Inverse Laplace Transform of Sunde’s Formula for the Ground Impedance of Buried Cables

The time-domain calculation of electromagnetic transients in multi-conductor lossy overhead lines and buried cables requires the evaluation of the transient ground resistance matrix. For the case of overhead lines, analytical expressions for the transient ground resistance obtained by solving the inverse Laplace transform of Sunde’s formula have been recently presented. This paper presents the expressions obtained by the analytical inverse Laplace transform of Sunde’s formula for the case of buried cables. The results provided by the proposed analytical expressions agree with those given by the numerical inverse transform of Sunde’s formula. The new expressions are adopted for the calculation of the per-unit-length voltage drop in a multiconductor underground line. The voltage drop waveforms are compared with those given by recently proposed time-domain analytical expressions that neglect displacement currents.