DOI: https://doi.org/10.15587/1729-4061.2018.134248

### Analysis of inrush currents of the unloaded transformer using the circuit­field modelling methods

Dmytro Yarymbash, Serhiy Yarymbash, Mykhailo Kotsur, Tetyana Divchuk

#### Abstract

We studied theoretically the transition processes that occur during tests of power transformers in the mode of experimental idling. A circuit-field model of electromagnetic processes is developed, based on a three-dimensional dynamical model of the magnetic field in a three-phase power transformer at idling.

Using a finite element method, we divided the region of field simulation into estimated zones with the magnetic field symmetry conditions for vertical and horizontal cross sections. The number of finite elements and the time for computing was reduced by four times without compromising the accuracy of our results.

It was established that in the circuit of the windings, connected into a triangle, there occurs a transitional levelling current, which fades over the initial switching time. The multiplicity of this current may reach 60‒70 % of the multiplicity of the input surge current.

We have developed relations for the approximation of transitional phase currents, which are represented by the aperiodic, periodic components and series with the basis Gaussian functions for phase current discrepancies between the circuit-field and circuit models.

We have proposed and implemented a refined approach for the calculation of input surge current based on the specifications for an idling mode of the transformer and a surge current coefficient, which is characterized by the high efficiency and accuracy of numerical realization.

To determine a functional dependence of the multiplicity coefficient for an input surge current on the input resistances, we applied a method of sorting out specialized functions. The approximation coefficients calculation was carried out based on the method of least squares. This allowed us to significantly reduce the level of error when calculating the multiplicity coefficient of input surge current based on the specifications of the transformer and testing equipment, by 2.1 %.

Using the 3D modeling reduces the calculation error of idling mode current surges by 2.4 % using a simplified procedure that employs specifications of the transformer.

#### Keywords

circuit-field model; three-phase transformer; idling mode; magnetization inrush currents

#### Full Text:

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#### References

C57.12.90-2006 – IEEE Standard Test Code for Liquid-Immersed Distribution, Power, and Regulating Transformers. doi: 10.1109/ieeestd.2006.320496

Lurie, A. I. (2008). Protsess vklyucheniya silovogo transformatora na kholostoy khod i korotkoye zamykaniye. Elektrotekhnika, 2, 2–18.

Lazarev, N. S., Shulga, R. N., Shulga, A. R. (2010). Toki vklyucheniya silovykh transformatorov. Elektrotekhnika, 11, 11–17.

Biki, M. A. (2013). Proyektirovaniye silovykh transformatorov. Raschet osnovnykh parametrov. Moscow: Znak, 612.

Gopika, R., Deepa, S. (2017). Study on Power Transformer Inrush Current. IOSR Journal of Electrical and Electronics Engineering, 2, 59–63.

Zhu, Y., Wang, Q., Bo, Z., Ma, X., Zhao, Y., Zhang, M. (2016). Simulation study of power transformer inrush current and internal fault. 2016 China International Conference on Electricity Distribution (CICED). doi: 10.1109/ciced.2016.7576049

Vanti, M. G., Bertoli, S. L., Cabral, S. H. L., Gerent, A. G., Kuo, P. P. (2008). Semianalytic Solution for a Simple Model of Inrush Currents in Transformers. IEEE Transactions on Magnetics, 44 (6), 1270–1273. doi: 10.1109/tmag.2007.916245

Cazacu, E., Ionita, V., Petrescu, L. (2013). Transformer inrush current predetermination for distorted waveform voltage supply. Revue Roumaine des Sciences Techniques – Serie Electrotechnique et Energetique, 58 (3), 242–251.

Novash, V. I., Tomkevich, A. P. (2005). Magnetizing current inrush in three phase power transformers during incomplete phase switching. Energetika. Proceedings of CIS higher education institutions and power engineering associations, 4, 5–12.

Vahidi, B., Tavakoli, M. R. B., Gharehpetian, G. B., Hosseinian, S. H. (2006). An Algorithm for Evaluating Inrush Current in Transformers Using Jiles-Atherton Theory of Ferromagnetic Hysteresis. TENCON 2006 – 2006 IEEE Region 10 Conference. doi: 10.1109/tencon.2006.343701

Lindberg, E. (1981). ANP3 & NAP2 – A package for circuit and systems simulation. Proceedings of the 2’nd International Conference on Engineering Software. London, 686–700.

