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2.2 Model of dynamic capacity fade and rebalance Whereas prior models assumed fixed performance over time, here, we include a dynamic physical model of the battery to track the capacity and energy stored (Et) over time, which allows for the incorporation of capacity fade and recovery via rebalancing. We assume linear capacity fade over extended cycling, as this behavior has been implied in prior work [24,33], and validate this assumption with a survey of the recent peer-reviewed literature as shown in Figure II-2 [12,25,31,32,44,48,52,66,67]. It is important to note the limited amount of long-term VRFB cycling data in the open literature as compared to shorter-term cell tests (i.e., cyclic voltammograms, IV polarizations, etc.), likely because cycling analyses are both more time- consuming and experimentally challenging. While the data in Figure II-2 was not collected under identical conditions (see Table S1 in the Supporting Information, SI, of the published version of this chapter for full operating conditions of each data set [60]), all were based on cycling of a single redox flow cell in an academic laboratory. Almost all sources used comparable Nafion membranes and heat-treated carbon electrodes; had similar electrolyte compositions of 1-2 M V in 2-5 M H2SO4 and volumes of 50-80 mL per reservoir; and were cycled at current densities between 50- 80 mA/cm2. The active areas ranged from 5 to 103 cm2, though the volumetric flow rates generally correlated to the active area. There are many other potentially-relevant conditions that are not reported but could significantly impact performance including cell temperature, use of humidified nitrogen purging, reservoir seal, and cell compression. Finally, we note that the use of a plot digitizer adds a small source of error to the values extrapolated from the data (≤0.5% per data point) [68]. As illustrated in Figure II-2, significant variations among the capacity fade rates can be seen in the data. The outlier [52] was the only data set that used a porous Daramic separator rather than an ion-selective Nafion membrane. Additionally, this data set had the longest theoretical duration of 8.6 h, while the duration of most other data sets was less than 2 h. These two observations explain the notably higher fade rate. We assume the apparent performance increase at the beginning of life for some data sets is due to cell conditioning or imbalanced electrolytes. We include two additional data points obtained from a recent review on VRFB component degradation by Yuan et al. [8,69,70], which cites two experimental values for the rate of capacity decay as 1.3% and 0.067% per cycle (not shown in Figure II-2 because cycling data was not provided). If considered along 23PDF Image | Bringing Redox Flow Batteries to the Grid
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