A Multi-Period Topology and Design Optimization Approach for District Heating Networks

TL;DR

This work addresses the challenge of designing district heating networks that operate across temporal variations in demand and heat supply. It introduces a multi-period topology optimization framework that uses density-based topology optimization to relax pipe placement, while solving a nonlinear, physics-based network model under representative time periods. The method yields integrated meshed network topologies that maximize waste-heat utilization and resilience, demonstrated by a Waterschei case where waste-heat share rises from $8.5\%$ to $51.3\%$ and total project cost drops by $17.9\%$; accounting for heat-source unavailability further shows robust design with a $59.5\%$ waste-heat share. With added heat producers, emergent ring/meshed topologies further increase connectivity and reduce costs (up to $31.99\,\mathrm{M}\€$ and $81.7\%$ waste-heat share), illustrating the approach’s potential for next-generation, renewable-integrated DHNs. The study highlights the importance of time aggregation and nonlinear physics in obtaining scalable, cost-effective, and redundant district heating designs.

Abstract

The transition to 4th generation district heating creates a growing need for scalable, automated design tools that accurately capture the spatial and temporal details of heating network operation. This paper presents an automated design approach for the optimal design of district heating networks that combines scalable density-based topology optimization with a multi-period approach. In this way, temporal variations in demand, supply, and heat losses can be taken into account while optimizing the network design based on a nonlinear physics model. The transition of the automated design approach from worst-case to multi-period shows a design progression from separate branched networks to a single integrated meshed network topology connecting all producers. These integrated topologies emerge without imposing such structures a priori. They increase network connectivity, and allow for more flexible shifting of heat loads between different producers and heat consumers, resulting in more cost-effective use of heat. In a case study, this integrated design resulted in an increase in waste heat share of 42.8 % and a subsequent reduction in project cost of 17.9 %. We show how producer unavailability can be accounted for in the automated design at the cost of a 3.1 % increase in the cost of backup capacity. The resulting optimized network designs of this approach connect multiple low temperature heat sources in a single integrated network achieving high waste heat utilization and redundancy, highlighting the applicability of the approach to next-generation district heating networks.

Figures (14)

• Figure 1: A SINH-like penalization approach for the fixed-term investment cost $\bar{\kappa}_0$, which leads to a penalization of the investment cost $J_{pipe,CAP}$. Visualized for different values of the penalization parameter $\xi$.
• Figure 2: Illustration of time series aggregation for heat demand time series of a demand point in the a) commercial zone and b) the outdoor temperature. The heat demand time series are aggregated into three representative periods $\{Q_{\mathrm{d},,ij,1},Q_{\mathrm{d},,ij,2},Q_{\mathrm{d},,ij,3}\}$ and a peak period $Q_{\mathrm{d},,ij,t_{\textrm{peak}}}$ using k-medoids clustering.
• Figure 3: View of the Waterschei neighborhood in Genk, Belgium, showing the location of the waste heat sources (southeast and southwest) and the proposed peak gas boiler (north), along with the distribution of the 217 aggregated demand points.
• Figure 4: Optimized network topology and pipe sizing for a considering only worst case conditions. The line thickness represents the installed pipe diameter. The waste heat source in the southeast supplies only two heat consumers in the immediate vicinity.
• Figure 5: Optimized network topology and pipe sizing for a considering multiple periods. The line thickness represents the installed pipe diameter. A backbone connects the waste heat source and the gas boiler, allowing for greater integration of waste heat into the network.