Relaxing Complementarity Constraints of Energy Storage with Feasibility and Optimality Guarantees

The fast development of energy storage is attracting attention in storage-concerned power system optimization. The complementarity constraints of energy storage introduce non-convexity, which increases the complexity of power system optimization. To circumvent such non-convexity, this paper studies the relaxation for the inherent fulfillment of complementarity constraints in general storage-concerned power system optimization. This paper first develops a linear constraint to replace the complementarity constraint in the original optimization problem. It is proven that the resulting solution can be recovered to a feasible solution of the original problem. Backed by the previous feasibility guarantee, this paper further studies the ex-ante sufficient conditions with which the optimality of the original problem will not be affected under the relaxation of complementarity constraints. Numerical experiments in five transmission and distribution systems, including four IEEE test systems and one utility system, verify the effectiveness of the proposed method.