Robust design of multi-energy systems accounting for mixed-integer operational problems

Applied Energy, vol. 426, pp. 128684

Abstract

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 the 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.

Authors 3

1. Moritz Wedemeyer Aachen

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Institute of Climate and Energy Systems, Energy Systems Engineering (ICE-1), Forschungszentrum Jülich GmbH, Jülich 52425, Germany

   RWTH Aachen University, Aachen 52062, Germany

2. Alexander Mitsos Aachen

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   Institute of Climate and Energy Systems, Energy Systems Engineering (ICE-1), Forschungszentrum Jülich GmbH, Jülich 52425, Germany

   JARA-ENERGY, Jülich 52425, Germany

   RWTH Aachen University, Process Systems Engineering (AVT.SVT), Aachen 52074, Germany

3. Manuel Dahmen corresponding

   Forschungszentrum Jülich

   Affiliation as printed

   Institute of Climate and Energy Systems, Energy Systems Engineering (ICE-1), Forschungszentrum Jülich GmbH, Jülich 52425, Germany