Improved loop-flow method for hydraulic analysis of water distribution systems

Zeljko Vasilic*, Milos Stanic, Zoran Kapelan, Damjan Ivetic, Dusan Prodanovic

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


Different methods have been developed in the past to formulate and solve steady-state hydraulics of a water distribution system (WDS). The most widely used method nowadays is probably the global gradient algorithm (GGA). The loop-flow method (also known as the ΔQ method) represents a viable alternative to GGA, especially when combined with suitably preprocessed network data. The main advantage of the ΔQ method over the GGA is in the smaller number of unknowns to solve for, which is coming from the fact that real WDSs typically have far less loops than nodes. A new loop-flow-type method, relying on the novel triangulation based loops identification algorithm (TRIBAL) that was implemented in the corresponding new hydraulic solver (ΔQ), is presented in this paper (TRIBAL-ΔQ). The new method aims to exploit this advantage, while overcoming key drawbacks of existing ΔQ methods. The performance of the TRIBAL- ΔQ-based solver is compared with the GGA-based solver on four large real networks of different complexity and topology. The results obtained demonstrate that, despite requiring an increased number of iterations to converge, the TRIBAL-ΔQ method-based solver is substantially computationally faster, has slightly better numerical stability, and is equally accurate in making predictions when compared with the GGA-based hydraulic solver.

Original languageEnglish
Article number04018012
JournalJournal of Water Resources Planning and Management
Issue number4
Publication statusPublished - 1 Apr 2018
Externally publishedYes


  • Global gradient algorithm (GGA)
  • Loop flow
  • Minimal loops
  • WDS analysis
  • ΔQ method


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