Density-based Topology Optimization for District Heating Networks

According to the Intergovernmental Panel on Climate Change, limiting global warming will require significant changes in the energy system over the next 30 years (IPCC report 2022). While the role of efficient and low-carbon heating technologies continues to grow, fossil fuels still meet over 60% of heating energy demand (IEA Heating 2022). This dependence on fossil fuels in the heating sector requires new perspectives in the planning and design of heating technologies, in which district heating networks play a crucial role. The complex characteristics of modern low-carbon district heating networks and the resulting design challenges require accurate planning of network design and topology based on detailed knowledge of the network and its future operation. Many state-of-the-art approaches to topology optimization of district heating network design either sacrifice details in the physical modeling of district heating network operation through linearization, or are not scalable to relevant problem sizes.

Given the pressing need for modern low-carbon district heating networks and the lack of automated design tools to plan them in an energy and cost efficient way, the objective of this thesis is to develop an automated design tool for the topology and design optimization of modern district heating networks based on a nonlinear physics model.

Motivated by the success in other areas, a density-based topology optimization approach for district heating networks is developed for this design tool. First, a density-based approach is formulated for the pipe placement problem of heating networks. This approach is then extended to include discrete diameter selection based on a multi-material formulation. By testing the density-based topology optimization approach on an academic case study, the approach is able to produce clear topological separations between networks of different temperatures and achieve discrete pipe diameter selection. The study highlights the potential of economic topology and design optimization, especially in the early design phases of district heating networks, as it allows for rapid scenario analysis of different price scenarios and other parameters. Overall, the application of density-based methods proved to be a viable alternative to combinatorial approaches for the topology optimization of district heating networks. The method is shown to produce near-discrete optimal network topologies and pipe designs, while maintaining physical accuracy with nonlinear network models.

Next, a performance comparison with state-of-the-art approaches is necessary to evaluate the scalability and usability of the density-based approach. Therefore, the performance of two different approaches to nonlinear topology optimization of district heating networks is compared. A combinatorial approach that solves a complete Mixed Integer Nonlinear Program, resolving the discrete nature of pipe routing, and the density-based topology optimization approach developed in this thesis. The benchmark shows an exponential scaling of computational complexity with network size for the combinatorial approach, making optimization of large networks with thousands of potential pipe connections intractable. The density-based approach, on the other hand, maintains a polynomial scaling of computational cost, making optimizations of large district heating networks feasible. Further investigation of the optimality gap shows that solving the discrete pipe placement constraint in a combinatorial approach does not necessarily lead to superior network designs in the cases studied.

After developing and benchmarking the topology and design optimization tool for district heating networks, temporal resolution is added. By considering the temporal resolution of heat demand and outdoor temperature, more integrated network topologies are designed that allow for spatial and temporal shifting of head loads. This leads to optimized networks with higher connectivity and overall smaller diameters, resulting in higher waste heat shares and overall lower costs. The temporal resolution also allows for producer unavailability to be included in the optimization, resulting in more robust network designs.