Booster Disinfection Scheduling under Uncertainty in Water Distribution Systems: Approximate Robust Reformulation Approach

Abstract

One key aspect of ensuring water safety in water distribution systems (WDS) is the controlled use of disinfectants like chlorine within these systems. The amount of disinfectant levels in WDS directly impacts the quality and safety of the water supplied to consumers thus chlorine/disinfectant regulation in WDS is paramount. An upper residual Chlorine limit controls the formation of disinfection by-products, while a lower residual Chlorine limit guarantees that the water remains free of organic contaminants. However, accurately modelling the Chlorine reaction in WDS is a complex task due to various influencing factors, including pipe material, pipe age, water pH, temperature, and more. The variability in the Chlorine reaction rate in WDS poses a significant challenge in accurately predicting water quality provided to the consumers and also affects the optimal scheduling of Chlorine booster injections. To ensure the water quality remains within the acceptable range, we consider the chlorine reaction rate as an uncertain parameter and propose an approximate robust reformulation approach for the booster chlorination scheduling problem. We utilize two benchmark WDS systems to perform rigorous testing and analysis of our methodology. The proposed approach provides a systematic and robust method to obtain chlorine injection scheduling that adheres to predefined aims to maintain safe water quality levels while considering the uncertain reaction rate coefficients to be within ellipsoidal uncertainty sets.