Direct numerical evaluation of earth return path impedances of underground cables

The lossy earth return path influences significantly the impedances of underground power cables, especially in cases where transient simulation models are of interest. The use of approximations for the calculation of the earth correction terms proves to be inaccurate, especially at high frequencies or for low earth resistivities. A novel direct numerical integration scheme for the evaluation of the infinite integral terms is presented. The new method proves to be numerically stable and efficient in all cases examined. Results obtained by the novel integration scheme are compared with those obtained by other approaches, as well as by a finite-element method formulation for several single-core cable configurations and for cases of homogeneous and multilayered earth.