## 3 Results
### Faulty Cell Localization  
The dynamic tests found the most significant differences in positive and negative directions. The constant case indicates a good condition for all battery cells. Thus, the more significant outliers occurred in the dynamic case but may not necessarily represent a faulty cell. Next, the deviation of different cells from the average voltage was investigated to determine the defective cases. For the first case, the number of times the cells deviated from the average voltage during different measurements was analyzed, see Figure 11.  
Figure 11 indicates the number of discrepancies on the vertical axis and the cell ID on the horizontal axis. A relatively large number of cells deviate from the mean, and some deviate in 90% of the measurements. However, in this analysis, deviations of smaller orders of magnitude of mV ('millivolt') are also counted. Therefore, in the following, the authors have examined the difference between the average voltage of 12 mV (1% of the measurement range), 60 mV (5% of the measurement range), and 120 mV (10% of the measurement range), i.e., how many times the cells deviate during the different tests; see Figure 12.  
Figure 10: Different ways of averaging the voltage values of the measurements (the different color lines indicate the 88 battery cells). The deviation from 12 mV in part (a), from 60 mV in part (b), and from 120 mV in part (c) have been analyzed (see Figure 12). It can be seen that as the deviation limit is increased, the number of deviations from the average voltage is continuously reduced. When analyzing 60 mV, it can be seen that there is almost no deviation at constant loads. The best range for analyzing very critical/large deviations is 120 mV (measurement range 10%), which may also indicate a possible battery cell error. Even then, there is a probability  
Figure 11: Number of deviations from the average voltage. Figure 12: Number of deviations from the average voltage of 12 mV/60 mV/120 mV. that a large transient load will cause a significant cell voltage drop, which is strongly influenced by the reading timing. However, the readout sequence always started with cell No. 1 and ended with cell ID No. 88, and an additional twelve data (temperature, current, voltage, etc.) have been read. They would increase the possibility of a significant mismatch region forming in the first or last part of the stack. Therefore, the different measurements were weighted and averaged to select the faulty battery cells and compensate for possible erroneous cases. For weighting and averaging, the results from the 0 mV measurement were aggregated first; see Equation (1). \[V_{diff,_{0}\;(x_{1},x_{2},\ldots,x_{n})}=\frac{1}{3}\left(\frac{V_{diff,_{0} \text{X}_{n}}+V_{diff,_{0}\text{X}_{n}}+V_{diff,_{0}\text{X}_{n}}+V_{diff,_{0} \text{X}_{n}}X_{n}}{4}\right)+\frac{2}{3}\left(\frac{V_{diff,_{0}\text{X}_{n} }+V_{diff,_{0}\text{X}_{n}}+V_{diff,_{0}\text{X}_{n}}}{3}\right) \tag{1}\]  
In Equation (1), \(X_{1}\;\ldots\;X_{2}\;\ldots\;X_{n}\), represents cells with different IDs. In \(V_{diff,_{0}}\;0\) means the deviation from the average voltage, \(C\)-constant is the load, and the number after it is the speed. \(SC\) indicates a stepped constant, and \(D\) means a dynamic test. Based on Equation (1), all cells with the same index were summed, but the constant and dynamic cases were weighted separately. Constant cases were weighted 1/3 and dynamic cases 2/3. The procedure was quite similar for 12 mV, 60 mV, and 120 mV cases; see Equations (2)-(4). \[V_{diff,_{120}\;(x_{1},x_{2},\ldots,x_{n})}=\frac{1}{3}\left(\frac{V_{diff,_{ 20}\text{X}_{n}}+V_{diff,_{20}\text{X}_{n}}+V_{diff,_{20}\text{X}_{n}}+V_{diff,_{20}\text{X}_{n}}}{4  
5% and 3% of the data set. The cell IDs which were detected with an average voltage greater than 5% based on the aggregate measurement results were included in the possible error category (results above the red line).