基于精化Arnoldi方法的小信号稳定性关键特征值计算

将精化Arnoldi方法引入到大型电力系统小信号稳定性关键特征值的计算。为了求解在给定位移点附近的特征值,先对状态矩阵作位移求逆变换。由于精化向量包含更多的子空间信息,可用精化向量代替相应的Ritz向量作为特征向量的近似,用精化位移代替准确位移作为位移量来改进Arnoldi方法。在重启动的选择上,用隐式重启动技术加速算法的收敛。算例分析表明,精化Arnoldi方法能够可靠和有效地计算大型电力系统的关键特征值。

Application of the refined Arnoldi method to the calculation of critical eigenvalues in small signal stability analysis

The refined Arnoldi method is applied to calculate critical eigenvalues in small signal stability in the paper.Shift and invert transformation is used for computing a number of eigenvalues close to a given shift.Because the refined Ritz vectors contain more information about the subspace,the Ritz vectors are replaced by the corresponding refined Ritz vectors and the exact shifts are also replaced by the refined shifts.In order to improve the convergence,an implicit restarted scheme is applied to this method.Numerical experiment indicates that the proposed method can calculate the critical eigenvalues of the large power systems reliably and effectively.