Minimization of Water Age in Water Distribution Systems under Uncertain Demand †

Most existing approaches to ensuring water quality in water distribution systems (WDSs) are deterministic, i.e., they do not consider uncertainties, although they may have significant impacts on the water quality. It is well recognized that water demand represents a predominant uncertainty in a WDS. In addition, water age is often used as an important parameter to describe the water quality in a WDS and can be influenced by water demand and control elements such as pressure-reducing valves (PRVs). Therefore, the aim of this study is to carry out a probabilistic analysis of the impact of demand uncertainty on the water age in the distribution network. Based on the solution of deterministic optimization to minimize the water age, Monte Carlo simulation will be carried out by sampling the uncertain demand to evaluate the stochastic distribution of water age, as well as other operating variables like pressure and flow. As a result, the probability of violating the constraints of such variables can be determined, with the reliability of the operating strategy (e.g., the settings of the PRVs) given by deterministic optimization provided. In cases of low reliability, it is necessary to modify the operating strategy in order to decrease the probability of constraint violation. For this purpose, a chance-constrained optimization problem is formulated, and its benefits for ensuring the user-defined reliability are studied. A benchmark network is used to verify the proposed approach.