Abstract
This paper presents a two-stage method for simultaneous least-cost design and operation of looped water distribution systems (WDSs). After partitioning the network into a chord and spanning trees, in the first stage, a reformulated linear programming (LP) method is used to find the least cost design of a WDS for a given set of flow distribution. In the second stage, a non-linear programming (NLP) method is used to find a new flow distribution that reduces the cost of the WDS operation given the WDS design obtained in stage one. The following features of the proposed two-stage method make it more appealing compared to other methods: (1) the reformulated LP stage can consistently reduce the penalty cost when designing a WDS under multiple loading conditions; (2) robustness as the number of loading conditions increases; (3) parameter tuning is not required; (4) the method reduces the computational burden significantly when compared to meta-heuristic methods; and (5) in oppose to an evolutionary “black box” based methodology such as a genetic algorithm, insights through analytical sensitivity analysis, while the algorithm progresses, are handy. The efficacy of the proposed methodology is demonstrated using two WDSs case studies.
Highlights
Water distribution systems (WDSs) are critical infrastructures that deliver potable water from water sources to end-users
Results from the two case studies demonstrate that the proposed two-stage method (1) can consistently drop the penalty cost in the linear programming (LP) stage, (2) exhibit high robustness when compared to the non-linear programming (NLP) method that is used as the baseline, (3) produce comparable results for smaller network when compared to the NLP formulation, such as Case Study 1, and produce better solution for a bigger network when compared to the NLP formulation, such as Case Study 2
This paper presents an efficient iterative two-stage LP-NLP method for finding the least-cost operation and design of a water distribution system
Summary
Water distribution systems (WDSs) are critical infrastructures that deliver potable water from water sources to end-users. There are two disadvantages that are associated with the LPG method when it is used to solve the design-operation problem: (1) the loop and quasi-loops energy equations are unlikely to be balanced when the number of loading conditions and the size of the network increase; (2) flows from the water sources must be pre-selected for each of the loading conditions It is proposed in the LPG paper [2]. Given the flow distribution in the network, the first stage of the proposed two-stage method solves the design problem as an LP by utilizing the segmentation technique described earlier This reformulated LP stage represents a significant improvement when compared to the LP stage of the LPG method as the penalty cost can be dropped consistently by carrying out the LP solver repeatedly as an inner-loop (as will be explained in Methodology Section), thereby unlike the LPG method, there is no need to add additional network elements. These results are discussed and conclusions are drawn in the last section
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