Earth return path impedances of underground cables for the two-layer earth case

The influence of earth stratification on underground power cable impedances is investigated in this paper. A rigorous solution of the electromagnetic field for the case of underground conductors and a two-layer earth is presented. Analytic expressions for the self and mutual impedances of the cable are derived. The involved semi-infinite integrals are calculated by a novel, numerically stable, and efficient integration scheme. Typical single-core cable arrangements are examined for a combination of layer depths and earth resistivities, based on actual measurements. The accuracy of the results over a wide frequency range is justified by a proper finite-element method formulation. The differences in cable impedances due to earth stratification are presented. Finally, a simple switching transient simulation is examined to evaluate the influence of the earth stratification on transient voltages and currents.