Enforcing Passivity for Admittance Matrices Approximated by Rational Functions

A linear power system component can be included in a transient simulation as a terminal equivalent by approximating its admittance matrix Y by rational functions in the frequency domain. Physical behavior of the resulting model entails that it should absorb active power for any set of applied voltages, at any frequency. This requires the real part of Y to be positive definite (PD). We calculate a correction to the rational approximation of Y that enforces the PD criterion to be satisfied. The correction is minimal with respect to the fitting error. The method is based on linearization and constrained minimization by quadratic programming. Examples show that models not satisfying the PD criterion can lead to an unstable simulation, even though the rational approximation has stable poles only. Enforcement of the PD criterion is demonstrated to give a stable result.