A full-space conformal mapping for the calculation of series impedance of overhead transmission lines and underground cables

摘要

This paper introduces a 2-dimensional conformal transformation scheme for the parameter extraction of an arbitrary overhead transmission line or underground cable in an unbounded lossy space. The quasi-magnetic Helmholtz equation is solved using the finite element method (FEM). A modified bilinear transformation is employed to transform the unbounded domain to a bounded domain that is more efficiently handled in FEM simulations. Due to conformality of the transformation, the magnetic stored energy, which is used to calculate the per-unit-length inductance matrix, L, is independent from the mapping factor while the longitudinal current and its corresponding dissipated energy, which is used to calculate the per-unit-length resistance matrix, R, are functions of the mapping factor. Numerical results for an overhead transmission line and a buried multiconductor cable are compared with those calculated using Carson's approximation and Wedepohl's formula from near DC to the high frequency range.