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

Jakub Murat, Adam Smyk, Rafal Marcin Laskowski


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


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

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