Novash, I. V., Rumiantsev, Y. V. (2015). Three-phase transformer parameters calculation considering the core saturation for the matlab-simulink transformer model. Energetika. Proceedings of CIS higher education institutions and power engineering associations, 1, 12–24.

Kotsur, M., Yarymbash, D., Bezverkhnia, I. K. Y., Bezverkhnia, D. A. Y., Andrienko, D. (2018). Speed synchronization methods of the energy-efficient electric drive system for induction motors. 2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET). doi: 10.1109/tcset.2018.8336208

Kotsur, M., Kotsur, I., Bezverkhnia, Y., Andrienko, D. (2017). Increasing of thermal reliability of a regulated induction motor in non-standard cycle time conditions. 2017 International Conference on Modern Electrical and Energy Systems (MEES). doi: 10.1109/mees.2017.8248960

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

Heinemann, R. (2005). PSPICE. Modelirovaniye raboty elektronnykh skhem. Moscow: DMK, 336.

Jamali, M., Mirzaie, M., Asghar-Gholamian, S. (2011). Calculation and Analysis of Transformer Inrush Current Based on Parameters of Transformer and Operating Conditions. Electronics and Electrical Engineering, 109 (3). doi: 10.5755/j01.eee.109.3.162

Singh, A. K., 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.

Taghikhani, M. A., Sheikholeslami, A., Taghikhani, Z. (2015). Harmonic Modeling of Inrush Current in Core Type Power Transformers Using Hartley Transform. IJEEE, 11 (2), 174–183. Available at: http://ijeee.iust.ac.ir/browse.php?a_id=741&sid=1&slc_lang=fa

Chiesa, N., Mork, B. A., Høidalen, H. K. (2010). Transformer Model for Inrush Current Calculations: Simulations, Measurements and Sensitivity Analysis. IEEE Transactions on Power Delivery, 25 (4), 2599–2608. doi: 10.1109/tpwrd.2010.2045518

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: 10.1016/j.epsr.2010.01.011

Tykhovod, S. M. (2014). Transients modeling in transformers on the basis of magnetoelectric equivalent circuits. Electrical Engineering and Power Engineering, 2, 59–68. doi: 10.15588/1607-6761-2014-2-8

Podoltsev, A. D., Kontorovich, L. N. (2011). Chislenniy raschet elektricheskih tokov, magnitnogo polya i elektrodinamicheskih sil v silovom transformatore v avariynyh rezhimah s ispol'zovaniem Matlab/Simulink i Comsol. Tehnichna elektrodinamіka, 6, 3–10.

Yarymbash, D. S., Oleinikov, A. M. (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. doi: 10.3103/s1068371215020121

Yarymbash, D. S. (2015). The research of electromagnetic and thermoelectric processes in the AC and DC graphitization furnaces. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 3, 95–102.

Kotsur, M., Yarymbash, D., Yarymbash, S., Kotsur, I. (2017). A new approach of the induction motor parameters determination in short-circuit mode by 3D electromagnetic field simulation. 2017 IEEE International Young Scientists Forum on Applied Physics and Engineering (YSF). doi: 10.1109/ysf.2017.8126620

Yarymbash, D., Kotsur, M., Subbotin, S., Oliinyk, A. (2017). A new simulation approach of the electromagnetic fields in electrical machines. 2017 International Conference on Information and Digital Technologies (IDT). doi: 10.1109/dt.2017.8024332

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

Yarymbash, D., Yarymbash, S., Kylymnyk, I., Divchuk, T., Litvinov, D. (2017). Features of defining three-phase transformer no-load parameters by 3D modeling methods. 2017 International Conference on Modern Electrical and Energy Systems (MEES). doi: 10.1109/mees.2017.8248870

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. 2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET). doi: 10.1109/tcset.2018.8336209

Leytes, L. V. (1981). Elektromagnitnye raschety trasnfomatorov i reaktorov. Moscow: Energiya, 365.

Bessonov, L. A. (2003). Teoreticheskie osnovy elektrotekhniki. Moscow: Vysshaya shkola, 317.

Korn, G. A., Korn, T. M. (2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. New York: Dover Publications, 1151.

