In urban drainage systems (UDS), a proven method for reducing the combined sewer overflow (CSO) pollution is real-time control (RTC) based on model predictive control (MPC). MPC methodologies for RTC of UDSs in the literature rely on the computation of the optimal control strategies based on deterministic rain forecast. However, in reality, uncertainties exist in rainfall forecasts which affect severely accuracy of computing the optimal control strategies. Under this context, this work aims to focus on the uncertainty associated with the rainfall forecasting and its effects. One option is to use stochastic information about the rain events in the controller; in the case of using MPC methods, the class called stochastic MPC is available, including several approaches such as the chance-constrained MPC(CC-MPC) method. In this study, we apply CC-MPC to the UDS. Moreover, we also compare the operational behavior of both the classical MPC with perfect forecast and the CC-MPC based on different stochastic scenarios of the rain forecast. The application and comparison have been based on simulations using a SWMM model of the Astlingen urban drainage benchmark network. From the simulations, it was found that CSO volumes were larger when CC-MPC had overestimating forecast biases, while for MPC they increased with any presence of forecast biases.

在城市排水系统 (UDS) 中，基于模型预测控制 (MPC) 的实时控制 (RTC) 是减少合流下水道溢流 (CSO) 污染的一种行之有效的方法。文献中用于 UDS 的 RTC 的 MPC 方法依赖于基于确定性降雨预测的最优控制策略的计算。然而，在现实中，降雨预报存在不确定性，严重影响最优控制策略计算的准确性。在这种背景下，这项工作旨在关注与降雨预测及其影响相关的不确定性。一种选择是在控制器中使用有关下雨事件的随机信息；在使用 MPC 方法的情况下，可以使用称为随机 MPC 的类，包括几种方法，例如机会约束 MPC(CC-MPC) 方法。在这项研究中，我们将 CC-MPC 应用于 UDS。此外，我们还比较了具有完美预报的经典 MPC 和基于不同降雨预报随机场景的 CC-MPC 的操作行为。应用和比较基于使用 Astlingen 城市排水基准网络的 SWMM 模型的模拟。从模拟中发现，当 CC-MPC 高估预测偏差时，CSO 数量更大，而对于 MPC，它们随着任何预测偏差的存在而增加。