A Direct Approach for the Near-Optimal Design of Water Distribution Networks Based on Power Use

Abstract

In recent years, iterative computational techniques have been considered as the most effective methods to tackle the problem of Water Distribution System (WDS) minimum-cost design. Given their stochastic nature, these approaches involve a large number of hydraulic simulations in order to obtain suitable results. Herein, a WDS design methodology based entirely on hydraulic principles is presented. This methodology, named Optimal Power Use Surface (OPUS), focuses on both reaching low-cost designs and diminishing the number of hydraulic executions (iterations), by establishing efficient ways in which energy is dissipated and flow is distributed throughout the system. The algorithm was tested in four well known benchmark networks, previously reported in the literature. OPUS proved that following hydraulic principles is a fair choice to design WDS, showing plenty of potential in other water distribution mathematical modeling applications and offering an alternative for the extensive search process undertaken by metaheuristics.

Fractal Analysis of the Optimal Hydraulic Gradient Surface in Water Distribution Networks

“…Therefore, the objective function to minimize was defined in terms of the capital cost required to install a new WDN depending on its diameter sizes. A commonly used mathematical expression for this purpose is a summation of the individual cost of each pipe, calculated as follows according to its diameter and cost per unit length (Wu 1975;Saldarriaga et al 2020):…”

“…Nevertheless, it should be noted that the analysis was restricted to gravity-driven networks, i.e., without pumping devices. As stated by Saldarriaga et al (2020), the OPUS methodology was originally made to be applied to gravity-driven WDNs. Coding adjustments of the original algorithm are required if networks with pumps will be included in the analysis (Saldarriaga et al 2020).…”

“…As stated by Saldarriaga et al (2020), the OPUS methodology was originally made to be applied to gravity-driven WDNs. Coding adjustments of the original algorithm are required if networks with pumps will be included in the analysis (Saldarriaga et al 2020). Consequently, so as to maintain the current OPUS version unaltered, the analysis was only conducted in gravity-driven networks.…”

“…Subsequently, Featherstone and El-Jumaily (1983) extended Wu's criterion to looped networks, and the idea was further developed when the optimal power use surface (OPUS) methodology was introduced (Saldarriaga et al 2010). OPUS requires the calculation of the optimal hydraulic gradient surface (OHGS), a discontinuous three-dimensional (3D) geometrical entity formed by the nodal piezometric head values that guarantee the calculation of a least-cost set of diameter sizes (Saldarriaga et al 2005(Saldarriaga et al , 2010(Saldarriaga et al , 2013(Saldarriaga et al , 2020. In a similar manner to Wu's (1975) observations, the OHGS establishes the way in which the available energy should be spent within the system to ensure an optimal design while satisfying the minimum water pressure and nodal flow demands (Saldarriaga et al 2005(Saldarriaga et al , 2010(Saldarriaga et al , 2013.…”

“…In a similar manner to Wu's (1975) observations, the OHGS establishes the way in which the available energy should be spent within the system to ensure an optimal design while satisfying the minimum water pressure and nodal flow demands (Saldarriaga et al 2005(Saldarriaga et al , 2010(Saldarriaga et al , 2013. Although the resulting initial design is given in continuous pipe sizes, OPUS executes rounding procedures so that the final design is consistent with the commercial diameters and meets the hydraulic constraints (Saldarriaga et al 2010(Saldarriaga et al , 2020. Several tests with benchmark networks have shown that OPUS can obtain high-quality solutions with very slight differences when compared to the minimum cost solutions reported in the literature (Saldarriaga et al 2010).…”