A bilevel programming formulation and trust region approach for closest critical point of voltage stability

A new load distribution domain (hyper-pyramid) model is presented for calculating closest critical point of voltage stability considering uncertainties of load change. The nonlinear bilevel programming formulation and the trust region based algorithm are used to search the closest critical point. Firstly, the critical point along a known load change direction is determined, then an approximate formulation with simple upper and lower bounds is built. An iterative process is established to search the closest critical point based on the idea of trust region method. The reactive power limits of generators are considered in calculating the critical points. Case studies show that the proposed method is fast and robust and have good global searching performance. The weak areas and nodes of the system for voltage stability can also be found.