In flow batteries, efficient operation is strongly related to a sophisticated volumetric flow rate control of the electrolyte. The optimal flow rate is a compromise between prevented losses caused by concentration over-potential and additional pump losses. Beside experimental approaches, model-based studies are often used for flow rate optimization. Therefore, we first present a multi-physical flow battery model which covers ohmic losses, shunt current losses, concentration over-potential and pump losses. The losses introduced by the energy conversion system for grid connection are included as well. A new method of efficiency determination is proposed, which allows for the determination of system efficiency depending on battery's state of charge and power as an alternative to the round-trip efficiency. With the SOC and power dependent efficiency, we develop an optimal flow rate control. While previous works achieved highest efficiencies with variable flow rates but constant flow factors, we propose to use a variable flow factor. It is demonstrated that this allows for a further increase in efficiency and a reduction of the required pump size. Furthermore, the reduced peak volumetric flow rate enables the use of smaller pipe diameters, which saves space and installation costs. Smaller pipe diameters will also decrease shunt current losses, which occur in the outer circuitry if two or more stacks are electrically connected in series.
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