2016 Volume 9 Issue 6 Pages 242-250
Recently, an orthodox decomposition method for optimization problems by pricing mechanism based on Lagrange multipliers method has been interested as a distributed optimization approach for electric power supply problems with an electricity trading market. However, the approach can be applied to a convex case only, where the objective function is convex and the constraint set is convex, that is, Lagrange multipliers method cannot be used to nonconvex cases theoretically. In this paper, we propose to utilize the augmented Lagrangian method available to nonconvex cases. However, it is impossible to separate the augmented Lagrangian into mutually independent sub-objective functions, because squared penalty terms are added to the Lagrangian. Therefore, we regard a group of the mutually dependent sub-problems with interfered objective functions as a game problem, and present a new decomposition method in which Nash equilibrium as a rational solution is required. Availability of the presented decomposition method is verified by applying to simple energy flow problems with non-convexity, for example, electric power flow interchanging through nonlinear converter from gas energy and also market is allocated on the power flow.