Storage-like devices in load leveling: Complementarity constraints and a new and exact relaxation method

Storage-like devices (SLDs), which include energy storage systems as well as devices with similar properties such as electric vehicles, can be exploited for load leveling. However, to prevent simultaneous charging and discharging of an SLD, complementarity constraints should be included in the optimization model, which makes the problem strongly non-convex. Mixed-integer programming (MIP) methods are commonly used to solve such problems; however, this results in long solution time to achieve an approximate optimal solution. Therefore, a method to efficiently find optimal solutions of load-leveling problems with SLDs is desirable. Here, we report a load-leveling optimization model for a system with SLDs and show that the complementarity constraints can be exactly relaxed under two sufficient conditions so that a convex relaxed model can be solved instead. Moreover, the exactness of the relaxation can be determined prior to solving the relaxed model, and the sufficient conditions are usually satisfied in practical situations. The numerical studies verify the theoretical analysis and show that an equally good optimal solution of the load-leveling problem with SLDs can be obtained far more efficiently by using the proposed method than a commonly used MIP method.