Optimal Localization of Pressure Reducing Valves in Water Distribution Systems by a Reformulation Approach

AbstractWater loss reduction in water distribution systems (WDSs) is a challenging task for water utilities worldwide. One of the most reliable and cost-effective ways to reduce water loss is to properly regulate operational pressure of the system through optimizing pressure reducing valve (PRV) placements. This well-known engineering problem can be casted into a mixed-integer nonlinear program (MINLP) where binary variables are introduced to represent positions of PRVs. Many works in the literature applied heuristic algorithms to address the optimization problem. In this paper, at first, we proposed a new optimization model and reformulated it as the mathematical program with complementarity constraints (MPCCs). It is due to the fact that the stationary point of the MPCCs is likely to be trapped into bad local solutions, a soft heuristic method is then proposed to determine the MINLP local solution in each iteration before a stationary point of the MPCCs is reached. This method not only enhances the quality of MINLP solution, but also decreases computation time for solving the MPCCs. The newly formulated MPCCs is applied to determine optimal localization of PRVs for two WDS benchmarks and a real-world WDS in Vietnam. The results are compared with others in the literature demonstrating that using our new optimization model, better and more reliable MINLP solution can be found for large scale WDSs.

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A MINLP Model for Optimal Localization of Pumps as Turbines in Water Distribution Systems Considering Power Generation Constraints

Water ◽

10.3390/w12071979 ◽

2020 ◽

Vol 12 (7) ◽

pp. 1979 ◽

Cited By ~ 1

Author(s):

Khoa Dang Nguyen ◽

Pham Duc Dai ◽

Dong Quoc Vu ◽

Bui Manh Cuong ◽

Vu Phi Tuyen ◽

...

Keyword(s):

Distribution Systems ◽

Water Distribution ◽

Water Distribution Systems ◽

Mixed Integer ◽

Nonlinear Program ◽

Bound Constraints ◽

Minimum Power ◽

System Pressure ◽

Minlp Model ◽

Optimal Localization

Pressure reducing valves (PRVs) are commonly used for pressure control in water distribution systems (WDSs) by means of dissipating the pressure excess. The use of pumps as turbines (PATs) is an alternative and more favorable system since they not only control the system pressure to decrease water leakage, but also utilize the pressure excess to generate electrical energy. The optimal localization of PATs can be casted into a mixed-integer nonlinear program (MINLP) where binary variables are used to represent the presence of PATs on links. Most of the available MINLP models for optimal PAT localization adopted the optimization approaches for PRV localization without considering the bound constraints on flow rates and heads of PATs. As a result, such an optimization model may make PATs delivering a non-desired output. In this paper, we propose a new MINLP model for optimal PAT localization. Instead of using a constraint on the maximum number of PATs to be placed in a WDS, new constraints relating to the minimum power generated by PAT are introduced to find links having adequate flows and head drops for placing PATs. Moreover, constraints are used to restrict flows and heads of PATs to their feasible operating range, so that the problem can be efficiently solved. The proposed MINLP model is applied to the optimal localization of PATs for a WDS benchmark and a real-world WDS in Vietnam. The results demonstrate that the new MINLP model can efficiently identify optimal locations for PAT placement where the specified working range and minimum power generated by the PATs are ensured.

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