Source Treatment Level Optimization in Water Distribution Networks Considering Mixing Uncertainty at Cross Junctions: A Robust Counterpart Approach

A water distribution system (WDS) comprises several uncertain parameters. This uncertainty makes the optimal management and design of a WDS a complex problem. Often parameters that explicitly affect water quality are ignored. The contaminant mixing at a junction is assumed to be uniform and instantaneous. Multiple studies prove this assumption wrong, and new water quality modelling methodologies are proposed. The exact computation of the mixing level is complicated and computationally expensive. This study focuses on obtaining the optimal treatment levels at the sources, assuming the mixing levels as uncertain/unknown. A robust optimization approach is proposed to handle this uncertainty. The proposed methodology is explained using an illustrative example 4 × 4 grid network. The objective of the problem is to obtain the water treatment levels at the sources to satisfy the water quality requirements at the demand nodes and be immune to variations in mixing levels at cross junctions. The results showed a significant variation in cost between complete mixing and non-uniform mixing. The obtained treatment levels were verified through Monte-Carlo simulations.