Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

Abstract

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.

Adaptive Model Predictive Control for Fire Incidents in Water Distribution Networks

“…Furthermore, the valves considered are pressure reducing valves (PRVs). The pump modelling and the heuristic differ from the previous literature (for example [37,35]) and thus we present them in this section for more clarity. The rest of the modelling techniques, for steady-state hydraulics, are well known (see for example [7]) and thus, we will only go into further details in Sections 4 and 5, where the formulations for the normal and fire control are presented respectively.…”

“…A number of approaches, for the control of pumps and valves in WDNs, have been proposed under the framework of Model Predictive Control (MPC) also known as Receding Horizon Control (RHC) (see for example [29,23,16,14,28,15,36,37,27,35]). Although not guaranteeing global optimality with respect to the MINLP problem, the MPC methodology is computationally faster (thus more scalable) and better suited for dealing with uncertainties compared to approaches mentioned in the previous paragraph (such as [11,31,21,10]), since the control can be adjusted at each timestep.…”

“…In [27], Sampathirao et al develop a GPU-accelerated stochastic MPC method, considering mass-balance hydraulics. In [35], Wang et al apply MPC with a geometric programming formulation along with a binary search heuristic.…”

Cyber-Physical Systems for Smart Water Networks: A Review

“…The non-convexity is attributed due to presence of the non-convex sign function. Some of the techniques to address the non-convexity of head loss equations are linearization [106], Big-M [101] and Geometric Programming [107].…”

Optimal Pump Control for Water Distribution Networks via Data-based Distributional Robustness

“…The flexibility of water flow manipulators (pumps and valves) in water networks has been utilized to optimize various objectives, including production and transportation costs, water quality, safe storage, smoothness of control actions, etc. [15,11,22,46,38,9,27,47,40,39]. However, most optimal water flow control methods use deterministic point forecasts of exogenous water demands, which neglects their inherent stochasticity.…”