Efficient multi-scenario Model Predictive Control for water resources management with ensemble streamflow forecasts

Model Predictive Control (MPC) is one of the most advanced real-time control techniques that has been widely applied to Water Resources Management (WRM). MPC can manage the water system in a holistic manner and has a flexible structure to incorporate specific elements, such as setpoints and constraints. Therefore, MPC has shown its versatile performance in many branches of WRM. Nonetheless, with the in-depth understanding of stochastic hydrology in recent studies, MPC also faces the challenge of how to cope with hydrological uncertainty in its decision-making process. A possible way to embed the uncertainty is to generate an Ensemble Forecast (EF) of hydrological variables, rather than a deterministic one. The combination of MPC and EF results in a more comprehensive approach: Multi-scenario MPC (MS-MPC). In this study, we will first assess the model performance of MS-MPC, considering an ensemble streamflow forecast. Noticeably, the computational inefficiency may be a critical obstacle that hinders applicability of MS-MPC. In fact, with more scenarios taken into account, the computational burden of solving an optimization problem in MS-MPC accordingly increases. To deal with this challenge, we propose the Adaptive Control Resolution (ACR) approach as a computationally efficient scheme to practically reduce the number of control variables in MS-MPC. In brief, the ACR approach uses a mixed-resolution control time step from the near future to the distant future. The ACR-MPC approach is tested on a real-world case study: an integrated flood control and navigation problem in the North Sea Canal of the Netherlands. Such an approach reduces the computation time by 18% and up in our case study. At the same time, the model performance of ACR-MPC remains close to that of conventional MPC.