Water distribution networks optimization considering uncertainties in the demand nodes

Abstract The design of water distribution networks (WDN) can be formulated as an optimization problem. The objective function, normally, is the network cost, given by the installation cost, which depends on the pipe diameters and by the operation cost, given by the pumping costs associated to the network, which depends on the hydraulic pumps necessary in the system. The water demand can be variable in the network nodes and this variability can be modeled by a finite set of scenarios generated by a normal distribution. In the present paper a disjunctive Mixed Integer Nonlinear Programming (MINLP) formulation optimization problem is proposed to model the design of WDN under uncertainties in the nodes demand. Flow directions are considered unknown and a deterministic approach is used to solve the problem in three steps. Firstly, the problem is solved considering only a nominal value to each uncertain parameter. In the second step, the problem is solved for all the scenarios, being the scenario independent variables fixed to the solution achieved in the first step, which is a deterministic solution. Finally, all the scenarios are solved without fixing any variable value, in a stochastic approach. Two case studies were used to test the model applicability and global optimization techniques were used to solve the problem. Results show that the stochastic solution can lead to optimal solutions for robust and flexible WDN, able to work under distinct conditions, considering the nodes demand uncertainties.