Virchenko, N. O., Liashko, I. I. (1996). Hrafiky elementarnykh ta spetsialnykh funktsiy. Kyiv: Naukova dumka, 582.

Kotsur, M. I., Andrienko, P. D., Kotsur, I. M., Bliznyakov, O. V. (2017). Converter for frequency-current slip-power recovery scheme. Scientific Bulletin of National Mining University, 4, 49–54.

#### GOST Style Citations

C57.12.90-2006 – IEEE Standard Test Code for Liquid-Immersed Distribution, Power, and Regulating Transformers. doi: 10.1109/ieeestd.2006.320496

Lurie A. I. Protsess vklyucheniya silovogo transformatora na kholostoy khod i korotkoye zamykaniye // Elektrotekhnika. 2008. Issue 2. P. 2–18.

Lazarev N. S., Shulga R. N., Shulga A. R. Toki vklyucheniya silovykh transformatorov // Elektrotekhnika. 2010. Issue 11. P. 11–17.

Biki M. A. Proyektirovaniye silovykh transformatorov. Raschet osnovnykh parametrov. Moscow: Znak, 2013. 612 p.

Gopika R., Deepa S. Study on Power Transformer Inrush Current // IOSR Journal of Electrical and Electronics Engineering. 2017. Vol. 2. P. 59–63.

Simulation study of power transformer inrush current and internal fault / Zhu Y., Wang Q., Bo Z., Ma X., Zhao Y., Zhang M. // 2016 China International Conference on Electricity Distribution (CICED). 2016. doi: 10.1109/ciced.2016.7576049

Semianalytic Solution for a Simple Model of Inrush Currents in Transformers / Vanti M. G., Bertoli S. L., Cabral S. H. L., Gerent A. G., Kuo P. P. // IEEE Transactions on Magnetics. 2008. Vol. 44, Issue 6. P. 1270–1273. doi: 10.1109/tmag.2007.916245

Cazacu E., Ionita V., Petrescu L. Transformer inrush current predetermination for distorted waveform voltage supply // Revue Roumaine des Sciences Techniques – Serie Electrotechnique et Energetique. 2013. Vol. 58, Issue 3. P. 242–251.

Novash V. I., Tomkevich A. P. Magnetizing current inrush in three phase power transformers during incomplete phase switching // Energetika. Proceedings of CIS higher education institutions and power engineering associations. 2005. Issue 4. P. 5–12.

An Algorithm for Evaluating Inrush Current in Transformers Using Jiles-Atherton Theory of Ferromagnetic Hysteresis / Vahidi B., Tavakoli M. R. B., Gharehpetian G. B., Hosseinian S. H. // TENCON 2006 – 2006 IEEE Region 10 Conference. 2006. doi: 10.1109/tencon.2006.343701

Lindberg E. ANP3 & NAP2 – A package for circuit and systems simulation // Proceedings of the 2’nd International Conference on Engineering Software. London, 1981. P. 686–700.

Novash I. V., Rumiantsev Y. V. Three-phase transformer parameters calculation considering the core saturation for the matlab-simulink transformer model // Energetika. Proceedings of CIS higher education institutions and power engineering associations. 2015. Issue 1. P. 12–24.

Speed synchronization methods of the energy-efficient electric drive system for induction motors / Kotsur M., Yarymbash D., Bezverkhnia I. K. Y., Bezverkhnia D. A. Y., Andrienko D. // 2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET). 2018. doi: 10.1109/tcset.2018.8336208

Increasing of thermal reliability of a regulated induction motor in non-standard cycle time conditions / Kotsur M., Kotsur I., Bezverkhnia Y., Andrienko D. // 2017 International Conference on Modern Electrical and Energy Systems (MEES). 2017. doi: 10.1109/mees.2017.8248960

Schiop A., Popescu V. Pspice simulation of power electronics circuit and induction motor drives // Revue Roumaine des Sciences Techniques – Serie Electrotechnique et Energetique. 2007. Vol. 52, Issue 1. P. 33–42.

Heinemann R. PSPICE. Modelirovaniye raboty elektronnykh skhem. Moscow: DMK, 2005. 336 p.

