基于Pade近似的时滞特征值计算方法

Overtranscendental terms appear in characteristic equaiton of a power system when time delays of wide area feedback signals are considered. This make it is very difficult to obtain system critical eiganvalues via direct solution of the equation. In this paper, a method for computation of part eigenvalues of time-delayed power system is proposed by using Pade rational polynomials to approximate the time delay terms. The approximating rational polynomial is firstly transformed into equivalent state space expression then balanced. Based on interconnections with the original the power system without time delay and the wide area damping controller, the linear model for the time-delayed power system is established. Lastly, sparse eigenvalue algorithms can be used to compute part eigenvalues of the system according to the sparse characteristic of system coefficient matrices. The method make it is possoble to analysis power system small disturbance stability and design wide area damping controller by inheriting the converntional eigenvalue method and theoretical framwork. The results of the two-area four-machine system demonstate that the proposed method can accurately obtain some eigenvalues relating to system dynamic components. The number of correctly solved eigenvalues corresponding to the time delay and their accuracy strongly relates to order of the Pade rational polynomial.