Battery Optimization for Power Systems: Feasibility and Optimality

The deployment of battery energy storage systems (BESS) is necessary to integrate terawatts of renewable generation while supporting grid resilience and reliability efforts. Optimizing battery dispatch requires predictive battery models that accurately characterize the battery state of charge (SOC) to ensure that the battery operates within the energy and power limits and avoids unexpected saturation effects. Furthermore, most BESS are unable to simultaneously charge and discharge, which begets an additional, non-convex complementary constraint. This paper presents and compares recently developed predictive battery models that side-step the non-convexity while providing supporting analysis on modeling error and optimal parameter selection. Specifically, insights for four different predictive BESS formulations are presented, including non-linear, mixed-integer, linear convex relaxation, and linear robust formulations. Additionally, two two-stage approaches are also considered. Analysis is conducted on optimal parameter selection for two of the methods, as well, as providing a new and improved SOC error bound on the relaxed formulation and the role of sustainability constraints on the robust formulation. Through the lens of relevant BESS use-cases, the paper discusses optimality and feasibility guarantees between