Optimal Dispatch of Battery Energy Storage System Using Convex Relaxations in Unbalanced Distribution Grids

This paper presents second-order cone programming (SOCP) and semidefinite programming (SDP) models to solve the multiperiod optimal control problem of unbalanced three-phase distribution grids with battery energy storage systems. The decision variables are the active and reactive power of the battery energy storage system. The objective is to minimize the power loss and energy purchase cost from the distribution substation. The optimal dispatch problem requires solution by volt/VAR optimization. The SOCP and SDP models ensure global optimum of original nonconvex nonlinear programming problem. Multiobjective volt/VAR optimization is performed and the benefits of reactive power support from battery energy storage systems are explored. A simulation-based heuristic to extract rank-one solution from the higher rank solution of SDP model is also proposed. Empirical results show the numerical stability and exactness of the proposed three-phase SOCP and SDP models.