This paper studies the problem of optimal geographic placement of water quality (WQ) sensors in drinking water distribution networks (WDNs), with a specific focus on chlorine transport, decay, and reaction models. Such models are traditionally used as suitable proxies for WQ. The literature on this topic is indeed inveterate, but has a key limitation: it utilizes simplified single-species decay and reaction models that do not capture WQ transients for nonlinear, multi-species interactions. This results in sensor placements that do not account for nonlinear WQ dynamics. Furthermore, and as WQ simulations are parameterized by hydraulic profiles and demand patterns, the placement of sensors are often hydraulics-dependent. This study produces a simple algorithm that addresses the two aforementioned limitations. The presented algorithm is grounded in nonlinear dynamic system sciences and observability theory, and yields sensor placements that are robust to hydraulic changes. Thorough case studies on benchmark water networks are provided. The key findings provide practical recommendations for WDN operators.

The operation and regulation of water distribution networks is a complex procedure aimed at efficiently supplying consumers with sufficient water while ensuring its safe quality. A critical aspect is the direct impact of the network’s hydraulics on the dynamics of water quality; the former is typically needed to inform the latter. Previous studies have tackled hydraulic optimization and water quality regulation as separate problems, although they are naturally coupled. While some attempts have been made to couple these problems into a single one, such studies have neglected control-theoretic virtues of the integrated problems. This paper fills this research gap by formulating a pump control problem that accounts for water quality controllability via classic Gramians. This is achieved by integrating water quality controllability metrics into the control problem, the goal is to enhance both water quality regulation and reducing pumping costs. A case study is presented to illustrate that utilizing controllability Gramians leads to an improved overall system performance.

The operation of drinking water distribution networks (WDNs) involves complex processes aimed at delivering sufficient water quantity while preserving its safety. These processes are governed by hydraulics and water quality (WQ), with hydraulics focusing on maintaining adequate pressure for efficient delivery and supply, and WQ ensuring compliance with safety standards. The objective of this dissertation is to address the challenges inherent in managing hydraulics and WQ within WDNs through a holistic monitoring and feedback control framework. This framework is based on: (i) advanced WQ modeling of the system's disinfectant (i.e., chlorine), incorporating nonlinear multi-species dynamics for a more realistic representation of real-world scenarios, including contamination events; (ii) acknowledging the dependency between the hydraulic and WQ dynamics and analyzing its influence on system performance, and using these insights to guide; (iii) the development of a joint control approach with the objective of obtaining optimal hydraulic settings while attaining an adequate level of chlorine control coverage across the system; and (iv) control-oriented strategic placement of actuators and sensors to maximize the performance of the monitoring and control computational algorithms while ensuring responsiveness and adaptability to dynamic conditions. This framework bridges significant research gaps in the literature, which often rely on oversimplified single-species WQ models, treat hydraulic optimization and WQ regulation as independent problems, or couple these problems without performance guarantees, leading to trade-offs between objectives. Additionally, traditional methods for determining actuator and sensor placements often prioritize specific objectives, such as cost minimization or simplified design, without considering their influence on the system's controllability, observability, and overall operational efficiency. The presented computational algorithms are validated through different case studies, demonstrating their operational effectiveness, practicality, scalability, and contribution to enhancing the resilience of WDNs in the face of dynamic and uncertain challenges.

Effective disinfection is essential for maintaining water quality standards in distribution networks. Chlorination, as the most used technique, ensures safe water by maintaining sufficient chlorine residuals but also leads to the formation of disinfection byproducts (DBPs). These DBPs pose health risks, highlighting the need for chlorine injection control (CIC) by booster stations to balance safety and DBPs formation. Prior studies have followed various approaches to address this research problem. However, most of these studies overlook the changing flow conditions and their influence on the evolution of the chlorine and DBPs concentrations by integrating simplified transport-reaction models into CIC. In contrast, this paper proposes a novel CIC method that: (i) integrates multi-species dynamics, (ii) allows for a more accurate representation of the reaction dynamics of chlorine, other substances, and the resulting DBPs formation, and (iii) optimizes for the regulation of chlorine concentrations subject to EPA mandates thereby mitigating network-wide DBPs formation. The novelty of this study lies in its incorporation of time-dependent controllability analysis that captures the control coverage of each booster station. The effectiveness of the proposed CIC method is demonstrated through its application and validation via numerical case studies on different water networks with varying scales, initial conditions, and parameters.

