An Improved Contour-Integral Algorithm for Calculating Critical Eigenvalues of Power Systems Based on Accurate Number Counting

This paper proposes an improved contour-integral algorithm based on exact number counting inside the interesting region to calculate critical eigenvalues of large-scale power systems. Firstly, the difference between the eigenvalues inside and outside the region of the non-hermitian matrix is derived using trapezoidal integral. Based on this difference, a small matrix can be skillfully constructed with reasonable parameters so that the exact number of eigenvalues is precisely equal to the eigenvalue number of the small matrix whose real parts are larger than 0.5. Further, rational parameters can be adaptively adjusted to obtain exact results exploiting the minimum of eigenvalues of the constructed matrix. The exact eigenvalue number can help set the contour-integral algorithm's initial subspace. We automatically expand the space by comparing the results of each iteration with the exact number to ensure that all eigenvalues are obtained. Numerical experiments demonstrate the effectiveness and reliability of the precise number counting algorithm and the improved contour integral algorithm.