Optimal scheduling of battery energy storage system operations under load uncertainty

This paper investigates the optimal scheduling of battery energy storage system operations considering energy load uncertainty. We develop a novel two-stage distributionally robust optimization model to determine an optimal battery usage schedule that minimizes the worst-case energy costs considering peak load costs. The model leverages deep-learning-based probabilistic forecasting in the construction of the ambiguity set. Specifically, we develop a Deep Autoregressive Recurrent Networks model to generate a probabilistic forecast of energy loads over a time horizon. The output of the forecasting model is then used to construct a marginal-moment ambiguity set for the distributionally robust optimization model. To solve the proposed model, we establish a closed-form characterization of the optimal second-stage objective function value. Leveraging this closed-form expression and using second-order conic duality, we derive an exact single-level mixed integer second-order conic reformulation of the problem. Extensive computational experiments, conducted on a real dataset, demonstrate the value of our proposed model and the effectiveness of the resulting battery schedule. The results show that the proposed model outperforms several benchmarks, including two-stage stochastic programming. Furthermore, the accuracy of the load forecast significantly impacts the effectiveness of the optimal battery schedule in eliminating peak loads by achieving up to 18% reduction in the maximum energy load.