Generating Scenarios of Cross-Correlated Demands for Modelling Water Distribution Networks

This paper presents a methodology for the generation of a limited and representative number of water demand scenarios, taking into account the natural variability and spatial correlation of nodal consumption in a Water Distribution Network (WDN), and estimates their corresponding occurrence probabilities. Scaling laws are used to evaluate the statistics of water consumption at each node as a function of the number of users, considering the main statistical features of the unitary user's demand. Besides, consumption at each node is considered to follow a Gamma probability distribution. A high number of groups of cross-correlated demands, i.e. scenarios, for the entire network were generated using Latin Hypercube Sampling (LHS) and the numerical procedure proposed by Iman and Conover. The Kantorovich distance is used to reduce the number of scenarios and estimate their corresponding probabilities, while keeping the statistical information on nodal consumptions. By hydraulic simulation, the whole number of generated demand scenarios was used to obtain a corresponding number of pressure scenarios on which the same reduction procedure was applied. The probabilities of the reduced scenarios of pressure were compared with the corresponding probabilities of demand.