D., Kontorovich, L.N. (2011). Numerical calculation of electric currents, magnetic field and electrodynamic forces in a power transformer in emergency conditions using MATLAB / SIMULINK and COMSOL. Tekhnichna elektrodinamika, 6, 3–10.

[24] 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.

[25] Yarymbash, D., Kotsur, M., Yarymbash, S., Kylymnyk, I., Divchuk, T. (2018). An Application of Scheme and Field Models for Simulation of Electromagnetic Processes of Power Transformers. 14th International Conference: Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET), February 20-24, Lviv–Slavske, Ukraine, 308–313. DOI: 10.1109/TCSET.2018.8336209.

[26] Cundeva, S. A. (2008). Transformer Model Based on the Jiles-Atherton Theory of Ferromagnetic Hysteresis. Serbian Journal of Electrical engineering, 5, 1, 21–30. DOI: 10.2298/SJEE0801021C.

[27] Bastos, J. P., Sadowski, A. N. (2003). Electromagnetic Modeling by Finite Element Methods. Boca Raton: CRC Press, 510. ISBN 9780203911174. DOI: 10.1201/9780203911174



How to Cite

Divchuk, T., Yarymbash, D., Kotsur, M., & Yarymbash, S. (2019). A IDLE CURRENTS HARMONIC COMPOSITION OF POWER TRANSFORMER. Electrical Engineering and Power Engineering, (1), 42–51. https://doi.org/10.15588/1607-6761-2019-1-4