Water distribution systems connectivity analysis

A water distribution system is a collection of hydraulic control elements jointly connected to convey quantities of water from sources to consumers. Such a system can be described as a graph with the nodes representing the sources and consumers, and the arc – the connecting elements (e.g., pipes, pumps, and valves). Theoretically, the flow in each arc can reach either direction, resulting in 2ⁿ possible digraphs, where n equals the number of arcs. However, this number is substantially reduced as Kirchoff's Laws 1 and 2 (continuity of mass and energy, respectively) hold, and as in certain arcs the flow is constrained to only one direction (e.g., the pipe leading out of a well). This study describes a methodology for establishing the most flexible pair: Operational and backup digraphs of a water distribution system that maintains Kirchoff's Laws 1 and 2, and yields (if possible) a one-level system redundancy (i.e., if one arc fails, at least one path from at least one source to all consumers is retained by the operational or backup digraphs). The proposed methodology is cast in a genetic algorithm framework and demonstrated through two example applications.