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Section 3.4 Efficiency definitions Faraday’s constant, it can be interpreted as an electric current, as shown in Eq. (3-6) for the negative tank and in Eq. (3-7) for the positive tank. As identical flow rates for each cell are assumed, the flow rate is placed in front of the summation. NC ITIn FQC c2Ck k=1 NC ITIn FQC c5Ck k=1 (3-6) (3-7) By multiplying the equivalent tank current with the open circuit voltage (OCV) of the corresponding tank (positive or negative), the equivalent electrochemical tank power, PT, is computed. It is split into the input tank power, PTIn, shown in Eq. (3-8) and the output tank power, PTout, shown in Eq. (3-9). We can compute the tank output power more easily as there is only one ionic concentration of interest per positive and negative tank. PTIn EOCVT⋅ITIn EOCVT⋅ITIn (3-8) PTOut FQTc2T⋅EOCVT c5T⋅EOCVT (3-9) To derive the OCV of the negative and the positive electrolyte in the tank, the Nernst equation is applied, as shown in Eq. (3-10). In [41], formal half-cell potentials of 0.207 V and 1.182 V are measured for the negative half-cell and positive half-cell, respectively. EOCVT 0.207 V GT lnc2Tc3T (3-10) EOCVT 1.182 V F lnc5Tc4T The actual electrochemical tank power is the difference between the input and output tank power, as shown in Eq. (3-11). PT |PTIn PTOut| (3-11) System power PSys As mentioned before, this work considers the pump power as the only external source of losses. A positive system power corresponds to the charging operation. Thus, power is taken from the grid. The pump power is always positive and always taken from the grid. Consequently, the sign of the pump power does not change for the discharging operation. PSys EPCSIPCS PPumps (3-12) 62PDF Image | Model-based Design Vanadium Redox Flow Batteries
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