A Novel Multi-Cayley Transform for Judging Small Signal Stability of Large-Scale Power Systems

In this paper, a novel multi-Cayley transform is proposed to judge the small signal stability of large-scale power systems. Firstly, the relationships among the Cayley transform, exponential transform, and proposed multi-Cayley transform are given. As an improvement of the exponential transform, since the multi-Cayley transform has well spectral performance, the unstable eigenvalues are easy to coverage. Then, because the direct calculations of the exponential matrix and vector (EM-V) multiplications are avoided, the calculation accuracy of the proposed method is improved. Furthermore, the efficiency is also enhanced owing to the reduction of the forward and backward substitutions and the avoidance of the EM-V multiplications. Finally, case studies on the Xingo6u and Xingo3012 systems show that compared with the exponential transform method, the calculation accuracy is improved by about three orders of magnitude and the calculation time is shortened by more than 80% when calculating the unstable eigenvalues without omission.