A Novel Method to Compute Multiple Optimal Solutions for ACOPF Problems

The AC optimal power flow (ACOPF) problem is nonlinear and non-convex, which is a great challenge in obtaining the global optimal solution. Popular OPF methods are local improvement search methods that produce solutions with local optimality. Two issues need to be solved to explore the global optimal solution: (i) escape from the existing local solution, and (ii) find a superior solution. In this paper, a systematic methodology based on an augmented quotient gradient system (AQGS) is proposed to address both of these issues. The method consists of two main stages. Stage I relaxes the OPF problem and detects the disappearance of the optimal solution, and Stage II restores the original problem and finds a superior optimal solution. The proposed method is illustrated in several well-known multi-solution IEEE systems and results show that the proposed method can escape from current local solution and obtain higher-quality optimal solutions, and even the global optimal solution, effectively.