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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Combined sewer overflows (CSO) of mixed stormwater and wastewater pollute nearby receiving surface waters and pose a risk to the environment and human health. We use “integrated stormwater inflow control” to mitigate CSO by dynamically controlling the inflow of stormwater to the combined sewer system in real time, expanding the physical space of traditional real‐time control. This control is carried out with model predictive control (MPC), which we base on convex optimization including a linear internal surrogate model of the controllable aboveground and belowground infrastructure. A detailed hydrodynamic model is used to evaluate the results and recursively initialize the surrogate model. MPC dynamically decides when to let stormwater enter the sewer system and when to store and convey excess stormwater in the aboveground infrastructure otherwise intended for passive cloudburst management. The performance was quantified in a simulation study in Copenhagen, Denmark, using a 1‐D distributed hydrodynamic model and 32 rain events from 2016, of which 18 caused CSO in the situation without control. Four of the 18 CSO events were avoided with MPC, and the total CSO volume was reduced by 98.4% of the potential reducible volume. For one event, stormwater was unnecessarily kept on the surface because the surrogate model wrongly predicted a CSO. The computational cost was in all cases compatible with an operational implementation. With the invention of proper actuators for control of stormwater inflows, we show that MPC of stormwater inflows may be a viable supplement to more traditional passive ways of managing stormwater in urban areas.

High quality on-line flow forecasts are useful for real-time operation of urban drainage systems and wastewater treatment plants. This requires computationally efficient models, which are continuously updated with observed data to provide good initial conditions for the forecasts. This paper presents a way of updating conceptual rainfall-runoff models using Maximum a Posteriori estimation to determine the most likely parameter constellation at the current point in time. This is done by combining information from prior parameter distributions and the model goodness of fit over a predefined period of time that precedes the forecast. The method is illustrated for an urban catchment, where flow forecasts of 0-4 h are generated by applying a lumped linear reservoir model with three cascading reservoirs. Radar rainfall observations are used as input to the model. The effects of different prior standard deviations and lengths of the auto-calibration period on the resulting flow forecast performance are evaluated. We were able to demonstrate that, if properly tuned, the method leads to a significant increase in forecasting performance compared to a model without continuous auto-calibration. Delayed responses and erratic behaviour in the parameter variations are, however, observed and the choice of prior distributions and length of auto-calibration period is not straightforward.

Globally, smart meters measuring the water consumption with a high temporal resolution at the consumers' households are deployed at an increasing rate. In addition to their use for billing or leak detection purposes, smart meters may provide a detailed knowledge of the wastewater inflow to the sewer systems in space and time and open up for new types of system analyses aimed at closing the urban water balance. In this study, we first validate the smart meter data against other, independent water distribution data. Subsequently, we use a detailed hydrodynamic sewer system model to link the smart meter data from almost 2,000 consumers with in-sewer flow observations in order to simulate the wastewater component of the dry weather flow (DWF) and to identify potential anomalies. Results show that it is feasible to use smart meter data as input to a distributed urban drainage model, as the temporal dynamics of the model results and in-sewer flow observations match well. Furthermore, the study suggests that in-sewer flow observations may be subject to unrecognised uncertainties, which make them unsuitable for advanced investigations of the DWF composition, and this underlines the necessity of collecting data from independent sources. The study also exemplifies that digital system integration in the water sector may be complicated. However, overcoming these obstacles may improve both offline and real-time urban drainage management.