Passivity Enforcement of Rational Models via Modal Perturbation

Most methods for passivity enforcement of rational models are based on perturbing the model parameters in a postprocessing step. In some situations, even a small perturbation can result in a significant change to model behavior, depending on the model terminal conditions and the admittance matrix eigenvalues. This paper presents a new perturbation method that is significantly less prone to model corruption by focusing on the admittance matrix eigenvalues (modes), instead of elements. This is achieved by enforcing that the relative change to the eigenvalues is minimized in the least-squares sense. By combining this approach with precise passivity checking via the Hamiltonian matrix, a guaranteed passive model is obtained. The new approach (modal perturbation) is compared to previously developed methods in terms of perturbation size, model behavior, and computational efficiency.