Computation, properties, and realizability of the characteristic immittance matrices of nonuniform multiconductor transmission lines

Power lines are longitudinally nonuniform, nonsymmetrical systems, where ordinary modal analysis, originally conceived for uniform multiconductor transmission lines (MTL), can be utilized only as a zeroth-order approximation. In this paper, we present an accurate analysis of nonuniform MTLs based on the frequency-domain transmission-matrix formalism for 2n-port systems, where two unequal characteristic immittance matrices need to be defined, one for forward propagation and another for backward propagation. This paper, focused on the characteristic (or surge) immittance matrices, shows how they can be computed, describes their general properties, and reveals, for the first time, that in some cases they may not be physically realizable, meaning that a matched termination made of purely passive lumped components may not exist. The matrix theory developed in the paper is illustrated with simulation results concerning three-phase power line configurations where resonance phenomena take place at certain critical frequencies.