Assessment of approximate formulas for calculating overhead-line earth-impedances

In this paper an assessment of approximate formulas for calculating Carson´s integral is presented. This integral is widely used when computing the self and mutual impedances of transmission lines above an imperfect earth plane. In order to provide a reliable comparison a hybrid method of numerical integration for solving Carson´s integral is presented here. In addition, contour maps obtained from a parametric form of Carson´s integral are used to show the error ranges for each approximate formula. Finally an electromagnetic transient example involving induction to a nearby distribution line is used to analyze the errors when approximating Carson´s integral with the different formulas being here.