Mixed-Integer Nonlinear Optimization of District Heating Networks

Reducing carbon emissions in the energy sector, especially within the heating sector, is of great importance in the fight against climate change. To achieve this, lower heating temperatures and the use of renewable energy and waste heat is essential. Thus, the existing heating networks need to be transformed and require new operating strategies.

The thesis approaches this topic by considering the optimization of the operation of district heating networks. We state the optimization problem, which is based on the physical properties of a district heating network, focusing on the stationary case. Since the resulting problem consists of nonlinear constraints and binary variables, it is in general hard to solve. In the first part of this thesis, we therefore consider approaches to reduce the model size and introduce two heuristics that aim to find feasible solutions for the problem. To demonstrate the advantages of the model reduction and the heuristics, we implement the model and perform numerical tests on a large test set of randomly generated networks.

In the second part of the thesis, we consider heating networks that are coupled over multiple time steps via heating storages. Heating storages are an important tool for managing peak loads in the network or fluctuations due to renewable energy. To attach the increasing model size and complexity of the problem, we present a decomposition approach where the optimization model is divided into two smaller subproblems. We show that the decomposition approach yields an optimal solution for the original problem if the storage is coupled to a supplier. We demonstrate the numerical results for a minimal example network.

Lastly, we consider example networks that are based on the real district heating networks of the city of Darmstadt. We evaluate the developed methods and take a more detailed look at the optimal operating strategies.