Control Node Placement and Structural Controllability of Water Quality Dynamics in Drinking Networks

TL;DR

This paper presents a novel control- and graph-theoretic approach for optimal placement of booster stations in water distribution networks, considering dynamic hydraulics to improve chlorine coverage and system controllability.

Contribution

It introduces a new formulation that maximizes controllability with minimal energy, accounting for time-varying hydraulics and network topology, unlike traditional static methods.

Findings

Effective booster station placement improves chlorine coverage.

Method scales well to large networks.

Validated on multiple network configurations.

Abstract

Chlorine, the most widely used disinfectant, needs to be adequately distributed in water distribution networks (WDNs) to maintain consistent residual levels and ensure safe water. This is performed through control node injections at the treatment plant via booster stations distributed across the WDNs. While previous studies have applied various optimization-based approaches for booster station placement, many have failed to consider the coverage of the station injections and the dynamic nature of WDNs. In particular, variations in hydraulics and demand significantly impact the reachability and efficacy of chlorine injections which then impact optimal placement of booster stations. This study introduces a novel formulation that combines control- and graph-theoretic approaches to solve the booster station placement problem. Unlike traditional methods, our approach emphasizes maximizing the system's ability to control disinfectant levels with minimal control energy, taking into account the time-varying hydraulic profiles that lead to different optimal station placements. We propose a simple weighting technique to determine the placements by assessing the structural controllability of each configuration, based on the network's topology, independent of specific parameters like decay rates or pipe roughness. This method ensures effective chlorine coverage across the network. Our approach is validated on different networks, demonstrating its operational effectiveness, scalability, and practicality.