Robust Sample Average Approximation for Optimal Chlorine Disinfection under Multiple Uncertainties

Ensuring the safe quality of drinking water requires effective disinfection. Chlorine injection into water distribution systems is the most widely used method for this purpose. Scheduling the injection rates of chlorine from different available boosters poses a significant challenge, as the chlorine concentrations throughout various sections of the network must be maintained as close as possible to the desired levels and without violating lower and upper bounds. This task is highly complex due to the high dimensionality of water networks, the nonlinearity of hydraulics, and water quality dynamics. Furthermore, inherent uncertainties such as chlorine decay processes and variations in consumer demands exacerbate the complexity of decision-making. This study proposes a straightforward, yet practical approach based on sample average approximation (SAA) combined with robust optimization (RO). The proposed approach employs a linear model that minimizes the expected deviation of chlorine residuals from a target level across various demand scenarios, accounting for uncertainties in consumer demand. The uncertainty in the chlorine bulk reaction rate is addressed using robust optimization with a box uncertainty set. The method is tested on a benchmark water distribution system with different levels of uncertainty, and the results are compared with the deterministic case.