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Section 2.6 Open circuit voltage (OCV) 2.6 Open circuit voltage (OCV) 2.6.1 Derivation of the full equations If we do not attach the battery to any source or load for a longer period of time, it will reach its equilibrium state. The voltage which we then measure between the two electrodes of this battery cell is the so-called open circuit voltage (OCV) [42]. For the VRFB, we can calculate the OCV from the Nernst equation, as shown in Eq. (2-41) [40, 43]. EOCV E0 GT ln aV2+aVO+2 a2(H+) F aV3+ aVO2+ a(H2 O) (2-41) Wherein: a Activity E0 Cell standard potential EOCV Open-circuit-voltage F Faraday constant G Gas constant T Temperature (-) 1.255 V (V) 96,485 As·mol-1 8.314 J(molK)-1 (K) The activity a describes the deviating behavior of real mixtures from the behavior of ideal mixtures [17]. It is proportional to the product of activity coefficient and ionic concentration, c. For VRFB modeling, it is most often assumed that the activity coefficients of all ionic species and the water molecules are unity [17]. In this case, the activity of an ionic species is equal to its concentration. As shown in Eq. (2-42), we can calculate the cell OCV, EOCVC, from the ionic concentrations. Herein, cH denotes the concentration of hydrogen protons. GT c ⋅c ⋅c2 EOCVC E0 ln 2C 5C HC (2-42) F c3C ⋅c4C We can relate the concentration of the vanadium ions to the SoC and the total vanadium concentration, as shown in the Eqs. (2-43) and (2-44). SoCC c2C c5C (2-43) cV cV 1 SoCC c3C c4C (2-44) cV cV For hydrogen protons, the correlation shown in Eq. (2-11) on page 17 is used. Finally, we yield Eq. (2-45), in which the OCV only depends on the SoC as a time variant quantity. GT SoCC 2 EOCVC E0 F ln 1 SoCC2 cHC+(SoCC 0) SoCCcV2 (2-45) 35PDF Image | Model-based Design Vanadium Redox Flow Batteries
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