改进的精化Cayley-Arnoldi算法计算电力系统关键特征值

Improvement of the Refined Cayley-Arnoldi Algorithm for Computing the Critical Eigenvalues of Power Systems

在用于电力系统关键特征值计算的精化Cayley-Arnoldi算法中,采用精化Ritz对替代原来的Ritz对,从而形成改进型算法。由于精化Ritz向量包含更多的子空间信息,精化Ritz值更接近其最终收敛的Ritz值,改进后的算法更有利于迭代计算的收敛;精化Ritz对能够廉价可靠地求得,计算时间增加有限。算例分析表明,仅需1次Cayley变换即可把复平面特定区域内的特征值转换为主特征值,并能明显区分相近特征值,验证了所提出算法的计算速度和收敛特性。

In the refined Cayley-Arnoldi algorithm for computing critical eigenvalues of power system, the Ritz pairs are replaced by the corresponding refined Ritz pairs to form an improved algorithm. As more subspace information is contained in the refined Ritz vectors, the refined Ritz values are closer to the finally convergent Ritz values. As a result, the improved algorithm is of advantage to the convergence of the iterative computation. The Ritz pairs can be obtained cheaply and reliably with limited increase of computing time. To transfer the concerned eigenvalues within the special area on the complex plane to dominant eigenvalues, the Cayley transformation is only required once, and the adjacent eigenvalues can be obviously distinguished. The computing speed and convergence characteristic of the proposed approach are validated on three testing systems.