A Homotopy-Based Method for Robust Computation of Controlling Unstable Equilibrium Points

This paper proposes a homotopy-based method for efficiently computing and precisely determining controlling unstable equilibrium points (CUEPs) in transient stability analysis and screening using direct methods. The proposed method is intended to overcome potential numerical convergence problems associated with computing CUEPs. These convergence problems are mostly due to irregularities in the region of convergence of CUEPs which make it difficult to determine suitable initial points. The most commonly used initial points in computing CUEPs are minimum gradient points (MGPs) on the stability boundary which in turn rely on the determination of exit points (EPs-points at which sustained-fault trajectories exit system stability boundaries). However, determination of MGPs and EPs are computationally involved and sophisticated numerical methods have been introduced such as stability-boundary-following procedure and shadowing method to correct the solution trajectory. The proposed method does not depend on MGPs and also does not require accurate EPs. The proposed method maps the solution from EPs to the CUEPs. The proposed method is applied on several known systems including the NE 39 bus system and the reduced WECC system and the results are provided. The results are compared with the traditional methods such as Boundary of stability region based CUEP method (BCU method).