An adaptive sampling technique to correct large passivity violations

Rational functions for approximation of the admittance matrix elements of a linear power system/component are used to increase the computational efficiency for the analysis of electromagnetic transients. The challenge in this regard is passivity enforcement of the resultant model to guarantee numerical stability of the analyses. The main cause of passivity violation of the equivalent model of a passive system/ component, in a specific frequency region, is the selection of unsuitable and/or insufficient number of frequency samples for fitting. The more severe the passivity violations are, the more effort is required to enforce passivity. This paper presents an adaptive sampling technique for passivity enforcement as a post-processing tool. This approach can effectively correct large passivity violations. Based on this method a non passive region is identified via a pure algebraic method exploiting the existence of pure imaginary eigenvalues in the Hamiltonian matrix of the system state space equations. A bisection method is employed to determine the adaptive frequency samples which are added to the existing samples in a refitting process. The proposed method is applied to correct passivity violation of the admittance model of a two winding transformer.