A Parallelized Contour Integral Rayleigh-Ritz Method for Computing Critical Eigenvalues of Large-Scale Power Systems

A contour integral based spectrum transform (CIST) is first introduced for computing critical eigenvalues of power systems. Different from commonly-used shift-invert and Cayley transforms, CIST is able to give equal dominance to the eigenvalue set in a customizable complex plane area, which is defined by a given integral curve. The spectral property of CIST brings high distinctiveness of eigenvalues enclosed by the integral curve in transformed spectrum, along with well convergence of these eigenvalues in subspace methods. With CIST, Rayleigh-Ritz process is used to build subspace and extract eigenvalues. An iterative scheme is proposed for subspace refinement. The iterative contour integral Rayleigh-Ritz method is implemented with full utilization of parallel potentiality in contour integral numerical evaluation. Experiments on three test systems of different scales are performed to validate the reliability, computational efficiency, and parallel scalability of the proposed method.