Load Control Problems in Direct Current Distribution Networks: Optimality, Equilibrium of Games

Due to the promising development of direct current (dc) distribution networks, we focus on the demand-side management (DSM) problems which aim at the minimization of operational costs in dc distribution networks. Based on the established voltage model of power electronic loads, we formulate a DSM optimization problem that coordinates the bus voltage by minimizing the system cost, and the underlying optimization problem is nonconvex. In order to solve this nonconvex problem, we first reformulate it as a difference of convex programming problem, and then propose a novel algorithm based on branch and bound to implement the optimal solution. It is shown that the system is guaranteed to converge to the global optimum under the proposed method. As demonstrated with numerical examples, we analyze the convergence and global optimality of the proposed method, and discuss the computational complexity and scalability with respect to the size of distribution networks. Moreover, in case each of individual loads can make its own decisions by itself, the underlying optimization problem is implemented in the context of the noncooperative game. The existence of the Nash equilibrium is verified and demonstrated through simulation results.