Chance-constrained stochastic MPC of Astlingen urban drainage benchmark network. (October 2021) - Svensen, Jan Lorenz; Sun, Congcong; Cembrano, Gabriela; Puig, Vicenç
Abstract: 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. Graphical abstract: Highlights: Stochastic MPC has been designed to the urban drainage systems using revised chance-constrained method. Rainfall input has been considered as stochastic disturbance, ranging from biases in the forecast to the size of the uncertainty. Operational behaviors have been compared between MPC with perfect forecast and the chance-constrained MPC based on different scenarios. Optimal strategies can be obtained by stochastic MPC with less overflow released to the environment.