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with the data plotted in Figure II-2, these final fade rates effectively represent lower and upper bounds. The average of the 11 fade rates – 0.442% capacity loss per cycle – was used as a baseline, though we perform sensitivity analyses to probe a range of possible fade rates. Note that here we assume single cell data is representative of stack performance, though the time scales of operation are different and stacks experience other losses such as those due to shunt currents. Single-cell cycling data is limited, but stack-level cycling data is even more scarce. As we assume capacity fade rates and all other performance metrics are independent of battery size (bs) or duration, these variables do not affect the LCOS in the current model. Rather, the fade rates are on a per cycle basis and do not take into account varying durations that would have a marked effect on fade rate since crossover under galvanostatic conditions is largely time-dependent rather than cycle-dependent. Additionally, the data shown in Figure II-2 is from cells cycled repetitively between upper and lower voltage limits at a constant current. This may not be realistic for or representative of practical applications, which are anticipated to operate under variable and potentially intermittent power loads, and, consequently, may result in different fade rates. Incorporation of operationally-dependent fade rates are beyond the scope of this initial study but will be contemplated in the future work. 110 100 90 80 70 60 50 40 30 20 10 Figure II-2 – Literature review of capacity fade as a function of cycle number, adapted from: [12,25,31,32,44,48,52,66,67]. Dots represent the data and dashed lines represent the linear fit for each set. Note: the y-intercept of each fit was fixed at 100%. 0.930% cap.fade/cycle 0.255% cap.fade/cycle Baseline value: 0.442% cap. fade/cycle Digitized data Linear fit Li et al. Kim et al. Luo et al. Zeng et al. Kumar et al. Xi et al. Jiang et al. Zhang et al. Wang et al. 0 20 40 60 80 100 120 140 160 180 200 Cycle Number 24 Capacity Retention (%)PDF Image | Bringing Redox Flow Batteries to the Grid
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