Optimal Valve Control in Water‐Distribution Networks

Jowitt, Paul; Xu, Chengchao

doi:10.1061/(asce)0733-9496(1990)116:4(455)

Cited by 205 publications

(155 citation statements)

References 6 publications

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“…The network has 22 nodes, 37 pipes and 3 reservoirs. Details on pipes' characteristics, nodal demands and reservoirs' levels are presented in [13,24]. We set minimum pressure at each node to 30 m and maximum velocity in each pipe to 1 m/s.…”

Section: Case Studymentioning

confidence: 99%

Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

2016

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In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided.

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Section: Case Studymentioning

confidence: 99%

Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

2016

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“…5. Details on pipes' characteristics and nodal demands can be found in Jowitt and Xu (1990) and Araujo et al (2006), respectively. The resulting MINLP has 2304 continuous variables, 74 binary variables, 566 linear constraints and 3552 nonlinear constraints.…”

Section: Case Studymentioning

confidence: 99%

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

Pecci

Abraham

Stoianov

2016

Struct Multidisc Optim

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In this paper, we study the multiobjective codesign problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model.

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“…Jowitt and Xu [3] developed an algorithm to determine the values of flow control valve settings to minimize leakage. The non-linear basic hydraulic equations of the network, which describe the node heads and the flow rates in the pipes, are augmented by terms that explicitly account for pressure-depended leakage by terms that model the effect of valve actions.…”

Section: Literature Reviewmentioning

confidence: 99%

Non-elastic matrix model for hydraulic networks calculation

Diniz¹,

Souza²,

L.³

2007

WIT Transactions on Ecology and the Environment, Vol 103

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This paper presents a non-elastic matrix model to calculate hydraulic networks, based on a method created by Nahavandi and Catanzaro (Journal of Hydraulics Division, 99(HY1), pp.47-63, 1973). It is a method that calculates the discharges and pressure heads in hydraulic networks for the steady state, for the extended period and for the transient state. This method has advantages concerning the Cross method, because the latter does not allow the calculation of transient situations such as the settings of valves, the starting and stopping of boosters, the branch ruptures, etc. The applicability of the method created by Nahavandi and Catanzaro was enhanced, because the programming and input data to consider the presence of valves, reservoirs or boosters in the hydraulic network were developed. Furthermore, the mathematical formulation and programming to calculate the extended period and transient state were also developed. The matrix method is working well, because the model was applied to calculate some hydraulic networks used as examples and the values calculated by the model are similar to the ones obtained from the technical literature.

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Optimal Valve Control in Water‐Distribution Networks

Cited by 205 publications

References 6 publications

Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

Non-elastic matrix model for hydraulic networks calculation

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