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The application of mathematical optimization methods for water supply system design and operation provides the capacity to increase the energy efficiency and to lower the investment costs considerably. We present a system approach for the optimal design and operation of pumping systems in real-world high-rise buildings that is based on the usage of mixed-integer nonlinear and mixed-integer linear modeling approaches. In addition, we consider different booster station topologies, i.e. parallel and series-parallel central booster stations as well as decentral booster stations. To confirm the validity of the underlying optimization models with real-world system behavior, we additionally present validation results based on experiments conducted on a modularly constructed pumping test rig. Within the models we consider layout and control decisions for different load scenarios, leading to a Deterministic Equivalent of a two-stage stochastic optimization program. We use a piecewise linearization as well as a piecewise relaxation of the pumps’ characteristics to derive mixed-integer linear models. Besides the solution with off-the-shelf solvers, we present a problem specific exact solving algorithm to improve the computation time. Focusing on the efficient exploration of the solution space, we divide the problem into smaller subproblems, which partly can be cut off in the solution process. Furthermore, we discuss the performance and applicability of the solution approaches for real buildings and analyze the technical aspects of the solutions from an engineer’s point of view, keeping in mind the economically important trade-off between investment and operation costs.
Water distribution systems are an essential supply infrastructure for cities. Given that climatic and demographic influences will pose further challenges for these infrastructures in the future, the resilience of water supply systems, i.e. their ability to withstand and recover from disruptions, has recently become a subject of research. To assess the resilience of a WDS, different graph-theoretical approaches exist. Next to general metrics characterizing the network topology, also hydraulic and technical restrictions have to be taken into account. In this work, the resilience of an exemplary water distribution network of a major German city is assessed, and a Mixed-Integer Program is presented which allows to assess the impact of capacity adaptations on its resilience.