Disinfection scheduling in water distribution networks considering input time-delay uncertainty

A significant challenge when attempting to regulate the spatial-temporal concentration of a disinfectant in a water distribution network is the large and uncertain delay between the time that the chemical is injected at the input node and the time that the concentration is measured at the monitoring output nodes. Uncertain time delays are due to varying water flows, which depend mainly on consumer water demands. Existing approaches cannot guarantee that the concentration of the disinfectant will remain within a specified range at the output, even though bounds on time-delay uncertainty may be known. In this work, given bounded water -flow uncertainty, we use the input-output modeling approach to develop a disinfectant scheduling methodology that guarantees a bounded output disinfectant concentration. The proposed methodology creates an input-output model uncertainty characterization by utilizing estimated bounds on water-quality states using the backtracking approach. An optimization problem is formulated and solved to find an input schedule that keeps the disinfectant concentration within predefined bounds for a specified time horizon. Simulation results in two case studies where water demands varied between +/- 20% of their nominal value show that the proposed scheduler is able to avoid lower bound violations of disinfectant concentration.