Inverse methods: How feasible are spatially low-resolved capacity expansion modeling results when dis-aggregated at high resolution?

Spatially highly-resolved capacity expansion models are computationally intensive. As a result, models are often simplified to a lower spatial resolution by clustering multiple regions to a smaller number of representatives. However, when capacity expansion is modeled for electricity systems at a coarse resolution, the aggregation mixes sites with different renewable features while removing transmission lines that can cause congestion. As a consequence, the modeling results may represent an infeasible electricity system when the capacities are fed back into higher spatial detail. Thus far there has been no detailed investigation of how best to dis-aggregate the capacity expansion results into its original resolution and whether the spatially highly-resolved dis-aggregated model is technically feasible. This is a challenge since there is no unique or obvious way to invert the clustering. In this paper we proceed in two stages. First, we propose three methods to dis-aggregate spatially low-resolved model results into higher resolution: (a) uniformly distribute the regionalised results across their original set of regions, (b) re-optimising each clustered region separately at high resolution (c) a novel approach that minimises the custom "excess electricity" function. Second, we investigate the resulting highly-resolved models' feasibility by running an operational dispatch. While re-optimising yields the lowest amounts of load-shedding and curtailment, our novel inverse-method provides comparable results for considerably less computational effort. Feasibility-wise, our results strengthen previously published research that modeling every country by a single region is insufficient. Beyond that, we find that results obtained from state-of-the-art reduced models with 100-200 regions for Europe still yield 3-7% of load-shedding, depending on the model resolution and inverse method.