A Refined Mathematical Model of Physical Processes in a Conductor at a High-Current Pulse Discharge

Main Article Content

Yevgen Bajda
Michael Pantelyat


A novel mathematical model describing physical processes during the flow of an aperiodic pulse current with amplitude of 100 kA along a conductor with a circular cross-section is proposed and investigated. It is shown how a short-term electric discharge of an aperiodic shape affects the distribution of the current density in the cross-section of the conductor, causing its nonuniform heating and the appearance of significant thermal forces as well as mechanical stresses and strains. Based on the developed mathematical model, the relationship between electromagnetic, thermal and mechanical phenomena is shown, allowing a deeper understanding of the multiphysics processes taking place. The maximum values of the current density are calculated, which on the surface of the conductor reach values of 47 kA/mm2, while the temperature rise of a copper conductor with a diameter of 2.44 mm is no more than 80ºC at high temperature gradients, which causes the appearance of thermal stresses that have value (40–50)% of the value of the short-term strength limit of electrical copper. Utilization of this model allows to more accurately determine the required conductor cross-section based on the characteristics of electromagnetic, thermal and mechanical processes. It is shown that the simplified model (the condition for the uniform distribution of the current over the cross-section) gives significantly underestimated values of temperatures and does not take into account temperature deformations.

Article Details

How to Cite
Bajda, Y., & Pantelyat, M. (2021). A Refined Mathematical Model of Physical Processes in a Conductor at a High-Current Pulse Discharge. Lighting Engineering & Power Engineering, 60(3), 124–132. https://doi.org/10.33042/2079-424X.2021.60.3.05
Author Biographies

Yevgen Bajda, National Technical University “Kharkiv Polytechnic Institute”, Ukraine

D.Sc., Associate Professor of the Department of Electrical Apparatus

Michael Pantelyat, National Technical University “Kharkiv Polytechnic Institute”, Ukraine

Ph.D., Associate Professor of the Department of Electrical Apparatus


SAE International. (2013). Aircraft lightning environment and related test waveforms (SAE Standard No. ARP5412B:2013). https://doi.org/10.4271/ARP5412B

SAE International. (2013). Aircraft lightning test methods (SAE Standard No. ARP5416A:2013). https://doi.org/10.4271/ARP5416A

Baranov, M.I. (2018). A choice of sections of electric wires and cables in circuits of devices of high-voltage high-current impulse technique. Electrical Engineering & Electromechanics, (6), 56–62. https://doi.org/10.20998/2074-272X.2018.6.08

Baranov, M.I. (2019). Calculation and experimental determination of critical sections of electric wires and cables in the circuits of devices of high-voltage high-current pulse technique. Electrical Engineering & Electromechanics, (2), 39–46. https://doi.org/10.20998/2074-272X.2019.2.06

Baranov, M.I. (2019). Peculiarities of the manifestation and influence on the electromagnetic processes of the transient skin effect in metal conductors with pulsed current. Electrical Engineering & Electromechanics, (4), 41–47. https://doi.org/10.20998/2074-272X.2019.4.06

Baranov, M.I. (2019). A choice of critical sections of electric wires and cables in power circuits of electrical equipment of power industry. Electrical Engineering & Electromechanics, (5), 35–39. https://doi.org/10.20998/2074-272X.2019.5.06

Baranov, M.I. (2020). A choice of acceptable sections of electric wires and cables in on-board circuits of aircraft electrical equipment. Electrical Engineering & Electromechanics, (1), 39–46. https://doi.org/10.20998/2074-272X.2020.1.06

Baranov, M.I., Buriakovskyi, S.G., & Kniaziev, V.V. (2021). Destruction of polymer insulation and threshold amplitudes of current pulses of different temporal shapes for electric wires and cables in the low- and high-current circuits of pulse power engineering, electrical engineering and electronic devices. Electrical Engineering & Electromechanics, (6), 31–38. https://doi.org/10.20998/2074-272X.2021.6.05

Kostiukov, I. (2021). Measurement of dissipation factor of inner layers of insulation in three-core belted cables. Lighting Engineering & Power Engineering, 60(1), 23–30. https://doi.org/10.33042/2079-424X.2021.60.1.04

Gerling, D. (2009). Approximate analytical calculation of the skin effect in rectangular wires. In 2009 International Conference on Electrical Machines and Systems (pp. 1–6). IEEE. https://doi.org/10.1109/ICEMS.2009.5382786

Koller, L., Novák, B., & Tevan, G. (2007). Heating effects of short-circuit current impulses on contacts and conductors – Part I. IEEE Transactions on Power Delivery, 23(1), 221–227. https://doi.org/10.1109/TPWRD.2007.905806

Hagglund, L., & Sandstrom, J. (2003). Current Distribution in Conductors (Report No. 2003:5). Uppsala University. http://www.it.uu.se/edu/course/homepage/projektF/vt03/projekt3.pdf

Mesiats, G.A. (2004). Pulse Power Engineering and Electronics. Nauka. (in Russian)

Waldow, P., & Wolff, I. (1985). The skin-effect at high frequencies. IEEE Transactions on Microwave Theory and Techniques, 33(10), 1076–1082. https://doi.org/10.1109/TMTT.1985.1133172

Voršič, Ž., Maruša, R., & Pihler, J. (2019). New method for calculating the heating of the conductor. Energies, 12(14), 2769. https://doi.org/10.3390/en12142769

Ramo, S., & Whinnery, J.R. (1964). Fields and Waves in Modern Radio (2nd ed.). John Wiley & Sons.

Baida, E.I. (2015). Peculiarities of calculation of magnetic systems with short-circuited secondary windings in in-plane formulation. Electrical Engineering & Electromechanics, (5), 18–22. https://doi.org/10.20998/2074-272X.2015.5.02 (in Rus-sian)

Carlslaw, H.S., & Jaeger, J.C. (2011). Conduction of Heat in Solids (2nd ed.). Oxford University Press.

Timoshenko, S.P., & Goodier, J.N. (2008). Theory of Elasticity (3rd ed.). McGraw-Hill.

Kuhn, H.-A., Altenberger, I., Käufler, A., Hölzl, H., & Fünfer, M. (2012). Properties of high performance alloys for electromechanical connectors. In L. Collini (Ed.), Copper Alloys – Early Applications and Current Performance – Enhancing Processes (pp. 51–68). IntechOpen. https://doi.org/10.5772/35148