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Section 2.2 State-of-charge of a Vanadium Redox Flow Battery 1 tEnd SoC(t) SoCt0+ C Itdt (2-1) Theo t0 Wherein: t Time (s) t0 Initial time (s) tEnd Time at end of calculations (s) SoC State-of-charge (-) CTheo Theoretical capacity (As) I Current (A) We can derive the theoretical capacity of a VRFB as shown in Eq. (2-2) [17]. The factor 1⁄2 is necessary because two electrolytes are required for a functioning flow battery. For the standard electrolyte with a total vanadium concentration of 1.6 molL-1, we can derive a specific theoretical capacity of 21.4 AhL-1. By multiplying this capacity with the open circuit voltage (OCV) of the electrolyte in a SoC of 50 %, which is around 1.4 V, we yield the capacity in WhL-1. The standard electrolyte yields a specific capacity of 30 WhL-1. However, we can only exploit this capacity if a SoC range between 0 % and 100 % is used with a completely lossless battery. Wherein: CTheo Theoretical capacity cV Total vanadium concentration F Faraday constant VTotal Total electrolyte volume (As) (molm-3) 96,485 As·mol-1 (m3) CTheo 12 VTotalcVF (2-2) In a VRFB, vanadium ions are reduced and oxidized during the charging and discharging process. As shown in the Eqs. (1-1) and (1-2), the completely discharged negative electrolyte with a SoC of 0 % only contains V3+ ions; the completely discharged positive electrolyte only contains VO2+ ions. Consequentially, the completely charged negative electrolyte with a SoC of 100 % only contains V2+ ions; the completely charged positive electrolyte only contains VO2+ ions. For a SoC between 0 % and 100 %, the negative and positive electrolyte consists of a fraction of the respective ion concentrations. In this work, the internal electrochemical quantities are denoted with subscripts in the following manner. The first subscript indicates the particular vanadium ion. The subscript ‘2’ denotes quantities referring to the vanadium ion V2+. Consistently, the subscript ‘3’ is used for the V3+ ions, ‘4’ for the VO2+ ions and ‘5’ for the VO2+ ions. The second subscript indicates the measurement location of the quantity. The subscript ‘T’ refers to the tank and the subscript ‘C’ refers to the cell. The third and final subscript indicates whether the quantity refers to the positive half-side (subscript ‘+’), or the negative half-side (subscript ‘−’). 14PDF Image | Model-based Design Vanadium Redox Flow Batteries
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