## 2 Overvoltage of a Battery
### Problem of Low Cell Balancing Current
#### 2.1.2 Aging Progression with and without Cell Balancing
During the experiment, it was found that the maximum voltage of Bat #3 exceeded the overvoltage protection (OVP) reference voltage of 4.3 V during the charge and discharge cycles. As the allowable capacity deviation increased, the energy required for cell balancing also increased. The effect of balancing was reduced due to the low cell balance current, making it difficult to distinguish the difference in the aging rate between cases with and without cell balancing. \begin{table}
\begin{tabular}{c c c c c c c c c c}  & & & & & & & & & & & & \\ \multicolumn{1}{c}{**Parameter**} & \multicolumn{5}{c}{**Serial Connected**} & \multicolumn{5}{c}{**With Cell Balance**} \\ \cline{3-10}  & & **Bat \#1** & **Bat \#2** & **Bat \#3** & **Bat \#4** & **Bat \#1** & **Bat \#2** & **Bat \#3** & **Bat \#4** \\ \hline Voltage & Min & 3.039 & 3.077 & 2.996 & 3.039 & 3.047 & 3.084 & 2.999 & 3.047 \\ (V) & Max & 4.128 & 4.105 & 4.165 & 4.128 & 4.129 & 4.105 & 4.165 & 4.129 \\ SOC & Min & 6.85 & 7.28 & 6.41 & 6.85 & 6.96 & 7.38 & 6.45 & 6.96 \\ (\%) & Max & 97.99 & 97.51 & 98.47 & 97.99 & 98.00 & 97.53 & 98.48 & 98.00 \\ SOH & & 62.04 & 62.66 & 61.42 & 62.04 & 62.04 & 62.66 & 61.42 & 62.04 \\ \hline \multicolumn{1}{c}{Time (Cycles)} & \multicolumn{5}{c}{1 Cycle} & \multicolumn{5}{c}{1 Cycle} \\ \hline Voltage & Min & 3.312 & 3.439 & 2.984 & 3.312 & 3.300 & 6.85 & 96.01 & 9.04 \\ (V) & Max & 4.147 & 4.117 & 4.198 & 4.147 & 4.144 & 4.128 & 4.213 & 4.144 \\ SOC & Min & 9.04 & 13.00 & 4.23 & 9.04 & 8.76 & 12.37 & 4.30 & 8.76 \\ (\%) & Max & 96.01 & 95.00 & 97.14 & 96.01 & 95.92 & 94.62 & 97.46 & 95.92 \\ SOH & & 23.63 & 25.05 & 21.12 & 23.63 & 23.54 & 24.94 & 22.02 & 23.54 \\ (Ah) & & & 4170 Cycles & & & & & & & \\ \hline \multicolumn{1}{c}{Time (Cycles)} & \multicolumn{5}{c}{4170 Cycles} & \multicolumn{5}{c}{4176 Cycles} \\ \hline \end{tabular}
\end{table} 
Table 2: Aging simulation results with allowable capacity deviation of \(\pm 1\%\). \begin{table}
\begin{tabular}{c c c c c c c c c c c}  & & & & & & & & & & & \\ \multicolumn{1}{c}{**Parameter**} & \multicolumn{5}{c}{**Serial Connected**} & \multicolumn{5}{c}{**With Cell Balance**} \\ \cline{3-10}  & & **Bat \#1** & **Bat \#2** & **Bat \#3** & **Bat \#4** & **Bat \#1** & **Bat \#2** & **Bat \#3** & **Bat \#4** \\ \hline Voltage & Min & 3.077 & 3.144 & 2.996 & 3.077 & 3.080 & 3.150 & 2.998 & 3.080 \\ (V) & Max & 4.123 & 4.102 & 4.204 & 4.123 & 4.123 & 4.102 & 4.203 & 4.123 \\ SOC & Min & 7.36 & 8.19 & 6.49 & 7.36 & 7.40 & 8.30 & 6.52 & 7.40 \\ (\%) & Max & 97.90 & 96.96 & 98.88 & 97.90 & 97.90 & 96.97 & 98.87 & 97.90 \\ SOH & & 62.04 & 63.28 & 60.80 & 62.04 & 62.04 & 63.28 & 60.80 & 62.04 \\ (Ah) & & & & & & & & & \\ \hline \multicolumn{10}{c}{Time (Cycles)} & \multicolumn{5}{c}{1 Cycle} & \multicolumn{5}{c}{1 Cycle} \\ \hline Voltage & Min & 3.456 & 3.562 & 2.992 & 3.456 & 3.442 & 3.552 & 3.000 & 3.442 \\ (V) & Max & 4.137 & 4.115 & 4.252 & 4.137 & 4.131 & 4.113 & 4.275 & 4.131 \\ SOC & Min & 13.77 & 20.08 & 4.34 & 13.77 & 13.21 & 19.38 & 4.41 & 13.21 \\ (\%) & Max & 95.80 & 93.91 & 98.13 & 95.80 & 95.61 & 93.49 & 98.55 & 95.61 \\ SOH & & 24.16 & 26.85 & 21.13 & 24.16 & 24.15 & 26.83 & 21.13 & 24.15 \\ (Ah) & & & & & & & & & & \\ \hline \multicolumn{10}{c}{Time (Cycles)} & \multicolumn{5}{c}{4230 Cycles} & \multicolumn{5}{c}{4226 Cycles} \\ \hline \end{tabular}
\end{table} 
Table 3: Aging simulation results with allowable capacity deviation of \(\pm 2\%\).