Passivity enforcement of wideband model through a new and full perturbation formulation

Passive component models are necessary to ensure numerical stability in the simulation of electromagnetic transients in power systems. However, it is challenging to represent transmission lines and cables with frequency-dependent wideband models that are accurate, efficient, and passive. This paper proposes a new method for the passivity enforcement of wideband line and cable models. The wideband models rely on pole-residue identification of characteristic admittance and propagation function in rational forms. In case the resulting models are not passive, the proposed method simultaneously applies perturbation to the residue matrices of characteristic admittance and propagation function. The set of equations related to passivity enforcement through the residues of propagation function in phase domain is complex and presented for the first time in this paper. The proposed approach minimizes the overall perturbation for maintaining passivity as opposed to the existing simplified approaches that rely on the perturbation of the residues of either characteristic admittance or diagonal elements of propagation function. The performance of the method is validated with application cases, and it is shown that it outperforms the existing methods that seek simplification in problem formulation.