Water Distribution Network Optimization Considering Uncertainties in the Nodes Demands

Abstract

The design of Water Distribution Networks (WDN) can be formulated as an optimization problem for the minimization of the total network cost, which depends on the pipe diameters and the pumping power required. The variability in water demand at nodes can be modelled as a set of finite scenarios generated from a multivariate normal distribution assuming correlations between the selected pair nodes of the network. A disjunctive stochastic Mixed Integer Nonlinear Programming (MINLP) model is proposed for the optimal synthesis of WDN considering correlated uncertainties in nodal demands. Strategies for avoiding nonconvex nonlinearities in the equations are applied to avoid unnecessary complexities. We analyse the effect of different correlation matrices to gather insight into how the model faces uncertainty. A case study was used to test the model and the optimization techniques proposed. Results show that under uncertainty the stochastic solution of the WDN improves the deterministic one (i.e. the design obtained for nominal values of nodes demand), evincing that neglecting uncertainty in the optimization process may lead to suboptimal or, even worse, infeasible design of WDNs.