Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems

Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply. Grid-tied batteries typically employ power converters, where part-load efficiencies vary non-linearly. While this non-linearity can be modeled with high accuracy, it poses challenges for optimization, particularly in ensuring computational tractability. In this paper, we consider a non-linear BESS formulation based on the Energy Reservoir Model (ERM). A data-driven approach is introduced with the input-convex neural network (ICNN) to approximate the nonlinear efficiency with a convex function. The epigraph of the convex function is used to engender a convex program for battery ERM optimization. This relaxed ICNN method is applied to a battery revenue maximization problem and is compared with three other ERM formulations (nonlinear, linear and mixed-integer). Specifically, ICNN-based method appear to be promising for future battery optimization with desirable feasibility and optimality outcomes across revenue maximization use-case.