Developing a combinatorial optimisation approach to design district heating networks based on deep geothermal energy

Jann Michael Weinand*, Max Kleinebrahm, Russell McKenna, Kai Mainzer, Wolf Fichtner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


Plants increasingly exploit high geothermal energy potentials in German district heating networks. Municipal planners need instruments to design the district heating network for geothermal heat. This paper presents a combinatorial mixed-integer linear optimisation model and a three-stage heuristic to determine the minimum-cost district heating systems in municipalities. The central innovations are the ability to optimise both the structure of the heating network and the location of the heating plant, the consideration of partial heat supply from district heating and the scalability to larger municipalities. A comparison of optimisation and heuristic for three exemplary municipalities demonstrates the efficiency of the latter: the optimisation takes between 500% and 1 × 107% more time than the heuristic. The deviations of the heuristic's calculated total investments for the district heating system compared to the optimisation are in all cases below 5%, and in 80% of cases below 0.3%. The efficiency of the heuristic is further demonstrated by comparison with the Nearest-Neighbour-Heuristic, which is less efficient and substantially overestimates the total costs by up to 80%. The heuristic can also be used to design district heating networks in holistic energy system optimisations due to the novel possibility of connecting an arbitrary number of buildings to the network. Future work should focus on a more precise consideration of heat losses, as well as taking additional geological and topographical conditions into account.

Original languageEnglish
Article number113367
Number of pages17
JournalApplied Energy
Early online date30 May 2019
Publication statusPublished - 1 Oct 2019

Bibliographical note

Acknowledgement The authors gratefully acknowledge the financial support of the PhD College “Energy and Resource Efficiency” (ENRES), from the Federal State of Baden-Wuerttemberg, for funding the first author’s PhD studentship. The contribution of the second author was supported by the Helmholtz Association under the Joint initiative“Energy Systems Integration”(funding reference: ZT-0002). The authors also thank three anonymous reviewers and the editor, who provided valuable comments on earlier versions of this manuscript. The usual disclaimer applies


  • Combinatorial optimisation
  • Deep geothermal energy
  • District heating network design
  • Geothermal plant
  • Graph theory
  • Location planning


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