Series-impedance of underground cable systems

A general solution for the magnetic field in the soil is developed that satisfies arbitrary conditions on a set of underground cylindrical surfaces at a finite depth below the earth/air surface. The solution takes into account singularities of all orders located in the axis of each circular boundary, allowing boundary conditions on the earth/air plane to be satisfied and imposing regularity at infinity. The method is used to evaluate the series-impedance matrix of a system comprising three underground cables in a flat configuration. Numerical results are presented for the contribution of the Earth return path to the cable self-impedances as well as for the mutual impedances between cables. The results are compared with Pollaczek´s classical solution