RODES: Robust Optimization for the Design of Energy Systems
In order to ensure a climate-neutral energy supply in the context of climate change, our energy systems must be massively expanded or redesigned, while at the same time ensuring permissible operation at all times. Fluctuating renewable energies and planning for the future introduce uncertainties into the optimization problems that are to be addressed in this project.
The mathematical modelling of energy systems provides very complex optimization problems, for example in the description of the conversion processes of different forms of energy into each other, as well as in the consideration of the respective storage systems. The design and operation variables are typically chosen to be mixed integer and the cost functions linear. The entire optimization problem is thus a (mixed-integer) linear program under uncertainties.
Various methods of robust optimization will be applied and extended to deal with uncertainties in such models.
Robust Optimization and Distributionally Robust Optimization of Energy Systems
The project focuses on optimizing the investment costs for the transformation of the energy system as well as the operating costs. These quantities are influenced by the uncertain forecasts of energy demand and price trends. Furthermore, the supply of electrical energy from renewable energy sources can only be predicted imprecisely. For this reason, the robust optimization of energy systems aims to calculate optimal decisions so that the solutions remain feasible for all uncertain parameters within an uncertainty set. The results of robust optimization are often too conservative. This excessive conservatism of the solutions is to be reduced with the distributional robustness approach, which optimizes with respect to probability distributions. The aim is to achieve good solvability and prediction of the decision variables. In addition, the complexity of the model is to be reduced by a suitable choice of scenarios without significantly losing quality in order to reduce the high computing time.
Contact: Mira Urban, Stefan Ulbrich
Sensitivities, Resiliency, Reduced Models and Symmetries
This part of the project focuses on the calculation of sensitivities, the analysis of resiliency and the reduction of the size of the optimization problems by searching for symmetries within the models.
Usually, large optimization problems for energy models are solved by using interior-point methods. A crossover to bases is often too slow and therefore the classical sensitivity analysis is not directly applicable. The question is whether sensitivities can be determined efficiently. Partially, this can be answered with existing methods, but a practicable solution is of great importance in application. Furthermore, the resiliency of the model in the event of component failure, similar to so-called interdiction problems, should be analyzed and addressed.
In addition, finding symmetries within the model and eliminating symmetric structures can help to reduce the size of the optimization problem without significant loss of quality.
Contact: Jonas Alker, Marc Pfetsch
Duration: October 2022 – September 2025 (supported by Bundesministerium für Bildung und Forschung)
Project partners: Technische Universität Darmstadt (head), Universität Trier, Siemens AG
Involved departments of TU Darmstadt: Optimization, EINS