Modeling battery aging in linear energy system optimizations by applying convex hulls - accuracy benefits and computational costs

Linear energy system optimization plays an important role in the design of future energy systems, due to its availability and low computational requirements. While linear optimization offers many benefits, the rise in popularity of battery storage and its use cases represents a challenge, commonly causing oversimplification by ignoring aging and its causes. Thus, this paper aims to include battery aging and subsequently battery optimized operation, to lower aging, into linear system optimization. Two approaches are highlighted, namely a basic linear aging implementation, as well as a convex hull approximation. These are then compared against the generic implementation found in oemof.solph, an open source energy modeling tool, to assess the benefits and drawbacks of including aging. The chosen case study for evaluation models a buffer storage for an overhead line island to reduce peak loads, enabling connections to weaker grids. The results show up to 46.9 % lower battery aging for the convex approach, compared to the generic baseline. Furthermore, the amount of aging is precisely determined by the convex approach, with errors below 0.4 % and the computational times close to the same magnitude, due to the lack of mixed integer linear programming. The suggested approaches of integrating battery aging into linear optimization should be integrated into future models to better predict and reduce battery lifetimes, allowing for better cost calculations in such systems.