The need for efficient pump operation in water supply systems (WSS) has become increasingly important over time, driven by the growing energy consumption and the associated energy costs. Forecasts for 2050 anticipate a global increase in water demand by 55%, indicating an increasing surge in WSS energy consumption. Control of pumping stations, which consume 70% of the energy in WSS, is the most critical area for optimization. This optimization challenge is commonly referred as the pump scheduling problem (PSP), and can be addressed using a variety of mathematical formulations. While numerous formulations exist to solve this optimization problem, the large majority of the studies are focus on the optimization techniques, sidelining the problem formulation. Due to the unique physical characteristics of each WSS, individual mathematical formulations may exhibit different levels of performance. In addition to general pumps’ operation optimization, the employment of variable speed pumps (VSP) can lead to significant energy savings compared to fixed speed pumps (FSP). However, despite their apparent benefits, many established optimization models for the PSP have not yet incorporated VSP decision variables into their formulations. Therefore, this work aims to review the main mathematical formulations for the pump scheduling problem for WSS with VSP and to present a quantitative comparative study of three mathematical formulations applied to a case study in the literature. The comparative analysis here presented revealed that the optimization model based on duty cycles is more cost-efficient when compared to alternative approaches discussed in the literature.

中文翻译：

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供水系统的成本效率：水泵调度问题优化模型的应用综述


随着能源消耗和相关能源成本的不断增长，供水系统 (WSS) 中对高效泵运行的需求变得越来越重要。预计到 2050 年，全球需水量将增加 55%，这表明 WSS 能源消耗将激增。泵站的控制消耗了 WSS 70% 的能源，是最关键的优化领域。这种优化挑战通常称为泵调度问题 (PSP)，可以使用各种数学公式来解决。虽然存在许多解决此优化问题的公式，但绝大多数研究都集中在优化技术上，而忽略了问题公式化。由于每个 WSS 的独特物理特性，各个数学公式可能表现出不同水平的性能。除了一般泵的运行优化之外，与定速泵（FSP）相比，使用变速泵（VSP）可以显着节省能源。然而，尽管有明显的好处，许多已建立的 PSP 优化模型尚未将 VSP 决策变量纳入其公式中。因此，本文旨在回顾带有 VSP 的 WSS 泵调度问题的主要数学公式，并对应用于文献中案例研究的三种数学公式进行定量比较研究。这里提出的比较分析表明，与文献中讨论的替代方法相比，基于占空比的优化模型更具成本效益。