# Decomposition Methods

The energy system optimization models we study all have in common that they are very large wherefore we come to the boundaries of what we can compute. Nevertheless, the models are also highly repetitive. For instance, replicable structures are found regarding the spatial resolution, e.g. a similar superstructure of technologies is found in every node, or the temporal resolution, e.g. the model for a storage is similar for every day.

This offers to opportunity of to pursue decomposition of the model. The condition is that the replicable structures are only weakly coupled. For instance, it is reasonable to assume that what happens on a given day only influences the next day in a weak manner, e.g., through the storage fill level at the end of the day. There are known techniques in the literature which we will use to exploit this structure, among these are Lagrangian relaxation or Benders decomposition. Those methods allow to distribute the work of finding an optimal solution to many different compute nodes by iteratively optimizing submodels of the original model, as visualized in Figure 1.

Our goal is to exploit these techniques for energy system models and show how they can be used to work in a high performance computing environment. Further, we want to benchmark them to existing solving approaches and make the implementation of the methods open-source available.