Optimization of installation and energy costs in water distribution systems with unknown flow directions

Cassiolato, Gustavo H. B.; Carvalho, Esdras P.; Ravagnani, Mauro A.S.S.

doi:10.2166/bgs.2022.003

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…Cassiolato et al (2022a) considered in the model unknown flow directions and SBB and BARON solvers were used to achieve the problem solution. Cassiolato et al (2022b) considered installation and energy costs, with unknown flow directions.…”

Section: Literature Reviewmentioning

confidence: 99%

Water Distribution Networks Optimization Considering Uncertainties in the Demand Nodes

Cassiolato,

Ruiz-Femenia,

Salcedo-Diaz

et al. 2024

Water Resour Manage

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The fluctuation in the consumption of treated water is a situation that distribution networks gradually face. In times of greater demand, this consumption tends to suffer unnecessary impacts due to the lack of water. The uncertainty that occurs in water consumption can be mathematically modeled by a finite set of scenarios generated by a normal distribution and attributed to the network design. This study presents an optimization model to minimize network installation and operation costs under uncertainties in water demands. A Mixed Integer Nonlinear Programming model is proposed, considering the water flow directions in the pipes as unknown. A deterministic approach is used to solve the problem in three steps: First, the problem is solved with a nominal value for each uncertain parameter. In the second stage, the problem is solved for all scenarios, with the independent variables of the scenario being fixed and obtained from the solution reached in the first stage, known as the deterministic solution. Finally, all scenarios are solved without fixing any variable values, in a stochastic approach. Two case studies were used to test the applicability of the model and global optimization techniques were used to solve the problem. The results show that the stochastic solution can lead to optimal solutions for robust and flexible water distribution networks, capable of working under different conditions, considering the uncertainties of node demand and variable pipe directions.

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Section: Literature Reviewmentioning

confidence: 99%

Water Distribution Networks Optimization Considering Uncertainties in the Demand Nodes

Cassiolato,

Ruiz-Femenia,

Salcedo-Diaz

et al. 2024

Water Resour Manage

Self Cite

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“…Cassiolato et al. (2022) applied convex hull relaxations and disjunctive programming techniques to solve an MINLP problem to minimize WDS operation and installation costs using the global solvers BARON and SBB (Bussieck & Drud, 2001; Tawarmalani & Sahinidis, 2005).…”

Section: Introductionmentioning

confidence: 99%

“…Eck and Mevissen (2012), Gleixner et al (2012), and Bonvin et al (2017) used quadratic approximations to represent the pipe head loss equations to construct optimization problems that could be solved with modern solvers. Cassiolato et al (2022) applied convex hull relaxations and disjunctive programming techniques to solve an MINLP problem to minimize WDS operation and installation costs using the global solvers BARON and SBB (Bussieck & Drud, 2001;Tawarmalani & Sahinidis, 2005).…”

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confidence: 99%

A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems

Thomas,

Sela

2024

Water Resources Research

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Water distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems. Applying the classical mixed integer linear programming (MILP) approach to model WDSs hydraulics within an optimization framework can contribute to higher solution accuracy with lower computational effort. However, adapting WDSs models to conform to a MILP formulation has proven challenging because of the intrinsic non‐linearity of system hydraulics and the complexity associated with modeling hydraulic devices that influence the state of the WDS. This paper introduces MILPNet, an adjustable framework for WDSs that can be used to build and solve an extensive array of MILP optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, hydraulic devices, control rules, and status checks. To conform to MILP structure, MILPNet employs piece‐wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Modeling accuracy was shown to be comparable to EPANET, a public domain software for hydraulic modeling, and sensitivity analyses were conducted to examine the impacts of the modeling assumptions on the performance of MILPNet. Additionally, application of the framework was demonstrated using pump scheduling optimization examples in single and rolling horizon scenarios. Our results show that MILPNet can facilitate the construction and solution of optimization problems for a range of applications in WDSs operations.

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Water distribution networks optimization considering uncertainties in the demand nodes

Ravagnani

Cassiolato

Ruiz‐Femenia

et al. 2023

Preprint

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The design of water distribution networks (WDN) can be formulated as an optimization problem. The objective function, normally, is the network cost, given by the installation cost, which depends on the pipe diameters and by the operation cost, given by the pumping costs associated to the network, which depends on the hydraulic pumps necessary in the system. The water demand can be variable in the network nodes and this variability can be modeled by a finite set of scenarios generated by a normal distribution. In the present paper a disjunctive Mixed Integer Nonlinear Programming (MINLP) formulation optimization problem is proposed to model the design of WDN under uncertainties in the nodes demand. Flow directions are considered unknown and a deterministic approach is used to solve the problem in three steps. Firstly, the problem is solved considering only a nominal value to each uncertain parameter. In the second step, the problem is solved for all the scenarios, being the scenario independent variables fixed to the solution achieved in the first step, which is a deterministic solution. Finally, all the scenarios are solved without fixing any variable value, in a stochastic approach. Two case studies were used to test the model applicability and global optimization techniques were used to solve the problem. Results show that the stochastic solution can lead to optimal solutions for robust and flexible WDN, able to work under distinct conditions, considering the nodes demand uncertainties.

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Optimization of installation and energy costs in water distribution systems with unknown flow directions

Cited by 3 publications

References 19 publications

Water Distribution Networks Optimization Considering Uncertainties in the Demand Nodes

Water Distribution Networks Optimization Considering Uncertainties in the Demand Nodes

A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems

Water distribution networks optimization considering uncertainties in the demand nodes

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