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Appendix B Additional data and calculations Appendix B Additional data and calculations Additional data and calculations B.1 CalculationofthetankSoCfromtheelectrolyteOCV In the model, the OCV is derived using the Nernst equation. With the assumption of a constant hydrogen proton concentration, Eq. (A-1) is derived. 0 GT c2T ⋅ c5T+ EOCV E F lnc ⋅c (A-1) Assuming an ideally balanced electrolyte, we can calculate the identical SoCs of both electrolytes as shown in Eq. (A-2). SoCT c2T c5T (A-2) 3T 4T+ c2T c3T c4T c5T The sum of the concentrations of V2+ and V3+ ions in the negative electrolyte and the sum of the concentrations of VO2+ and VO2+ ions in the positive electrolyte both equal the total vanadium concentration, cV, as shown in Eq. (A-3). c2T c3T c4T c5T cV (A-3) Now we can express the concentrations exclusively by SoC and total vanadium concentration, as shown in Eq. (A-4). c2T SoCT c3T 1 SoCT c (A-4) c4T 1 SoCT V c5T SoCT If we replace all concentrations in Eq. (A-1) by the expressions using the SoC, we can derive Eq. (A-5), which represents a common simplification for the OCV(SoC) relation. 0 GT SoCTcVSoCTcV EOCV E + F ln(1SoC )c (1SoC )c TV TV 0 GT SoCT2 (A-5) E+ F ln1SoCT2 The comparison of the argument of the logarithmic term in Eq. (A-1) with the one in Eq. (A-5) yields Eq. (A-6). SoCT2 c2T ⋅ c5T+ 1 SoCT2 c3T ⋅ c4T+ (A-6) Finally, a SoC dependence on all four different vanadium ions can be derived, as shown in Eq. (A-7). 151PDF Image | Model-based Design Vanadium Redox Flow Batteries
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