An efficient method for calculating power flow solutions and the closest bifurcation point using mathematical programming

This paper presents an efficient method for calculating the closest bifurcation point and a pair of multiple power flow solutions with mathematical programming. The formulation of the method may be expressed as the minimization problem to evaluate the closest bifurcation point for given initial conditions. Making use of the conditions of a pair of multiple power flow solutions, they are decomposed into the sum of the bifurcation point and the deviation vectors. The solution is evaluated by mathematical programming so that the closest bifurcation point is evaluated by minimizing the magnitude of the deviation vector to given power system conditions. The proposed method is successfully applied to a sample system