Bilevel optimization model for sizing of battery energy storage systems in a microgrid considering their economical operation

Abstract

Battery energy storage systems (BESSs) play extremely important roles in managing power supply and demand in a microgrid. The BESSs, on the other hand, have problems of high initial investment costs and limited lifetime. In this paper, a problem formulation and its solution are presented for sizing an aggregated BESS in a microgrid that minimizes the sum of initial costs of the aggregated BESS and operational costs of the microgrid. The target problem is originally categorized into a bilevel optimization because it comprises two optimization problems: the sizing of aggregated BESS and the operational scheduling of microgrid’s components. The authors, however, apply the Karush–Kuhn–Tucker approach and reformulate the target problem as a single-level optimization problem. This reformulation enables us to treat the problem as if it was a type of operation scheduling problems. That is, the solution techniques developed to obtain the optimal operation scheduling are applicable by the problem reformulation. As the basis for the solution method, an algorithm combining binary particle swarm optimization and quadratic programming is applied in this paper. To verify the validity of the proposal, numerical simulations are performed, and their results are discussed.

Keywords

• Microgrids
• Battery energy storage systems
• Bilevel optimization
• Karush–Kuhn–Tucker approach
• Sizing optimization
• Operation scheduling optimization