Analysis of exact and approximating dependences of active resistance of a conductor on the current frequency based on the influence of skin effect

Abstract

The operation of semiconductor power converters, which are part of tractionsubstations, frequency-controlled electric drives and other powerful nonlinear loads, cause asignificant emission of higher harmonics of currents to electrical networks. Higher harmonics ofcurrents in electrical networks cause a complex negative effect on the energy efficiency of thenetwork. The increase in power losses in the active resistance under the action of higher harmonicsis due to the increase in the root mean square value of the current and the action of the skin effect.Analytical expressions describing the dependence of the active and impedance of the electricnetwork on the current frequency are determined. Based on them, analytical expressions are obtainedfor the calculation of additional power losses under the action of higher harmonics of currents, whichare due to the skin effect. The dependences of the active resistance of the electric network on thefrequency of higher harmonics are determined on the basis of Bessel equations. The analysis of convergence of the received equations with the data of the international standard IEC 60287-1-1 iscarried out. For the high-frequency zone, simplified approximating dependences are given, whichdetermine the parabolic dependence of the active resistance on the frequency. Simplifiedapproximating dependences of active resistance on the frequency of higher harmonics are obtainedfor engineering calculations. The obtained equations can be used to determine additional powerlosses in the active supports of electrical networks, windings of electric machines, high-frequencytransformers from higher harmonics of currents at different nonlinear loads. In addition, the obtainedexpressions can be used to justify the use of filter-compensating devices.