Phase-domain transmission circuit model for electromagnetic transient analysis-representation of characteristic impedance matrix by a passive network

In the context of modeling in the phase-domain multi-conductor distributed-parameter transmission circuit for electromagnetic transient analysis performed in the discrete time domain, the paper develops a method based on passive network synthesis for representing the nonlinear frequency dependence of the characteristic impedance matrix function. The synthesized passive network of interconnected RLC elements preserves at any frequency the inherent stability property of this matrix function for any power transmission circuit. The network parameters are identified using the constrained optimization by which the synthesized network response is matched with the actual response derived from the characteristic impedance matrix. With the trapezoidal rule of numerical integration applied to individual elements of the synthesized network, discrete time-domain recursive sequences are derived, and then included in the overall transmission circuit model. The network synthesis procedure developed is applied to a representative transmission line, and comparative studies indicate high accuracy being achieved.