大规模电力系统关键特征值计算的Arnoldi-Chebyshev方法

Calculation of Critical Eigenvalues in Large-Scale Power Systems Using Arnoldi-Chebyshev Method

介绍了一种Chebyshev多项式加速的显式重启Arnoldi算法,并用其直接求取大规模电力系统小干扰稳定性分析中状态矩阵的按实部递减的部分特征值,即关键特征值.这种方法构造了一个包含不想要特征值的椭圆,用由此椭圆确定的Chebyshev多项式获取新的初始向量,增强右端特征值对应特征向量在基向量方向的分量;进而运用新的初始向量构造Krylov子空间,求取按实部递减的特征值.3机和46机两个系统的计算结果表明,所提算法能够准确有效地求出系统的关键特征值,适合于大规模电力系统的特征分析.

Eigenvalues ordered in decreasing real parts in large-scale power systems, i.e. critical eigenvalues, are directly computed by explicitly restarted Arnoldi method with Chebyshev acceleration, where an ellipse containing unwanted eigenvalues is constructed and the Chebyshev polynomial is adopted to acquire a restart vector to amplify the components in the direction of the basis vectors for the wanted eigenvalues and damp those in the direction of the remaining basis vectors. Numerical results of the systems with 3 and 46 machines verify that the critical set of eigenvalues of large-scale power systems can be found efficiently and accurately by the proposed method.