Analysis of Exact and Approximating Dependences of the Active Resistance of Conductor on the Frequency of Current Under the Action of Skin Effect

Abstract

Based on Maxwell’s equations, the dependences of the total and active resistance of the electrical network on the frequency of the flowing current are determined, which allows to determine the additional power losses due to higher harmonics of higher harmonics. The analysis of convergence of the received equations with expressions of the international standard IEC 60287-1-1 is resulted. It is shown that for the high frequency zone the expressions of the IEC 60287-1-1 standard describing the dependence of the active resistance on the frequency give a significant error. A simplified approximation dependence is proposed for the high-frequency zone, which makes it possible to determine the dependence of the active resistance on the frequency without the use of Bessel equations. The obtained equations can be used to determine additional power losses in the active supports of electrical networks, windings of electric machines, high-frequency transformers from higher harmonics of currents at different nonlinear loads. In addition, the obtained expressions can be used to justify the use of filter-compensating devices.