Towards globally optimal operation of water supply networks

Gleixner, Ambros; Held, Harald; Huang, Wei; Vigerske, Stefan

doi:10.3934/naco.2012.2.695

Cited by 53 publications

(59 citation statements)

References 12 publications

(18 reference statements)

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“…We assume that reservoirs have infinite water supply and the head of the i th reservoir is fixed [7]- [9], [41, Chapter 3.1], [44,Chapter 3]. This can also be viewed as an operational constraint (15b) where h R i is specified.…”

Section: Control-oriented Modeling Of Wdnsmentioning

confidence: 99%

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

Wang

Taha

Gatsis

et al. 2020

IEEE Trans. Control Netw. Syst.

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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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Section: Control-oriented Modeling Of Wdnsmentioning

confidence: 99%

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

Wang

Taha

Gatsis

et al. 2020

IEEE Trans. Control Netw. Syst.

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“…The pump scheduling problem can be posed as a mixed integer non-linear problem (MINLP) and solved using a branch and bound algorithm (Gleixner et al 2012;Burgschweiger et al 2008). For a special network structure the components can be approximated with convex relaxations, yielding a more tractable convex MINLP (Bonvin et al 2016).…”

Section: Review Of Mathematical Optimisation Approachesmentioning

confidence: 99%

“…However, convex relaxation can be formed by neglecting the concave constraints. These constraints are implemented using the big-M method detailed in Section 3.3 and Gleixner et al (2012). A set of linear constraints describing a convex set can also be considered to approximate the characteristic curve.…”

Section: Pump Approximationsmentioning

confidence: 99%

“…Such a formulation was used by Gleixner et al (2012). Often multiple pumps are installed in parallel or in series at pumping stations, such as pumps main 1 and main 2 in the Van Zyl network shown in Fig.…”

Section: Pump Approximationsmentioning

confidence: 99%

“…For the network models used the errors are small, the simplest pump cost approximation with a consideration for pump switching is used for all further analysis as outlined in Table 1. Bunn and Reynolds (2009) showed that in practice savings have been made through optimising the pump operations near the best efficiency point (BEP) while other applications such as Gleixner et al (2012) have used less detailed representations with good success.…”

Section: Objective Functionmentioning

confidence: 99%

See 2 more Smart Citations

Exploring Optimal Pump Scheduling in Water Distribution Networks with Branch and Bound Methods

Menke

Abraham

Parpas

et al. 2016

Water Resour Manage

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Water utilities can achieve significant savings in operating costs by optimising pump scheduling to improve efficiency and shift electricity consumption to low-tariff periods. Due to the complexity of the optimal scheduling problem, heuristic methods that cannot guarantee global optimality are often applied. This paper investigates formulations of the pump scheduling problem solved using a branch and bound method. Piecewise linear component approximations outperform non-linear approximations within application driven accuracy bounds and demand uncertainties. It is shown that the reduction of symmetry through the grouping of pumps significantly reduces the computational effort, whereas loops in the network have the opposite effect. The computational effort of including convex, non-linear pump operating, and maintenance cost functions is investigated. Using case studies, it is shown that linear and fixed-cost functions can be used to find schedules which, when simulated in a full hydraulic simulation, have performances that are within the solver optimality gap and the uncertainty of demand forecasts.

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Control of tree water networks: A geometric programming approach

Perelman

Amin

2015

Water Resources Research

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This paper presents a modeling and operation approach for tree water supply systems. The network control problem is approximated as a geometric programming (GP) problem. The original nonlinear nonconvex network control problem is transformed into a convex optimization problem. The optimization model can be efficiently solved to optimality using state-of-the-art solvers. Two control schemes are presented: (1) operation of network actuators (pumps and valves) and (2) controlled demand shedding allocation between network consumers with limited resources. The dual of the network control problem is formulated and is used to perform sensitivity analysis with respect to hydraulic constraints. The approach is demonstrated on a small branched-topology network and later extended to a medium-size irrigation network. The results demonstrate an intrinsic trade-off between energy costs and demand shedding policy, providing an efficient decision support tool for active management of water systems.

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Towards globally optimal operation of water supply networks

Cited by 53 publications

References 12 publications

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

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

Exploring Optimal Pump Scheduling in Water Distribution Networks with Branch and Bound Methods

Control of tree water networks: A geometric programming approach

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