Bringing Redox Flow Batteries to the Grid

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determining the yearly leasing fee that produces an LCOS under leasing equal to that without leasing. This essentially estimates the break-even cost of the leasing scheme, and can be determined analytically without calculating any LCOS values. We also calculate the internal rate of return (IRR) for the lessor under each scenario, assuming that the lessor provides an initial investment equal to the cost of electrolyte and receives the same, fixed annual fee every year throughout the 20-year operational life. Details of these calculations are provided in section S5 of the SI of the published version of this chapter [60]. For leasing to be an attractive option as compared to upfront purchase, vanadium prices must be sufficiently high and/or annual fees must be suitably low. At the time of writing, the price of vanadium pentoxide is ca. 16 $ kg-1 [39], which corresponds to 29 $ kg-1 of vanadium. Note that, in practice, electrochemical-grade vanadyl sulfate is used, but the costs associated with materials upgrading and refinement have not been articulated in the literature [6,19,21]. While, from a materials perspective, the costs to transform a vanadium precursor to vanadyl sulfate are expected to be low, especially at scale [87], the cost of electrolyte purification is unknown and will likely depend on the impurity profile of the precursor sources. Because of this uncertainty and the ongoing debate surrounding future vanadium pentoxide prices [85,88], we elect to vary the vanadium price both above and below the baseline of 29 $ kg-1. To translate the price of vanadium into the cost of electrolyte, we employ a bottom-up capital cost model previously developed by Darling et al. [61], using the baseline values from that publication and a 1.2 OF to mimic a commercial scenario (see section S4 of the SI of the published version of this chapter [60]). The final variable that can affect the feasibility and profitability of the leasing scheme is the annual discount rate on the lessee (defined earlier for all LCOS calculations as ry), which is varied in addition to vanadium price. The results of the leasing analysis are shown in Figure II-7. The left plot (Figure II-7a) represents the lessee: the maximum annual fees that they could pay to break-even on their initial upfront savings through leasing is shown by the solid lines as a function of the vanadium price. The colors of each line represent different discount rates for the lessee, except for the pink lines which represent the scenario where the annual fee is 10% of the electrolyte cost (the Skyllas-Kazacos case). As the price of vanadium and thus the upfront saving from leasing increase, the maximum competitive leasing fee must also increase, which is to say leasing becomes competitive for larger annual fees. For a specified discount rate, any annual fee below the corresponding solid line 37

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