Closed-form expressions for ground return impedances of overhead lines and underground cables

This paper presents an analysis of closed-form expressions for ground return impedance of overhead lines and underground cables. For the former an actual solution to Carson’s infinite integral is obtained via integral transformation techniques while for the latter an approximate expression based upon asymptotic expansion is presented. Numerical integration based upon Gauss-quadrature is performed for the comparison.Several test cases are presented considering different values for soil parameters. The results indicate that good accuracy was obtained. Limitations of the proposed expressions are also presented.