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This study presents convex modeling of drainage pumps so that real-time control systems can be implemented to minimize their energy use. A convex model is built based on pump curves and then used in mixed-integer optimization to allow pumps to be turned on or off. It is implemented as an extension to the open source software package RTC-Tools. The formulation is such that the continuous relaxations of the mixed-integer problem are convex, hence branch-and-bound techniques may be used to find a global optimum. The formulation can be used for variable-speed and constant-speed pumps. There are several possible applications, such as optimization of polder systems, pumped-storage systems, or certain water distribution networks. Finally, an example of the drainage pump is presented to compare the method to current methods and show that energy can be saved by using the proposed method.

Plain Language Summary Pumps are present in several water systems, like drinking water networks or drainage pumps. Drainage pumps are one of the greatest energy consumers in low-lying countries. Water managers decide when to turn them on depending on the sea level, weather prediction, and other factors. The operation costs depend on the time of operation. This article explains a method to decide when to turn these pumps on to use the least amount of energy, cheaper, and more sustainable drainage possible. The method can be further applied to any water systems containing pumps.