Selecting optimal pipeline diameters for a district heating network comprising branches and rings, using graph theory and cost minimization

  • Jakub Murat Institute of Heat Engineering, Warsaw University of Technology
  • Adam Smyk Institute of Heat Engineering, Warsaw University of Technology
  • Rafal Marcin Laskowski Institute of Heat Engineering, Warsaw University of Technology


Choosing the right pipeline diameter is essential for both newly designed district heating (DH) networks and existing onesundergoing upgrades. A multi-stage optimization algorithm was developed for the purpose of selecting optimal diameters ofpipelines in a DH network that has a complex layout including branches and rings. The DH network was represented as a setof graphs and then as matrices, which made hydraulic and heat-and-flow calculations possible for any network layout. Theoptimization algorithm was developed as a Visual Basic program consisting of 37 macros. The program considers hydraulicresistances, heat-balance equations, capital expenditure for DH pipelines of 32 to 1,100 mm in diameter, and the operatingcost, including the costs of heat transmission losses and DH water pumping. Microsoft Excel’s Solver tool was used to solvethe non-linear optimization algorithm with constraints. To provide an example of the program’s application, the paper includescalculations used to verify the correctness of selected diameters for part of an existing DH network in a large DH system inPoland.


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How to Cite
MURAT, Jakub; SMYK, Adam; LASKOWSKI, Rafal Marcin. Selecting optimal pipeline diameters for a district heating network comprising branches and rings, using graph theory and cost minimization. Journal of Power Technologies, [S.l.], v. 98, n. 1, p. 30–44, mar. 2018. ISSN 2083-4195. Available at: <>. Date accessed: 01 aug. 2021.
Research and Development in Power Engineering 2017


District heating networks; heat cost; optimum pipe diameter; graph theory

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