Inexact left-hand side two-stage chance-constrained programming for booster optimization in water distribution system.

In water distribution system (WDS), chlorine is often injected as disinfectant to control the growth of microorganism in WDS. However, the chlorine reacts with organism to form disinfectant byproduct, which can bring risk to human health. As such, the chlorine at nodes in WDS should be kept between acceptable range, which is simulated based on the response at nodes corresponding to unit injection mass at boosters. To deal with the uncertainty in chlorine decay process and lower and upper chlorine concentration limits, an inexact left-hand-side chance-constrained programming (ILCCP) model was proposed in this paper and applied to two WDSs. The response coefficients matrix was expressed as random variables with normal probability distribution in the constraints of lower and upper limits, which was obtained through Monte Carlo simulation by linking with EPANET software. The intervals of injection mass were obtained by solving the ILCCP model with a two-step algorithm. Moreover, the effects of random bulk decay coefficients and interval of chlorine limits on the injection mass were analyzed and compared. The results indicated that the lower bounds of optimal injection mass increased with the rise of probability lever for lower limits, while the upper bounds decreased with the rise of the probability level for upper limits. The results can help managers determine the chlorine injection mass under uncertain scenarios, and can be applied to more complicated WDS to obtain meaningful results.