基于数据分布鲁棒的给水管网水泵优化控制
Optimal Pump Control for Water Distribution Networks via Data-based Distributional Robustness
摘要：
在本文中，我们提出了一个基于数据的方法来解决多周期随机最优供水网络（WDN）的问题（OWF）。该框架明确地考虑了水泵计划和供水网络的水头水平与有限的信息的需求预测误差的延长期模拟。我们的目标是确定网络连接的组件，如标称泵的时间表和水箱的水头水平和储备政策，指定设备的反应，以预测误差的波动的水需求的住宿的最佳反馈决策。而不是假设整个水网络的不确定性是由一个规定的一定的分布产生的，我们认为模糊集的分布集中在一个经验分布，这是直接基于一个有限的训练数据集。我们使用基于距离的模糊集与Wasserstein度量来量化真实未知数据生成分布与经验分布之间的距离。这使得我们的多周期OWF框架能够权衡系统性能和训练数据集中固有的采样误差。三水箱配水网络的案例研究系统地说明了泵的运行成本，约束违反的风险，和样本外的性能之间的权衡。
英文摘要：
In this paper, we propose a data-based methodology to solve a multi-period stochastic optimal water flow (OWF) problem for water distribution networks (WDNs). The framework explicitly considers the pump schedule and water network head level with limited information of demand forecast errors for an extended period simulation. The objective is to determine the optimal feedback decisions of network-connected components, such as nominal pump schedules and tank head levels and reserve policies, which specify device reactions to forecast errors for accommodation of fluctuating water demand. Instead of assuming the uncertainties across the water network are generated by a prescribed certain distribution, we consider ambiguity sets of distributions centered at an empirical distribution, which is based directly on a finite training data set. We use a distance-based ambiguity set with the Wasserstein metric to quantify the distance between the real unknown data-generating distribution and the empirical distribution. This allows our multi-period OWF framework to trade off system performance and inherent sampling errors in the training dataset. Case studies on a three-tank water distribution network systematically illustrate the tradeoff between pump operational cost, risks of constraint violation, and out-of-sample performance.
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