Closed-Form Expressions for the Calculation of the Ground-Return Impedance and Admittance of Underground Cables

This paper proposes closed-form expressions for the calculation of the ground-return impedance and admittance of underground cables. The proposed expressions are shown to reproduce the integral equations of Xue with great accuracy for a wide range of ground resistivities and frequencies. An error analysis, a comparison with closed-form expressions available in the literature, and time-domain simulations demonstrate the performance of the proposed equations, which avoid the calculation of improper integrals and present an accurate performance for typical cable arrangements.