A Mixed Integer Non-Linear Programming Model for the Optimal Valve Placement within Water Distribution Networks

Water leakages represent a crucial aspect in the management of water distribution networks (WDNs). The pressure control, by means of pressure reducing valves, is an economical and viable strategy to contain water leakages and it has been deeply investigated in literature for many years. However, in the presence of high excess pressure and high discharges, thus high energy potential, it may be more convenient to install an energy production device (e.g., a turbine, a pump as turbine) in order not to dissipate the excess pressure, but rather to convert it into energy by means of an electrical generator. Nevertheless, whenever the pressure containment could ensure large water savings but small energy production, the installation of a pressure reducing valve may be more convenient due to the lower purchase and maintenance costs. In literature, many studies have dealt with the optimal location of such valves within WDNs in order to maximize leakage reduction. In this study, the optimization of both the number and location of pressure reducing valves is performed, with the aim of maximizing water savings and minimizing investment cost. Instead of employing external software to compute flow through links and pressure at nodes, the hydraulic resolution of the case study network is coupled with optimization procedure in one single mathematical model. Due to the strong non-linearities modelling of the hydraulic network, as well as the presence of both continuous and integer optimization variables, the resulting mathematical problem is mixed integer non-linear programming (MINLP). A global optimization solver is employed to solve the problem and the achieved results are presented with reference to a literature case study network. According to the results, the proposed optimization ensures an improvement in leakage reduction of 21%, compared to other studies on the same network.