Estimating Number of Critical Eigenvalues of Large-Scale Power System Based on Contour Integral

This paper proposes an improved stochastic estimation method based on contour integral to estimate the number of critical eigenvalues. The stochastic estimation method transforms the eigenvalue numbers' calculation into summing the traces of a series of inverse matrices. And then, a stochastic strategy is used to estimate the trace of the inverse matrix. However, the method results in an unacceptable error when the state matrices of many practical power systems are ill-conditioned. To solve this problem, the improved algorithm is proposed by formulating a satisfactory matrix for trace calculation artificially instead of randomly with the help of the well-known greedy algorithm based on graph coloring. It is proved to be much more reliable when dealing with ill matrix. The proposed method based on contour integral is very suitable for large-scale power systems due to the element distribution of descriptor matrices makes it possible to construct only one fixed matrix at all integral points. Moreover, the calculation efficiency is further improved by calculating implicitly without destroying the sparsity of descriptor systems. Numerical experiments indicate that the proposed method can significantly improve accuracy without considerably increasing the calculation time. And the approximate eigenvalue number can fully meet the needs of subsequent algorithms based on contour integral to calculate the specific eigenvalues.