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VRFBs (f), as well as the materials intensity (I), which is a conversion between the amount of vanadium needed for a given amount of storage deployed: πΌ = !(#$) (IV-4) &!'(Ο The calculation of I depends on the molecular weight of vanadium ((MW), 0.051 kg mol-1), the open-circuit cell potential (U, 1.4 V), the depth of discharge (c, 0.8), the number of moles of electrons transferred per mole of vanadium (ne, 1 mol(e-)/mol(V)), the Faraday constant (F, 96,485 C/mol(e-)), as well as other necessary unit conversions [12]. Further, the factor of two in the numerator accounts for the two electrolyte tanks per system (as vanadium is used on both sides of the cell). The value of I is found to equal 3.4 Γ 109 kg(V) per TWh of energy storage capacity. Next, the VRFB capacity that could be deployed in a future year n (dn, in units of energy/year) is calculated by scaling pn by f and I-1: π: = M)X ((1 + πΆπ΄πΊπ ): β 1) (IV-5) Y The subtraction of one is included to eliminate the present-day production quantity of vanadium from consideration for use toward VRFB deployment, as we assume existing supply is already accounted for. To determine the cumulative deployment in year N (DN), the annual deployments (dn) from each year beginning now through year N must be summed: Using the identities βZ :[V solution for DN: π· =βZ π (IV-6) Z :[V: π₯: = \*+,AF and βZ 1 = π + 1, we find a closed-form, analytical \AF :[V π·Z = M)X "(F@0]^S)*+,AF β 1 β π# (IV-7) Y 0]^S Equation IV-7 is used to determine the CAGRs needed to achieve varying total deployment scales in 2030 (Figure IV-3a, N = 10 years) and 2050 (Figure IV-3b, N = 20 years), relative to 2020, 72PDF Image | Bringing Redox Flow Batteries to the Grid
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