Determining Low-Frequency Earth Return Impedance: A Consistent Electromagnetic Approach

Abstract

In this paper, we present a new method for determining the earth return impedance. The proposed method, based on electromagnetic field theory, is very accurate and convenient for the analysis of earth behavior over a wide range of low frequencies. It takes into account all crucial physical events, including an exact treatment of the skin and proximity effects within the earth. Combining analytical and numerical procedures for finding the exact current distribution and the earth return impedance per unit length, we have developed an efficient and powerful tool that is described in this paper. In all calculations, real situations were considered, consisting of various soil resistivity values, overhead conductor heights, and combinations of parameters at various frequencies. Although most commonly applied simplified formulas give accurate results at industrial frequencies, significantly worse results are obtained in the presence of higher harmonics. Hence, verification of the developed method was achieved by comparing obtained results with the results of the Carson-Clem simplified formula and the FEM-based calculations. The generality of the developed program indicates that it may also be applied for calculating the earth return impedance in the presence of higher current harmonics.