# A Switching Observer for State-of-Charge Estimation of Reconfigurable Supercapacitors
## 4 Experimental Validation
### Experimental Results
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **First Convergence Time (s)** & **Final SOC (\%)** & **Maximum Absolute Error (\%)** \\ \hline
**Open-loop Observer** & null & 74.84 & \textgreater{}50 \\ \hline
**Classical Observer** & 8.446 & 58.81 & 2.735 \\ \hline
**Proposed Observer** & 2.821 & 58.13 & 0.433 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SOC estimation of the second cell. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **First Convergence Time (s)** & **Final SOC (\%)** & **Maximum Absolute Error (\%)** \\ \hline
**Open-loop Observer** & null & 57.17 & 10 \\ \hline
**Classical Observer** & 127.259 & 58.68 & 1.09 \\ \hline
**Proposed Observer** & 2.238 & 58.13 & 0.172 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: SOC estimation of the third cell. Figure 9: Comparison in active balancing charging process. (**a**) SOC estimation of the second supercapacitor. (**b**) SOC estimation of the third supercapacitor. As shown in the Figure 10, in both experiments, the open-loop observer's error is unacceptable, while both the Kalman Filter and the proposed observer exhibit stable performance. Although both converge to the actual SOC when charging stops, there are still some performance differences. According to Tables 6 and 7, during the period from 0 to 5 s when the supercapacitor is not charging, the SOC of the proposed observer quickly converges to the true value, while the Kalman Filter only approaches the true value after next 10 s of charging. However, after this period, the Kalman Filter still exhibits larger errors. Although these errors decrease over time as charging progresses, they do not fully converge even by the time charging stops. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **First Convergence Time (s)** & **Maximum Absolute Error (\%)** \\ \hline
**Proposed Observer** & 2.639 & \textless{}0.3 \\ \hline
**Open-loop Observer** & null & \textgreater{}50 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the proposed observer and Kalman Filter with 10% ESR variations. Figure 10: Comparison with Kalman Filter. (**a**) SOC estimation with 10% capacitance variations. (**b**) SOC estimation with 10% ESR variations. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **First Convergence Time (s)** & **Maximum Absolute Error (\%)** \\ \hline
**Proposed Observer** & 2.631 & \textless{}0.3 \\ \hline
**Kalman Filter** & 14.937 & 4.140 \\ \hline
**Open-loop Observer** & null & \textgreater{}50 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the proposed observer and Kalman Filter with 10% ESR variations. Furthermore, this experiment considers the impact of ESR variation on SOC estimation. Since the supercapacitor used in the experiment has a relatively small ESR, its parameter fluctuation has a relatively small impact on SOC estimation, similar to the same proportional change in capacitance. However, further discussion is needed for supercapacitors that have been used for a long time and have experienced significant ESR increases.