2026/04/30 by Moritz Wedemeyer, Alexander Mitsos, Manuel Dahmen
Mathematics · #math.OC
manuscript (44 pages, 7 figures, 2 tables); supplementary material (10 pages, 1 figure, 4 tables)
arxiv created 2026/08/03 · arxiv updated 2026/08/04
Identifying robust designs for multi-energy systems is computationally challenging. As rigorous approaches are often computationally intractable, heuristics are employed to generate candidate designs. Specifically, we consider a heuristic that iteratively identifies and adds extreme scenarios to the design problem. We theoretically investigate how three common nonconvexities, i.e., piecewise-linear energy inflow-outflow relationships, minimum part-loads, and storage complementarity, affect the robustness of designs identified by this heuristic. We find that, if surplus energy cannot be curtailed, any of these nonconvexities may cause the heuristic to fail. If curtailment is allowed, storage complementarity does not compromise robustness, and convex piecewise-linear inflow-outflow relationships can be reformulated linearly. However, minimum part-loads may lead to failure of the heuristic. Furthermore, if the optimal value function of the operational problem is nonconvex in the uncertain variables, the heuristic may fail. We demonstrate these findings using an illustrative multi-energy system case study, in which minimum part-loads and nonconvex dependence of the objective function on heat-pump efficiency are identified as possible failure modes. We rigorously verify the robustness of a design identified using the heuristic and find a scenario where, in one time step, 1.1 kW of the 313.6 kW electricity demand could not be satisfied. However, when the number of representative scenarios is increased from 4 to 6 or 8, the resulting designs are robust. This demonstrates that the heuristic can serve as an effective first step in identifying robust designs. However, when robustness guarantees are required, a rigorous solution method must be employed.