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Section 2.5 Shunt currents 2.5.7 Numerical example of shunt currents in a single stack Equivalent shunt current For all examples in this section, the VRFB is supplied with a flow rate corresponding to five times the stoichiometrically required flow rate for the particular operation. For more information on this flow rate control strategy, the reader is referred to Section 8.2, starting on page 120. The tank SoC is fixed at 50 % and a current density of 75 mAcm−2 is applied, if not stated otherwise. In a single stack, the shunt current magnitude mainly depends on the number of cells which are electrically connected in series and the cell geometry. For the numerical examples, two geometries introduced in Section5.3 on page 81 are employed. According to the introduced denomination, they are denoted as design 2.1 and 4.6. Cell design 2.1 has an electrode area of 2000 cm2, one and a half channel meanders and a channel width of 20 mm. Having a geometry factor of 11,644 m-1, it represents the design with the lowest geometry factor and thus with the largest shunt currents. Cell design 4.6 has an electrode area of 4000 cm2, two and a half channel meanders and a channel width of 10 mm. Having a geometry factor of 52,159 m-1, it represents the design with the highest geometry factor and thus the smallest shunt currents. Both designs are used to simulate a single stack with up to 40 cells, as shown in Figure 2-8. To evaluate the designs regarding shunt currents, the equivalent shunt current is introduced as shown in Eq. (2-37). We can directly relate the equivalent shunt current to the externally applied charging or discharging current. E.g., an equivalent shunt current of −1 A practically reduces any applied charging current by 1 A and increases the absolute value of any discharging current by 1 A. Under no load conditions, the battery behaves like we would externally apply a discharge current of −1 A. 1 NS NC IShuntIPCSNN ICmn C S m=1 n=1 Wherein: ICmn Internal cell current of cell n in stack m (A) IPCS Current, applied by the power conversion system (A) IShunt Equivalent shunt current (A) NC Number of cells per stack (-) NS Number of stacks (-) (2-37) The magnitude of the equivalent shunt current increases quadratically with the number of cells for both designs. The Eqs. (2-38) and (2-39) give the parameters of the fitted curves. We can use this approximation to quickly estimate the equivalent shunt current of a stack with a large number of cells from the measured or simulated equivalent shunt current of a short stack, e.g. with five cells. The geometry factor of design 4.6 is 4.48 times bigger than the one of design 2.1. This ratio reflects in the ratio of shunt current magnitudes as well, which is 4.44. This indicates that the channel geometry factor is reciprocally proportional to the shunt current magnitude. The reason for this is 30PDF Image | Model-based Design Vanadium Redox Flow Batteries
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