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

Abstract

A numerical approach for generating a limited number of water demand scenarios and estimating their occurrence probabilities in a water distribution network (WDN) is proposed. This approach makes use of the demand scaling laws in order to consider the natural variability and spatial correlation of nodal consumption. The scaling laws are employed to determine the statistics of nodal consumption as a function of the number of users and 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.

Bottom-Up Generation of Peak Demand Scenarios in Water Distribution Networks

“…In fact, in a generic peak scenario, the adoption of a single peak demand coefficient at all nodes, according to the deterministic top-down approach [5], may lead to an unrealistic representation of the peak demand in the WDN. One of the few works aimed at reconstructing the snapshot peak demand scenario in an entire WDN, as the combination of peak demands at all the nodes, is that of Magini et al [19]. In the methodology presented in [19], combinations of simultaneous nodal demands are first generated through the gamma probability distribution with parameters expressed as a function of the number of nodal users by means of scaling laws.…”

“…One of the few works aimed at reconstructing the snapshot peak demand scenario in an entire WDN, as the combination of peak demands at all the nodes, is that of Magini et al [19]. In the methodology presented in [19], combinations of simultaneous nodal demands are first generated through the gamma probability distribution with parameters expressed as a function of the number of nodal users by means of scaling laws. Then, nodal demand series are resorted to preserve correlation between nodes through the Iman-Canover method [20].…”

“…Then, nodal demand series are resorted to preserve correlation between nodes through the Iman-Canover method [20]. Though the methodology of Magini et al [19] performs effectively at reconstructing peak demands through the bottom-up approach, the following aspects in [19] require further analysis and are therefore explored in the present paper:…”

“…Being based on two parameters, the gamma probability distribution used in [19] enables respecting statistics of user demands only up to the second order, i.e., mean and standard deviation. Therefore, the question arises if more complex distributions, such as the beta distribution with tunable bounds [10], can be used to respect bounds and statistics of user demands up to the third order i.e., including the skewness;…”

Simulating Marginal and Dependence Behaviour of Water Demand Processes at Any Fine Time Scale

“…Furthermore, and though not proposing stochastic simulation models, it is worth to mention the work of Kossieris and Makropoulos [39] who study the statistical and distributional properties of residential water demand at various scales, as well as the study of Gargano et al [40] on the evaluation of probabilistic models to describe the peak residential water demand. Lastly, Magini et al [8,41] and Vertommen et al [42] studied the scaling properties of water demand at different spatial and temporal levels, while recently Magini et al [43] employed those properties to generate large number of scenarios of spatially correlated demand series at the node of a network.…”