Chance Constrained Scheduling and Pricing for Multi-Service Battery Energy Storage

Abstract

This paper studies optimal day-ahead scheduling of grid-connected batteries that simultaneously provide three services: 1) load shifting, 2) real-time balancing, and 3) primary frequency control (PFC). The uncertainties of load and frequency are incorporated in the cost-minimizing scheduling problem via chance constraints. The resulting chance-constrained problem is then reformulated into a mixed-integer second-order cone program (MISOCP) that can be solved by commercial solvers. However, it is computationally formidable to obtain the globally optimal solution to the MISOCP due to the big problem size. To obtain a suboptimal solution quickly, a heuristic based on penalty alternating direction method (PADM) is developed to solve the MISOCP. Fixing the integer solution returned by the heuristic, we adopt the duality of the second-order cone program (SOCP) to price the three services in the local market. Theoretical analysis of the market equilibrium, individual rationality, and balanced budget is given. Real-world data of load, frequency, and price in the French grid is used in simulation. The results show that the proposed heuristic is computationally efficient, and the pricing results can guarantee a positive utility for each of the batteries, incentivizing them to provide services.