Eddy Currents Induced in Two Parallel Round Conductors

Authors

  • Tomasz Szczegielniak Department of Automation, Electrical Engineering and Optoelectronics, Faculty of Electrical Engineering Czestochowa University of Technology, Armii Krajowej 17, 42-200 Czestochowa, Poland
  • Paweł Jabłoński Department of Automation, Electrical Engineering and Optoelectronics, Faculty of Electrical Engineering Czestochowa University of Technology, Armii Krajowej 17, 42-200 Czestochowa, Poland
  • Dariusz Kusiak Department of Automation, Electrical Engineering and Optoelectronics, Faculty of Electrical Engineering Czestochowa University of Technology, Armii Krajowej 17, 42-200 Czestochowa, Poland
  • Zygmunt Piątek Czestochowa University of Technology, Poland

Keywords:

Current density, eddy currents, proximity effect, round conductor

Abstract

The paper presents a method of analysis of eddy currents induced in a system of two parallel round conductors by a transverse alternating magnetic field generated by a current in one of them. The magnetic field is represented by means of magnetic vector potential as expansion into Fourier series. Using the Laplace and Helmholtz equations as well as the classical boundary conditions we determine analytically the current density induced due to the proximity effect. Power transmission lines with round conductors are widely used in distribution networks. Therefore, although the paper is theoretical, the determination of electromagnetic parameters of the power transmission lines is of huge practical significance.

Downloads

Download data is not yet available.

References

R. Benato and A. Paoluci, EHV AC Undergrounding Electrical Power: Performance and Planning, Springer-Verlag London Limited, 2010.

O. Coufal, “Current density in two solid parallel conductors and their impedance,” Electrical Engineering, vol. 96, pp. 287-297, 2014.

F. Capelli and J. R. Riba, “Analysis of formulas to calculate the AC inductance of different configurations of nonmagnetic circular conductors,” Electrical Engineering, vol. 99, pp. 827-837, 2017.

A. Pagnetti, A. Xemard, F. Pladian, and C. A. Nucci, “An improved method for the calculation of the internal impedances of solid and hollow conductors with inclusion of proximity effect,” IEEE Trans. On Power Delivery, vol. 27, pp. 2063- 2072, 2012.

T. Dlabać and D. Filipović, “Integral equation approach for proximity effect in a two-wire line with round conductors,” Technicki Vjesnik, vol. 22, no. 4, pp. 1065-1068, 2015.

D. Filipović and T. Dlabać, “Proximity effect in a shielded symmetrical three-phase line,” Serbian Journal of Electrical Engineering, vol. 11, no. 4, pp. 585-59, 2014.

P. Rolicz, “Eddy currents generated in a system of two cylindrical conductors by a transverse alternating magnetic field,” Electric Power Systems Research, vol. 79, pp. 295-300, 2009.

P. Jabłoński, “Cylindrical conductor in an arbitrary time-harmonic transverse magnetic field,” Przegląd Elektrotechniczny, r. 87, no. 5, 2011.

Z. Piątek, “Method of calculating eddy currents induced by the sinusoidal current of the parallel conductor in the circular conductor (in Polish),” ZN Pol. Śl. Elektryka, no. 75, pp. 137-150, 1981.

J. R. Riba, “Analysis of formulas to calculate AC resistance of different conductors’ configurations,” Electric Power Systems Research, vol. 127, pp. 93- 100, 2015.

J. R. Riba, “Calculation of AC to DC resistance ratio of conductive nonmagnetic straight conductors by applying FEM simulations,” European Journal of Physics, vol. 36, no. 5, 2015.

A. Shendge, “A study on a conductor system for investigation of proximity effect,” Journal of Electromagnetic Analysis and Application, no. 4, pp. 440-446, 2012.

H. A. Aebischer and H. Friedli, “Analytical approximation for the inductance of circularly cylindrical two-wire transmission lines with proximity effect,” Advanced Electromagnetic, vol. 7, no. 1, pp. 25-34, 2018.

Z. Piątek, “Self and mutual impedances of a finite length gas-insulated transmission line (GIL),” Electric Power Systems Research, no. 77, pp. 191- 201, 2007.

Z. Piątek, Impedances of Tubular High Current Busducts, Polish Acad. Sci. Committee Elect. Eng. Ser. Progress in High-Voltage Technique, vol. 28, Wyd. Pol. Czest., Czestochowa, 2008.

Z. Piatek, D. Kusiak, and T. Szczegielniak, “Electromagnetic field and impedances of high current busducts,” in Proceedings of the 2010 Proceedings of the International Symposium, Wroclaw, Poland, 20-22 Sept. 2010.

I. S. Gradsztejn and I. M. Ryżyk, Tables of Integrals, Sums, Series and Products, (in Polish), PWN, Warsaw, 1972.

Downloads

Published

2019-12-01

How to Cite

[1]
Tomasz Szczegielniak, Paweł Jabłoński, Dariusz Kusiak, and Zygmunt Piątek, “Eddy Currents Induced in Two Parallel Round Conductors”, ACES Journal, vol. 34, no. 12, pp. 1922–1930, Dec. 2019.

Issue

Section

Articles