A finite-element analysis of electromagnetic field produced by ELF sources enclosed by a nonlinear ferromagnetic pipe

The electromagnetic field produced by extremely-low-frequency (ELF) sources within a nonlinear ferromagnetic pipe is of practical interest especially for underground power cables. We present a finite element analysis for determining the electromagnetic field everywhere generated by ELF sources enclosed by a nonlinear ferromagnetic pipe, using an underground pipe-type cable as example. The finite-element method is employed to compute the potentials and fields in the interior region. The information on the potentials and fields obtained can be used to determine the cable parameters of practical interest, such as the zero-sequence impedance. In the finite-element solution, special attention is paid to the nonlinear B-H characteristics of the pipe, and an iterative procedure is employed to determine the varying permeability of the pipe. Then, to determine the fields in the region exterior to the pipe, we employ the equivalence principle to formulate a model equivalent to the exterior region. In the equivalent model, the equivalent surface currents can be obtained directly from knowledge of the fields on the outer surface of the pipe as the finite-element solutions. Using the equivalent surface currents, the magnetic field outside the pipe is computed.