On the optimal solutions for load-flow equations

A power system is always required to operate at least cost or least transmission losses when stability and reliability conditions are satisfied. The operation problems of power systems can be generally formulated as optimal power flow problems, which are nonlinear static optimization problems with a large number of equalities and inequalities. This paper aims to derive the detail conditions for the existence of an optimal power flow solution, which guarantee that a power system not only has a feasible solution but also can be operated optimally from the economic viewpoint.