An Exponential Transform Based Dual-Layer Krylov Subspace Method for Computing Unstable Modes of Power Systems

The detection and calculation of the rightmost modes are essential in the small signal stability assessment and control of power systems. This paper proposes an exponential transform based dual-layer Krylov subspace (DLKS) method for computing all unstable modes of power systems. Firstly, the exponential transform is introduced to map the unstable modes to the dominant modes outside the unit circle of the transformed spectrum. Then, based on the transformation, a Krylov decomposition is implemented to form the outer-layer Krylov subspace (OLKS) for solving the transformed dominant modes. In the process of forming the OLKS, the exponential matrix-vector multiplication (EMVM) needs to be solved. Next, combined with an accelerating convergence technique, the inner-layer Krylov subspace (ILKS) is formed to calculate the EMVM. Finally, four public source systems, namely the Xingo, Xingo6u, Juba5723 and Bauru5727 systems, are applied to verify the correctness and efficiency of the proposed method. Numerical experiments indicate that the proposed method can calculate all the unstable modes with high accuracy under the premise of ensuring calculation efficiency.