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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.