Earth conduction effects in systems of overhead and underground conductors in multilayered soils

Electromagnetic interference calculations in the case of overhead lines and underground insulated conductors require the determination of the self and mutual impedances of all conductors in the arrangement. For the calculation of these impedances in nonhomogeneous soils, the use of the finite-element method is suggested. However, this is generally a complicated and time-consuming task. Analytic expressions for these impedances are derived by a solution of the electromagnetic field equations for the case of n-layer soil. The infinite integrals involved are evaluated using a numerically stable and efficient integration scheme. A typical transmission line/underground insulated pipeline arrangement is examined for various two-layer earth models and over a wide frequency range. The validity of the proposed methodology is justified by a proper finite-element method formulation. The inclusion of earth stratification leads to substantially different results for the calculated impedances. These differences affect significantly the levels of voltages and currents induced on the pipeline, even for power frequencies, justifying the need for a more detailed earth model representation.