Reduced-order method for computing critical eigenvalues in ultra large-scale power systems

This study presents a novel reduced-order method to find critical eigenvalues of ultra large-scale power system. First, the numerical solution of matrix exponential is computed by precise time-step integration. Secondly, based on the numerical solution, the numerical curve of the trace of matrix exponential is formed. Thirdly, the candidates of critical eigenvalues are extracted from the numerical curve of the trace by Prony analysis, and finally, a set of weight coefficients is calculated to confirm critical eigenvalues from candidate eigenvalues. Since the trace contains all eigenvalues, no critical eigenvalue can be lost in analysing the numerical curve of the trace. In the later period of time integration, the effect of all non-critical eigenvalues to the trace is decayed and oppositely the effect of all critical eigenvalues is amplified. Thus, several rightmost eigenvalues can only be extracted from the numerical curve of the trace. Case studies for 16 and 9004 order system have validated that the proposed method can be used to find all critical eigenvalues of ultra large-scale power system.