On Passivity Tests for Unsymmetrical Models

Rational models (not including explicit sources as in the case of generators) must be passive in order to guarantee stable simulations. Passivity tests for use with perturbation-type passivity enforcement methods are usually based on frequency sweeping or calculation of the eigenvalues of a Hamiltonian matrix derived from the model´s parameters. Recently, half-size test matrices have been derived which reduce the computation time of eigenvalues by a factor of about eight. In this paper, we elaborate on the passivity assessment for unsymmetrical models. We show that the half-size test matrix approach is valid only for the symmetrical case, while the full-size Hamiltonian must be used for unsymmetrical models.