Jamali M., Mirzaie M., Asghar-Gholamian S. Calculation and Analysis of Transformer Inrush Current Based on Parameters of Transformer and Operating Conditions // Electronics and Electrical Engineering. 2011. Vol. 109, Issue 3. doi: 10.5755/j01.eee.109.3.162

Singh A. K., Patel S. Mitigation of Inrush Current For Single Phase Transformer by Control Switching Method // International Journal of Electronics, Electrical and Computational System. 2015. Vol. 4. P. 146–150.

Taghikhani M. A., Sheikholeslami A., Taghikhani Z. Harmonic Modeling of Inrush Current in Core Type Power Transformers Using Hartley Transform // IJEEE. 2015. Vol. 11, Issue 2. P. 174–183. URL: http://ijeee.iust.ac.ir/browse.php?a_id=741&sid=1&slc_lang=fa

Chiesa N., Mork B. A., Høidalen H. K. Transformer Model for Inrush Current Calculations: Simulations, Measurements and Sensitivity Analysis // IEEE Transactions on Power Delivery. 2010. Vol. 25, Issue 4. P. 2599–2608. doi: 10.1109/tpwrd.2010.2045518

Khederzadeh M. Mitigation of the impact of transformer inrush current on voltage sag by TCSC // Electric Power Systems Research. 2010. Vol. 80, Issue 9. P. 1049–1055. doi: 10.1016/j.epsr.2010.01.011

Tykhovod S. M. Transients modeling in transformers on the basis of magnetoelectric equivalent circuits // Electrical Engineering and Power Engineering. 2014. Issue 2. P. 59–68. doi: 10.15588/1607-6761-2014-2-8

Podoltsev A. D., Kontorovich L. N. Chislenniy raschet elektricheskih tokov, magnitnogo polya i elektrodinamicheskih sil v silovom transformatore v avariynyh rezhimah s ispol'zovaniem Matlab/Simulink i Comsol // Tehnichna elektrodinamіka. 2011. Issue 6. P. 3–10.

Yarymbash D. S., Oleinikov A. M. On specific features of modeling electromagnetic field in the connection area of side busbar packages to graphitization furnace current leads // Russian Electrical Engineering. 2015. Vol. 86, Issue 2. P. 86–92. doi: 10.3103/s1068371215020121

Yarymbash D. S. The research of electromagnetic and thermoelectric processes in the AC and DC graphitization furnaces // Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2015. Issue 3. P. 95–102.

A new approach of the induction motor parameters determination in short-circuit mode by 3D electromagnetic field simulation / Kotsur M., Yarymbash D., Yarymbash S., Kotsur I. // 2017 IEEE International Young Scientists Forum on Applied Physics and Engineering (YSF). 2017. doi: 10.1109/ysf.2017.8126620

A new simulation approach of the electromagnetic fields in electrical machines / Yarymbash D., Kotsur M., Subbotin S., Oliinyk A. // 2017 International Conference on Information and Digital Technologies (IDT). 2017. doi: 10.1109/dt.2017.8024332

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

Features of defining three-phase transformer no-load parameters by 3D modeling methods / Yarymbash D., Yarymbash S., Kylymnyk I., Divchuk T., Litvinov D. // 2017 International Conference on Modern Electrical and Energy Systems (MEES). 2017. doi: 10.1109/mees.2017.8248870

An application of scheme and field models for simulation of electromagnetic processes of power transformers / Yarymbash D., Kotsur M., Yarymbash S., Kylymnyk I., Divchuk T. // 2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET). 2018. doi: 10.1109/tcset.2018.8336209

Leytes L. V. Elektromagnitnye raschety trasnfomatorov i reaktorov. Moscow: Energiya, 1981. 365 p.

Bessonov L. A. Teoreticheskie osnovy elektrotekhniki. Moscow: Vysshaya shkola, 2003. 317 p.

Korn G. A., Korn T. M. Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. New York: Dover Publications, 2000. 1151 p.

Virchenko N. O., Liashko I. I. Hrafiky elementarnykh ta spetsialnykh funktsiy: dovidnyk. Kyiv: Naukova dumka, 1996. 582 p.

Converter for frequency-current slip-power recovery scheme / Kotsur M. I., Andrienko P. D., Kotsur I. M., Bliznyakov O. V. // Scientific Bulletin of National Mining University. 2017. Issue 4. P. 49–54.

Copyright (c) 2018 Dmytro Yarymbash, Serhiy Yarymbash, Mykhailo Kotsur, Tetyana Divchuk