Model predictive control (MPC) can be used to manage combined urban drainage systems more efficiently for protection of human health and the environment, but examples of operational implementations are rare. This paper reviews more than 30 years of partly heterogeneous research on the topic. We propose a terminology for MPC of urban drainage systems and a hierarchical categorization where we emphasize four overall components: the "receding horizon principle", the "optimization model", the "optimization solver", and the "internal MPC model". Most of the reported optimization models share the trait of a multiobjective optimization based on a conceptual internal MPC model. However, there is a large variety of both convex and non-linear optimization models and optimization solvers as well as constructions of the internal MPC model. Furthermore, literature disagrees about the optimal length of the components in the receding horizon principle. The large number of MPC formulations and evaluation approaches makes it problematic to compare different MPC methods. This review highlights methods, challenges, and research gaps in order to make MPC of urban drainage systems accessible for researchers and practitioners from different disciplines. This will pave the way for shared understanding and further development within the field, and eventually lead to more operational implementations.

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In this work, a revised formulation of chance-constrained (CC) model predictive control (MPC) is presented. The focus of this work is on the mathematical formulation of the revised CC-MPC, and the reason behind the need for its revision. The revised formulation is given in the context of sewer systems, and their weir overflow structures. A linear sewer model of the Astlingen benchmark sewer model is utilized to illustrate the application of the formulation, both mathematically and performance-wise through simulations. Based on the simulations, a comparison of performance is done between the revised CC-MPC and a comparable deterministic MPC, with a focus on overflow avoidance, computation time, and operational behavior. The simulations show similar performance for overflow avoidance for both types of MPC, while the computation time increases slightly for the CC-MPC, together with operational behaviors getting limited.

This study uses multi-objective optimization of an integrated weil fieid modei to improve the management of a waterworks. The weii fieid modei, caiied WELLNES (WELL field Numericai Engine Sheii) is a dynamic coupiing of a groundwater model, a pipe network model, and a weii modei.WELLNES is capabie of predicting the water ievei and the energy consumption of the individuai production weiis. The modei has been applied to S0nders0 waterworks in Denmark, where it predicts the energy consumption within 1.8% ofthe observed. The objectives ofthe optimization probiem are to minimize the specific energy of the waterworks and to avoid infiow of contaminated water from a nearby contaminated site. The decision variabies are the pump status (on/off), and the constraint is that the waterworks has to provide a certain amount of drinking water. The advantage of multiobjective optimization is that the Pareto curve provides the decision-makers with compromise soiutions between the two competing objectives. In the test case the Pareto optimai soiutions are compared with an exhaustive benchmark solution. It is shown that the energy consumption can be reduced by 4% by changing the pumping configuration without vioiating the protection against contamination.

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