Before drinking water leaves water treatment plants, chemical disinfection is typically applied to ensure the microbiological safety of the treated water. Water utilities worldwide rely on chlorine-based disinfectants due to their strong antimicrobial activity and low cost. Excess chlorine is usually applied at the treatment plant to prevent microbial recontamination of the treated drinking water as it moves through the pipes of water distribution networks (WDN).Residual chlorine concentrations are routinely monitored to verify that a sufficient residual is maintained throughout WDN. Maintenance of a detectable residual is also typically mandated by state and federal regulations in many countries. For instance, water utilities in the US are required to preserve detectable chlorine residual throughout their WDNs under the Surface Water Treatment Rule (SWTR) (Haas, 1999), and many states have established even more stringent numerical thresholds on the minimum residual concentration (Roth & Cornwell, 2018).Nevertheless, determining the appropriate chlorine dosage to ensure a sufficient residual, particularly at the far ends of WDNs where the water age is the highest, is rather challenging. Applying large doses of chlorine-based disinfectants at the treatment plant has been associated with multiple issues, including the excessive formation of disinfection byproducts as well as aesthetic issues with water taste and odor (Fisher et al., 2011;Hua et al., 2015). Alternatively, the disinfectant can be injected in smaller doses at multiple locations in the network, a practice commonly known as booster disinfection, to maintain a uniform disinfectant concentration throughout the WDN (Tryby et al., 1999). Most recently, to solve the problem of low disinfectant concentrations at critical dead-end nodes with no need of increasing disinfectant dose at sources or installing additional booster stations, the modulation of nodal outflows in WDN is proposed (Avvedimento et al., 2020). For more context of real-time control of water quality in WDN (see Creaco et al., 2019). Literature ReviewOver the past two decades, many studies have investigated the water quality control problem (WQC) of optimizing the locations and/or dosing schedules of booster disinfection systems.A wide range of optimization-based methods was used to solve the WQC problem, including linear programming (LP), quadratic programming (QP), heuristic algorithms such as genetic algorithm (GA), and
A state‐space representation of water quality (WQ) dynamics describing disinfectant (e.g., chlorine) transport dynamics in drinking water distribution networks has been recently proposed. Such representation is a byproduct of space‐ and time‐discretization of the partial differential equations modeling transport dynamics. This results in a large state‐space dimension even for small networks with tens of nodes. Although such a state‐space model provides a model‐driven approach to predict WQ dynamics, incorporating it into model‐based control algorithms or state estimators for large networks is challenging and at times intractable. To that end, this paper investigates model order reduction (MOR) methods for WQ dynamics with the objective of performing post‐reduction feedback control. The presented investigation focuses on reducing state‐dimension by orders of magnitude, the stability of the MOR methods, and the application of these methods to model predictive control.
Optimal, network-driven control of water distribution networks (WDNs) is very difficult: valve and pump models form non-trivial, combinatorial logic, hydraulic models are nonconvex, water demand patterns are uncertain, and WDNs are naturally large-scale. Prior research on control of Water Distribution Network (WDN)s addressed major research challenges, yet either (i) adopted simplified hydraulic models, WDN topologies, and rudimentary valve/pump modeling or (ii) used mixed-integer, nonconvex optimization to solve WDN control problems.The objective of this paper is to develop tractable computational algorithms to manage WDN operation, while considering arbitrary topology, flow direction, an abundance of valve types, control objectives, hydraulic models, and operational constraints-all while only using convex, continuous optimization. Specifically, we propose new Geometric Programming (GP)-based Model Predictive Control (MPC) algorithms, designed to solve the water flow equations and obtain WDN controls-pump/valve schedules alongside heads and flows. The proposed approach amounts to solving a series of convex optimization problems that graciously scale to large networks. Under demand uncertainty, the proposed approach is tested using a 126-node network with many valves and pumps and shown to outperform traditional, rule-based control. The developed GP-based MPC algorithms, as well as the numerical test results are all included on Github.
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