Closed-Form Expression for Ground Return Admittance in Underground Cables

This letter presents a closed-form expression for ground return admittance for a system of underground cables. It is based on the approximation of the infinite integral found using a quasi-TEM (transverse electromagnetic) formulation of the electromagnetic field. The results indicate that the frequency behavior of the closed-form expression provides useful responses up to a few megahertz, thus being a suitable alternative to the numerically challenging infinite integrals. The agreement of the closed-form results and those obtained using the infinite integrals is very good regardless of the ground conductivity considered.