Optimal Operation of Battery Energy Storage Under Uncertainty Using Data-Driven Distributionally Robust Optimization

•The participation of a battery in the demand side management along with day-ahead and real-time markets faces uncertainties in market-clearing prices, energy demand, and available power capacity.•To accommodate uncertain parameters in optimization problems, two common techniques include stochastic optimization (SO), and robust optimization (RO).•Th main drawback in SO is that it requires a large amount of historical data for accurate probability distributions, which in many cases is not available.•The challenge in RO is that the worst-case scenario is normally extreme with relatively low probability. Thus, the solution might be conservative and not necessarily the most economical solution.•The advantage of the proposed Data-Driven Distributionally Robust Optimization (DDRO) is to outperform SO and deterministic approaches in minimizing the cost of this multi-variable stochastic optimization problem in terms of out-of-sample performance. This paper proposes a conditional value-at-risk (CVaR)-based approach to deal with uncertainties in optimizing the participation of a battery storage in both the electricity market and demand-side management (DSM). A data-driven distributionally robust optimization (DDRO) methodology is used to solve the proposed mean-risk portfolio optimization model. The participation of a battery in DSM along with day-ahead and real-time markets (e.g., energy, spinning reserve, regulation up, and regulation down) faces uncertainties in market-clearing prices, energy demand, and available power capacity. Since in this application, the distribution of the uncertain parameters is only observable through a finite training dataset, the proposed DDRO methodology uses the Wasserstein metric to construct a ball in the space of probability distributions, which is centered at the uniform distribution on the training samples. Then, based on the worst-case distribution within this Wasserstein ball, it seeks decisions that perform best. The proposed DDRO problem over Wasserstein balls is reformulated as a finite convex problem, tested, and verified using real market data and supply/demand profiles. The results are compared with the ones obtained from other optimization methods, including deterministic and classical stochastic optimization, which validates the high performance of the proposed DDRO over finite historical sample data.