Chlorine, the most widely used disinfectant, needs to be adequately distributed in water distribution networks (WDNs) to maintain consistent residual levels and ensure water safety. This is performed through control node injections at the treatment plant via booster stations scattered in WDNs. While previous studies have applied various optimization metrics 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 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 and 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.

The operation of water distribution networks is a complex procedure aimed at efficiently delivering consumers with adequate water quantity while ensuring its safe quality. An added challenge is the dependency of the water quality dynamics on the system's hydraulics, which influences the performance of the water quality controller. Prior research has addressed either solving the optimum operational hydraulic setting problem or regulating the water quality dynamics as separate problems. Additionally, there have been efforts to couple these two problems and solve one compact problem resulting in trade-offs between the contradictory objectives. In contrast, this paper takes a novel approach by examining the water quality dependency on the hydraulics from a control-theoretic standpoint. More specifically, we explore the influence of accountability for water quality controllability improvement when addressing the pump scheduling problem. We examine its effects on the cumulative cost of the interconnected systems as well as the subsequent performance of the water quality controller. To achieve this, we develop a framework that incorporates different controllability metrics within the operational hydraulic optimization problem; its aim is attaining an adequate level of water quality control across the system. We assess the aforementioned aspects' performance on various scaled networks with a wide range of numerical scenarios.

Efficient water quality (WQ) control in distribution networks is pivotal for ensuring the delivery of safe and clean drinking water to consumers. Attaining this goal is complex due to the inherent intricacies of WQ systems, which often pose substantial challenges to achieving full controllability over their dynamics. Controllability, in this context, refers to the ability to effectively steer, regulate, and maintain disinfectant levels within the network to consistently meet the established water health standards. In addition, hydraulic conditions play a crucial role in influencing the level of WQ controllability. Hydraulic settings, including flow rates and directions, pressures, and network components, have a direct impact on how water quality dynamics propagate thereby influencing its controllability. In this study, we explore various metrics that provide both qualitative and quantitative assessments of water quality systems controllability. We examine the applicability of these metrics to the water quality systems taking into consideration network topology, booster stations’ locations, and changes in hydraulic settings. By applying a comprehensive framework to various case studies, we assess the performance, practicality, and limitations of these metrics across different network configurations and scenarios. The outcomes of this assessment not only enable water system operators to evaluate the state of system controllability but also provide a pathway for leveraging these metrics to enhance the efficiency and effectiveness of control and regulation strategies.

Tracing disinfectant (e.g., chlorine) and contaminants evolution in water networks requires the solution of one-dimensional (1D) advection-reaction (AR) partial differential equations (PDEs). With the absence of analytical solutions in many scenarios, numerical solutions require high-resolution time and space discretizations, resulting in large model dimensions. This adds complexity to the water quality control problem. In addition, considering multispecies water quality dynamics rather than the single-species dynamics produces a more accurate description of the reaction dynamics under abnormal hazardous conditions (e.g., contamination events). Yet, these dynamics introduce a nonlinear reaction formulation to the model. To that end, solving nonlinear 1D AR PDEs in real time is critical to achieving monitoring and control goals for various scaled networks with a high computational burden. In this work, we propose a novel comprehensive framework to overcome the large-dimensionality issue by introducing different approaches for applying model order reduction (MOR) algorithms to the nonlinear system followed by applying a real-time water quality regulation algorithm that is based on an advanced model to maintain desirable disinfectant levels in water networks under multispecies dynamics. The performance of this framework is validated using rigorous numerical case studies under a wide range of scenarios demonstrating the challenges associated with regulating water quality under such conditions.