A New Perspective on Optimal Power Flow: From Control Theory to Numerical Optimization

The optimal power flow (OPF) problem is a classical non-convex optimization problem with nonlinear constraints and multiple potential solutions. Existing methods often fail to find the global optimal solution, motivating the development of a method to identify multiple local solutions. This paper applies the optimal control principle to solve the OPF problem, aiming to systematically explore all feasible solutions within a single run. We first handle the constraints in the OPF problem using the penalty method and the Lagrange multiplier, and then reformulate it as an optimal control problem. The connection between the two problems is established by the maximum principle. Moreover, a numerical algorithm is proposed to solve this optimal control problem. The state trajectory of the system can rapidly and stably converge to the solution of the OPF problem. By designing the initial control sequence, the proposed method can successfully find multiple solutions and escape local solutions. Finally, simulations were conducted on several representative test systems to validate the potential of the proposed method in identifying multiple solutions for non-convex problems.