A Robust Mathematical Programming Model for Energy Storage Scheduling Using Minimax Decision Principles

Abstract

Integrating variable renewable resources into modern power systems requires scheduling methods for battery energy storage systems (BESS) that can operate under high net-load forecast errors and price uncertainty. Deterministic scheduling is subject to parameter mishaps, scenario-based stochastic programming suffers from scenario explosion and poor out-of-distribution performance, and conventional single-stage robust optimization methods are heavily criticized for being too economically conservative. In this paper, a two-stage minimax mathematical programming approach to BESS scheduling is proposed instead, where charging and discharging of batteries are carried out after uncertainty has been resolved while charging and discharging schedules are performed prior to uncertainty events using the worst-case net-load trajectory and price determined from a budget managed polyhedral uncertainty region. Transformation of the tri-level formulation into a solvable master space problem is carried out using strong duality theorem of linear programming. The model reformulated is then solved by the Column and Constraint Generation (C&CG) method which is known to provide finite convergence to globally epsilon-optimal solutions based on the limited number of vertices of the uncertainty set. The numerical experiments on the case study of a 24-hour operation of a lithium-ion battery of 500 kW are also conducted based on the evaluation of more than 1000 Monte Carlo out-of-sample scenarios. The results show that the new proposed methodology provides a solution after 5 iterations of C&CG in 12.4 seconds. While the in-sample costs of applying the proposed methodology amounted to 1410.30 against 1240.50 for the deterministic model, the worst-case out of-sample cost is reported to be 1485.60 for the proposed methodology compared to 2150.80 for the deterministic approach and 1820.10 for the conservative static approach. The success of the method in achieving the feasibility constraint of 0.0% in terms of violation rate is also remarkable. The results of the sensitivity analysis are showing that with moderate budget constraint settings, the maximum margins of robustness of 98.4% are possible while saving 73% in terms of economic savings.