Matthias Gramlich

University of Freiburg

Friday, January 10, 2025, 14:00 - 15:00

SR 01-012

As the climate crisis intensifies and fossil fuel suppliers become increasingly unreliable, the necessity for low-carbon and cost-effective heating alternatives is urgent. One possible solution is to enhance the control of the district heating networks (DHNs) by employing Optimal Control Problems (OCPs). This mathematical technique is capable of minimizing the heating costs of these DHNs, as well as considering their dynamics and constraints. The model dynamics incorporate nonlinear relationships between temperature, bidirectional mass flow, and pressure that arise from the spatially discretized one-dimensional heat equation and algebraic equations, such as conservation laws. In addition, the discrete behavior of multiple producers requires the implementation of binary variables. Once the OCP is discretized in time, an inherently complex Mixed-Integer Nonlinear Problem (MINLP) with Complementarity Constraints (CCs) is derived. The employment of Model Predictive Control (MPC) to

iteratively manage these networks is crucial, and therefore the necessity for obtaining solutions within a specific time frame is essential. 

This thesis demonstrates an optimized example of a small DHN and an actual aggregated DHN in Weil am Rhein, Germany, thereby providing crucial insights into the solvability of such MPCs. Moreover, a variety of techniques for reducing the complexity of the problem are employed, including the reduction of binary variables, and collocation points, the reclassification of variables, and different methods for handling complementarity constraints. The results demonstrate that the reclassification of variables and the reduction of collocation points can significantly decrease the solution time on average from 30 min to 15 min, respectively, from 30 min to 5 min. Ultimately, this should enable the use of MINLPs in actual DHNs.