This paper investigates the computation of daily schedules of pumps and boundary valves for the minimization of energy costs in water distribution networks (WDN) with dynamically adaptive configurations. The considered problem combines integer (“on”/“off”) pump control variables, non-convex energy conservation constraints and time-coupling mass conservation constraints. For operational WDNs, the resulting non-convex mixed-integer non-linear program (MINLP) is too large to be solved using available methods. We propose a tailored heuristic solution method based on the Alternating Direction Method of Multipliers which distributes and coordinates the solution of smaller problems corresponding to individual time steps of the original MINLP. The proposed method is applied to a large-scale WDN from the UK. The daily schedule of pumps and boundary valves obtained for the dynamically adaptive network configuration, computed in 12 min, is shown to be at most 6% suboptimal and nearly 5% cheaper than the globally optimal schedule corresponding to the traditional (sectorized) network configuration. The proposed algorithm outperforms alternative off-the-shelf and tailored approaches, providing a scalable method to compute good solutions to the complex day-ahead pump and valve scheduling problem in operational dynamically adaptive WDNs.

中文翻译：

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具有储能功能的动态自适应配水管网的日前泵和阀门调度问题的分布式解决方案


本文研究了泵和边界阀的日常时间表的计算，以最大限度地降低具有动态自适应配置的配水网络 （WDN） 中的能源成本。所考虑的问题结合了整数 （“on”/“off”） 泵控制变量、非凸能量守恒约束和时间耦合质量守恒约束。对于可操作的 WDN，生成的非凸混合整数非线性规划 （MINLP） 太大，无法使用现有方法求解。我们提出了一种基于乘子交替方向法的定制启发式求解方法，该方法分配和协调与原始 MINLP 的各个时间步相对应的较小问题的解决方案。所提出的方法应用于来自英国的大规模 WDN。在 12 分钟内计算出的动态自适应网络配置所获得的泵和边界阀的每日计划，比对应于传统（扇区化）网络配置的全局最优计划最多低 6%，便宜近 5%。所提出的算法优于其他现成的和定制的方法，提供了一种可扩展的方法来计算运行动态自适应 WDN 中复杂的日前泵和阀门调度问题的良好解决方案。