Optimal Control of Chlorine Disinfection Under Multiple Uncertainties Using Combined Sample Average Approximation and Robust Optimization

Abstract Submission: Ensuring safe drinking water quality requires effective and carefully controlled disinfection, with chlorination being the most prevalent method. The goal of chlorination is to maintain adequate chlorine residuals throughout the network while not violating lower and upper concentration bounds. However, scheduling chlorine injection rates from multiple boosters presents significant challenges due to the high dimensionality of water distribution systems and the nonlinear dynamics of hydraulics and water quality. Furthermore, inherent uncertainties such as chlorine decay processes, and variations in consumer demands exacerbate the complexity of the decision-making. In this study, we propose a practical, computationally efficient approach that integrates Sample Average Approximation (SAA) with Robust Optimization (RO). The approach uses a linearized model that minimizes the expected deviation of chlorine residuals from target levels across a range of demand uncertainties, while also safeguarding against worst-case scenarios within the chlorine reaction space. Our methodology is tested on a benchmark water distribution system under varying levels of uncertainty, and results are compared with a deterministic baseline.

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