A method to approximate a closest loadability limit using multiple load flow solutions

A new method is proposed to approximate a closest loadability limit (CLL), or closest saddle node bifurcation point for power systems, using a pair of multiple load flow solutions. More strictly, the obtainable points by the method are the stationary points including not only CLL but also farthest and saddle points. An operating solution and a low voltage load flow solution are used to efficiently estimate the node injections at a CLL as well as the left and right eigenvectors corresponding to the zero eigenvalue of the load flow Jacobian. They can be used in monitoring loadability margin, in identification of weak spots in a power system and in the examination of an optimal control against voltage collapse. Most of the computation time of the proposed method is taken in calculating the load flow solution pair. The remaining computation time is less than that of an ordinary load flow