This is SpArta: Rigorous Optimization of Regionally Resolved Energy Systems by Spatial Aggregation and Decomposition

Energy systems with high shares of renewable energy are characterized by local variability and grid limitations. The synthesis of such energy systems, therefore, requires models with high spatial resolution. However, high spatial resolution increases the computational effort. Here, we present the SpArta method for rigorous optimization of regionally resolved energy systems by Spatial Aggregation and decomposition. SpArta significantly reduces computational effort while providing a near-optimal solution at the full spatial resolution of sector-coupled energy systems. SpArta first reduces problem size by spatially aggregating the energy system using clustering. The aggregated problem is then relaxed and restricted to obtain a lower and an upper bound. The spatial resolution is iteratively increased until the difference between upper and lower bound satisfies a predefined optimality gap. Finally, each cluster of the aggregated problem is redesigned at full resolution. For this purpose, SpArta decomposes the original synthesis problem into subproblems for each cluster. Combining the redesigned cluster solutions yields an optimal feasible solution of the full-scale problem within a predefined optimality gap. SpArta thus optimizes large-scale energy systems rigorously with significant reductions in computational effort. We apply SpArta to a case study of the sector-coupled German energy system, reducing the computational time by a factor of 7.5, compared to the optimization of the same problem at full spatial resolution. As SpArta shows a linear increase in computational time with problem size, SpArta enables computing larger problems allowing to resolve energy system designs with improved accuracy.