In order to achieve a timely transition towards sustainable energy systems within a large landscape of multi-sectors and multi-technologies, decision-makers and industry practitioners can rely on time- and space-discretized energy system optimization models. However, such models are often burdened by the computational costs arising from the growing problem complexity, which is especially due to the time discretization. The common strategy to lower the computational cost is to uniformly reduce the temporal resolution, sacrificing the quality of the solution. In light of this, we propose the concept and a formulation of fully flexible temporal resolution, wherein each decision variable and constraint can have a separate temporal resolution. After introducing the formulation in detail, we demonstrate its capability by applying it to an EU-wide case study optimizing both capacity investment and operation decisions of the inter-connected energy system across the different countries. We show that the proposed flexible formulation allows us to flexibly remove variables and constraints that are not needed without losing accuracy, and to simplify the time discretization (e.g., in space) while pushing the Pareto front by simultaneously speeding up computation and limiting losses in accuracy. In conclusion, we highlight the promise of adopting fully flexible temporal resolution and encourage future research to explore further temporal resolution configurations beyond our examples.

In integrated power and gas energy system optimization models (ESOMs), pipeline gas transmission with linepack is a particularly complex problem due to its non-linear and non-convex character. For ESOMs based on mixed-integer linear programming, piecewise linearization is a well-established convexification approach for this problem, which, however, requires binary variables to model feasible combinations of linear gas flow and pressure segments and thus can quickly become computationally challenging. In order to improve computational performance, this paper proposes a piecewise linearization method specifically designed to be tight, resulting in a reduced problem space a solver can explore faster. We provide numerical results comparing the proposed formulation against two piecewise linearizations from the literature, both from a theoretical point of view and in terms of practical computational performance, with results showing an average speed-up of 2.57 times for our case study. Test cases are carried out on a modified 24-bus IEEE Reliability Test System and a 12-node gas system, considering discrete unit commitment decisions.