Robust computation of the controlling unstable equilibrium points in transient stability analysis

In power system transient stability assessment, direct methods have been used to estimate the critical clearing time on real-time applications. Direct methods that use the controlling unstable equilibrium point concept are accepted as efficient to first swing transient stability analysis. However, some difficulties are observed in the computation of the PEBS exit point and the controlling unstable equilibrium point (CUEP) in such studies. To improve the reliability in these computations, a new algorithm that can be applied to the exit point detection and to the CUEP detection is proposed in this paper. The proposed algorithm improves the PEBS exit point and the CUEP detection rates by verifying at some points if the attraction area was abandoned. This verification is done to precisely detect the CUEP stable manifold, even in regions where the vector field has abrupt directions changes, e.g. near equilibrium points. The proposed methodology is tested and compared with other direct methods for the IEEE 14-bus and New England systems.