Relaxation and Projection Alternating Direction Method of Multipliers for Unit Commitment Problem in Distributed EMS

A distributed energy management system (EMS) is designed to improve the efficiency of energy use across multiple EMSs by coordinating their operations. We previously proposed an optimization method using the alternating direction method of multipliers (ADMM). The unit commitment problem (UCP) involves determining the start-stop states and outputs of energy conversion equipment, where the decision variables include binary (0-1) variables. Since ADMM does not guarantee convergence for problems involving binary variables, it cannot be directly applied to UCP problem. A relaxation and projection method proposed by Takapoui et al. modifies ADMM to handle optimization problems with discrete variables. In this paper, we propose a method for applying ADMM with relaxation and projection to distributed EMSs.