arXiv subjects

Moritz Wedemeyer

Publications and source records attributed to Moritz Wedemeyer.

3 recordsLinked to original sources

arXiv2026

Robust Design of Multi-Energy Systems Accounting for Mixed-Integer Operational Problems

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.

math.OC↗

arXiv2026

Data-Driven Conditional Flexibility Index

With the increasing flexibilization of processes, determining robust scheduling decisions has become an important goal. Traditionally, the flexibility index has been used to identify safe operating schedules by approximating the admissible uncertainty region using simple admissible uncertainty sets, such as hypercubes. Presently, available contextual information, such as forecasts, has not been considered to define the admissible uncertainty set when determining the flexibility index. We propose the conditional flexibility index (CFI), which extends the traditional flexibility index in two ways: by learning the parametrized admissible uncertainty set from historical data and by using contextual information to make the admissible uncertainty set conditional. This is achieved using a normalizing flow that learns a bijective mapping from a Gaussian base distribution to the data distribution. The admissible latent uncertainty set is constructed as a hypersphere in the latent space and mapped to the data space. By incorporating contextual information, the CFI provides a more informative estimate of flexibility by defining admissible uncertainty sets in regions that are more likely to be relevant under given conditions. Using an illustrative example, we show that no general statement can be made about data-driven admissible uncertainty sets outperforming simple sets, or conditional sets outperforming unconditional ones. However, both data-driven and conditional admissible uncertainty sets ensure that only regions of the uncertain parameter space containing realizations are considered. We apply the CFI to a security-constrained unit commitment example and demonstrate that the CFI can improve scheduling quality by incorporating temporal information.

cs.LG↗

arXiv2024

Robust Energy System Design via Semi-infinite Programming

Time-series information needs to be incorporated into energy system optimization to account for the uncertainty of renewable energy sources. Typically, time-series aggregation methods are used to reduce historical data to a few representative scenarios but they may neglect extreme scenarios, which disproportionally drive the costs in energy system design. We propose the robust energy system design (RESD) approach based on semi-infinite programming and use an adaptive discretization-based algorithm to identify worst-case scenarios during optimization. The RESD approach can guarantee robust designs for problems with nonconvex operational behavior, which current methods cannot achieve. The RESD approach is demonstrated by designing an energy supply system for the island of La Palma. To improve computational performance, principal component analysis is used to reduce the dimensionality of the uncertainty space. The robustness and costs of the approximated problem with significantly reduced dimensionality approximate the full-dimensional solution closely. Even with strong dimensionality reduction, the RESD approach is computationally intense and thus limited to small problems.

math.OC↗