Optimal Operation of Water Distribution Systems under Uncertainty

The goal of water distribution systems (WDSs) is to supply water to consumers. Pumping and distributing water is an energy-intensive process, and it is also subject to different constraints such as demand satisfaction, water quality, pressure boundaries, etc. As such, finding an operation policy in which all constraints are satisfied while energy costs are minimized is a primary objective for water utilities. While many studies tackled the WDS optimal operation problem, most of them used deterministic approaches where all the problem parameters were assumed to be known. Recently, there is a growing interest in decision-making under uncertainty. One promising approach for utilizing optimization under uncertainty is robust optimization (RO) which assures a robust (feasible) solution to any realization of the uncertain parameters, within predefined bounds. In addition, RO does not depend on assuming the existence of probability density functions and is based on tractable formulations that converge to the global optimum. This study suggests utilizing RO to optimize the operation of WDSs under two types of uncertainties: consumers demand uncertainty and pumping cost uncertainty. The method is illustrated on a small illustrative network, showing how these uncertainties impact the operation policies.