Optimal Booster Chlorination Scheduling in WDS under uncertainty: A Robust counterpart approach

To ensure high quality water in water distribution systems (WDS), disinfectant generally chlorine is injected into the system. However, this chlorine limits should be kept within acceptable levels. The higher limit is enforced to control the disinfection by-products whereas lower limit is enforced to ensure that the water is organic contaminant free. The chlorine reaction rate within the pipe systems varies depending on the type of pipe, age, water PH level, temperature, and many other factors. This hinders the accurate water quality modelling in water distribution systems which in turn effects the optimal amount of booster injection rate. To minimize the risk of the uncertainty in chlorine reaction rate, current work suggests an robust counterpart reformulation of the optimal booster chlorination scheduling problem considering the rate of reaction of chlorination as uncertain. The proposed reformulation is tested on a benchmark WDS, and the results are compared with a deterministic case. The results indicated that with an increase in the protection level the injection mass increased and with very large protection levels, the formulation resulted in no solution. The proposed reformulation of the traditional approach can be applied to any WDS and obtain optimal scheduling with appropriate protection levels.