Accurate and Approximate Evaluation of Power-Line Earth Impedances Through the Carson Integral

Abstract

Earth impedances of aerial power-lines usually are calculated through methods and approximate formulas based on the Carson integral. This paper presents a methodology to evaluate their accuracy and to serve as aid to select an appropriate method or formula in specific applications. Reference values for the Carson integral are first obtained through a numerical algorithm guaranteeing relative errors below 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> . These values are first used to validate the general solution of Carson integral employing an algorithm proposed by Theodoulidis. The reference values are then used to produce maps of errors and of differences for the following methods: Carson series, Gary-Dubanton formulas, Alvarado-Betancourt formulas, and double symmetry-plane formulas. Improvements are further proposed for the Carson-series method and the Alvarado-Betancourt formulas. Finally, the effectiveness of the proposed methodology is illustrated through an application example.