A modified general Cayley transformation for the calculation of critical eigenvalues of large-scale power systems with DAE models

The computation of critical eigenvalues of a large-scale matrix in an efficient manner is challenging for small-signal stability analysis of power systems. Although the generalized Cayley transformation has been used extensively for calculating the critical eigenvalues, this approach breaks the sparsity of augmented state matrix during the transformation, and subsequently degrades the computation efficiency. In this paper, a modified generalized Cayley transformation is proposed to map the critical eigenvalues to the ones with the largest magnitudes. The biggest advantage of this method is that the proposed transformation can preserve the sparsity of the augmented state matrix, resulting in better performance, convergence and robustness, as compared to the conventional generalized Cayley transformation method. A rigorous proof is presented to show the accuracy and the effectiveness of the proposed method. Numerical experiments are tested on both the IEEE 118-bus system and the Hainan power grid to illustrate the validity of the proposed method.