## 2 Overvoltage of a Battery
### Problem of Low Cell Balancing Current
#### 2.1.2 Aging Progression with and without Cell Balancing  
Figure 4 shows the aging simulation results of Figure 1. Even in the aging simulation, the authors could not find significant differences due to the low current of the cell balancing. The voltage results without cell balancing are shown in Figure 4a, while Figure 4b shows the voltage results with cell balancing. There is no significant difference in the progression of aging between the two simulation results. Figure 4c,d compare the voltage results in an enlarged voltage range of 4.0-4.3 V. It can be observed that, due to the low cell balancing current, cell balancing actually results in a greater increase in the maximum voltage during the aging process. \begin{table}
\begin{tabular}{c l c c c c} \hline \multicolumn{2}{c}{**Parameter**} & **Bat \#1** & **Bat \#2** & **Bat \#3** & **Bat \#4** \\ \hline \multirow{4}{*}{Series connected} & Max. Volt. & 4.128 V & 4.105 V & 4.165 V & 4.128 V \\  & Min. Volt. & 3.039 V & 3.077 V & 2.996 V & 3.039 V \\  & Max. SOC & 98.00\% & 97.53\% & 98.49\% & 98.00\% \\  & Min. SOC & 6.85\% & 7.28\% & 6.41\% & 6.85\% \\ \hline \multirow{4}{*}{With cell balance} & Max. Volt. & 4.130 V & 4.105 V & 4.165 V & 4.130 V \\  & Min. Volt. & 3.047 V & 3.084 V & 2.999 V & 3.047 V \\ \cline{1-1}  & Max. SOC & 98.02\% & 97.54\% & 98.48\% & 98.02\% \\ \cline{1-1}  & Min. SOC & 6.96\% & 7.38\% & 6.45\% & 6.96\% \\ \hline \end{tabular}
\end{table} 
Table 1: Single-cycle simulation results with an allowable capacity deviation of \(\pm\)1%. Figure 5 shows simulation results that investigate the impact of aging on the state of charge (SOC). It can be observed that Bat #2, which has a relatively large capacity, experiences a reduction in its usable range as aging progresses. In contrast, Bat #3, which has a relatively small capacity, experiences an increase in its usable range. It can be inferred that batteries with larger capacities experience a slower progression of aging as their usable range decreases over time. Figure 6 shows the simulation results that observe the change in the state of health (SOH) during the aging process. No significant difference was observed in the two simulation results for the SOH. Figure 4: Voltage results of serial battery aging simulation. (**a**) Serial-connected; (**b**) with cell balance; (**c**) expanded results of serial-connected; (**d**) expanded results with cell balance. Table 2 summarizes the results of the aging simulation. The maximum voltage without cell balance was 4.198 V, compared to 4.213 V with cell balance. This shows that a low cell balance current has a negative effect on the overvoltage caused by the voltage distribution. In addition, the SOH of the battery was relatively quickly degraded in both cases. Table 3 presents the simulation results with a \(\pm\)2% variation in the battery capacity under the same conditions. The effect of cell balancing was found to be negligible during aging. However, it was observed that there was an impact on the maximum voltage at full charge as aging progressed. In Table 2, the maximum voltage of Bat #3 increased by 48 mV from 4.165 V to 4.213 V after aging. In Table 3, after the same duration of aging, the maximum voltage of Bat #3 increased by 72 mV from 4.203 V to 4.275 V. Additionally, by examining the range of SOC usage, it was found that 93.16% was used in Table 2, while 94.14% was used in Table 3. Consequently, the maximum SOC difference increased from 2.84% to 5.06%. The SOC difference in series-connected batteries leads to voltage redistribution in the CV region due to their different DCIRs [7]. Figure 5: SOC results of serial battery aging simulation. (**a**) Serial-connected; (**b**) with cell balance. Figure 6: SOH results of serial battery aging simulation. (**a**) Serial-connected; (**b**) with cell balance. Table 4 shows the simulation results for a serially connected battery with an allowable capacity deviation of \(\pm 3\%\).