Padé approximation based method for computation of eigenvalues for time delay power system

Transcendental terms appear in the characteristic equation of a power system and results in an infinite number of eigenvalues, when time delays in the feedback signals of power system wide-area damping controllers are considered. This makes it very difficult to obtain system eigenvalues via direct solution of the equation. In this paper, a method for computing a reduced set of eigenvalues of a time delay power system is proposed by using Padé rational polynomials to approximate the delays. The Padé polynomials are firstly transformed into their equivalent state space representations. By interconnecting the models of the open-loop power system, wide-area damping controllers and the state space representations of time delays, the linearized model for the closed-loop power system is then established and a reduced set of eignevalues of the system can be computed. The method has been tested on the New England 10-machine 39-bus test systems and compared with the eigenvalue computation method in the software package DDE-BIFTOOL. It shows that the proposed Padé approximation-based method can accurately obtain nearly all of the eigenvalues relating to system dynamic devices. The number of eigenvalues relating to time delays that can be correctly computed and their accuracy strongly relates to the orders of the Padé rational polynomials.