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.

In this paper, we review the emerging concept of digital twins (DTs) for urban water systems (UWS) based on the literature, stakeholder interviews and analyzing the current DT implementation process in the utility company VCS Denmark (VCS). Here, DTs for UWS are placed in the context of DTs at the component, unit process/operation or hydraulic structure, treatment plant, system, city, and societal levels. A UWS DT is characterized as a systematic virtual representation of the elements and dynamics of the physical system, organized in a star-structure with a set of features connected by data links that are based on standards for open data. This allows the overall functionality to be broken down into smaller, tangible units (features), enabling microservices that communicate via data links to emerge (the most central feature), facilitated by application programing interfaces (APIs). Coupled to the physical system, simulation models and advanced analytics are among the most important features. We propose distinguishing between living and prototyping DTs, where the term “living” refers to coupling observations from an ever-changing physical twin (which may change with, e.g., urban growth) with a simulation model, through a data link connecting the two. A living DT is thus a near real-time representation of an UWS and can be used for operational and control purposes. A prototyping DT represents a scenario for the system without direct coupling to real-time observations, which can be used for design or planning. By acknowledging that different DTs exist, it is possible to identify the value-creation from DTs achieved by different end-users inside and outside a utility organization. Analyzing the DT workflow in VCS shows that a DT must be multifunctional, updateable, and adjustable to support potential value creation across the utility company. This study helps clarify key DT terminology for UWS and identifies steps to create a DT by building upon digital ecosystems (DEs) and open standards for data.

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.

The advanced control of urban drainage systems (UDS) has great potential in reducing pollution to the receiving waters by optimizing the operations of UDS infrastructural elements. Existing controls vary in complexity, including local and global strategies, Real-Time Control (RTC) and Model Predictive Control (MPC). Their results are, however, site-specific, hindering a direct comparison of their performance. Therefore, the working group ‘Integral Real-Time Control’ of the German Water Association (DWA) developed the Astlingen benchmark network, which has been implemented in conceptual hydrological models and applied to compare RTC strategies. However, the level of detail of such implementations is insufficient for testing more complex MPC strategies. In order to provide a benchmark for MPC, this paper presents: (1) The implementation of the conceptual Astlingen system in an open-source hydrodynamic model (EPA-SWMM), and (2) the application of an MPC strategy to the developed SWMM model. The MPC strategy was tested against traditional and well-established local and global RTC approaches, demonstrating how the proposed benchmark system can be used to test and compare complex control strategies.