Improved community detection for WDN partitioning in the dual topology based on segments and valves

This paper proposes a formulation of modularity tailored to the dual water distribution network (WDN) topology based on segments and valves, to be conveniently adopted for the partitioning into district-metered areas (DMAs). Notably, it allows considering both properties to be made uniform across DMAs, such as water demand or total pipe length, and properties to be made uniform inside each DMA, such as nodal ground elevations or pipe age for the sake of pressure regulation or maintenance easiness, respectively. This paper also proposes a new algorithm for the identification of the optimal clustering of WDN segments into any desired number of DMAs. Taking as a starting point any WDN clustering solution, i.e., the solution obtained with Newman's fast algorithm for community detection, the novel algorithm operates by exploring changes in the community of belonging to segments lying in the boundary between adjacent communities, by applying an optimization inspired by the simulated annealing technique. The applications of the novel modularity formulation and optimization algorithm to two case studies yield well-performing clustering solutions in terms of engineering judgment criteria, such as the low number of inter-DMA boundary pipes, uniformity of DMAs and hydraulic performance.