Potential-game theoretical formulation of optimal power flow problems

This paper proposes a potential-game theoretical formulation of the optimal power flow (OPF) problem with practical operation constraints. Each generator operates as an independent player with marginal contribution utility function to minimize the generation cost. The proposed formulation alleviates the computational burden introduced by inequality constraints as they are converted to feasible action sets of players. Therefore, both the formulation and solution process of the constrained OPF problem are greatly simplified. A learning algorithm with guaranteed convergence to Nash equilibrium for potential games, called Carnot best response with inertia, is applied to solve the OPF. Analytical analysis on how players act as best responses to others is provided to investigate the economic reasoning of generator operations. As a numerical example, the solutions to a 15-unit system OPF by the proposed method are compared with solutions by particle swarm optimization (PSO) and genetic algorithms (GAs). The proposed formulation show faster convergence and better result in terms of less generation cost.