Robust Design of Pumping Stations in Water Distribution Networks

Abstract : Restricted to gravity-fed networks, most water network design models minimize investment costs under a static peak water demand scenario. In networks equipped with pumping stations, design models should also account for operation costs incurred by the pump energy consumption that depends on dynamic demand and tariff. Evaluating the lifetime operation costs amounts to solve a large-scale non-convex combinatorial optimization problem for each considered design. In this paper, we address the pressurized water network design problem with a joint optimization of the pump investment and operation costs through a stabilized Benders' decomposition. To reduce the complexity of the operational subproblem, we decompose the scheduling horizon in representative days, and relax the discrete and non-convex components of the hydraulic model. We also evaluate the design robustness on stress-day scenarios and derive feasibility cuts using a dominance argument. Experiments on a typical rural branched water distribution network with one year of historical data show the accuracy of our approximations and the significant savings expected from the optimal pump resizing.