Harder, better, faster, stronger: understanding and improving the tractability of large energy system models

Energy system models based on linear programming have been growing in size with the increasing need to model renewables with high spatial and temporal detail. Larger models lead to high computational requirements. Furthermore, seemingly small changes in a model can lead to drastic differences in runtime. Here, we investigate measures to address this issue. We review the mathematical structure of a typical energy system model, and discuss issues of sparsity, degeneracy and large numerical range. We introduce and test a method to automatically scale models to improve numerical range. We test this method as well as tweaks to model formulation and solver preferences, finding that adjustments can have a substantial impact on runtime. In particular, the barrier method without crossover can be very fast, but affects the structure of the resulting optimal solution. We conclude with a range of recommendations for energy system modellers: first, on large and difficult models, manually select the barrier method or barrier+crossover method. Second, use appropriate units that minimize the model’s numerical range or apply an automatic scaling procedure like the one we introduce here to derive them automatically. Third, be wary of model formulations with cost-free technologies and dummy costs, as those can dramatically worsen the numerical properties of the model. Finally, as a last resort, know the basic solver tolerance settings for your chosen solver and adjust them if necessary.