# A Switching Observer for State-of-Charge Estimation of Reconfigurable Supercapacitors
## 4 Experimental Validation
### Experimental Results
In summary, this experiment demonstrates the superior performance of the proposed observer in handling dynamic charging scenarios and adapting to switching events, further emphasizing its suitability for real-world supercapacitor applications where operating conditions can vary significantly. Since the proposed observer's estimation of the SOC remained very close to the actual SOC after the supercapacitor charging was completed in the next two experiments, the actual SOC values have been omitted from the subsequent tables. _(3) Case 3:_ This experiment investigates the observers' performance under a more complex scenario involving active balancing of the supercapacitor cells. We implemented the active balancing technique described in [19] to charge the second and third supercapacitors simultaneously. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **First Convergence Time (s)** & **Final SOC (\%)** & **Maximum Absolute Error (\%)** \\ \hline
**True Value** & null & 52.63 & 0 \\ \hline
**Proposed Observer** & 6.984 & 52.58 & 0.709 \\ \hline
**Classical Observer** & 10.527 & 52.89 & 3.602 \\ \hline
**Open-loop Observer** & null & 70.50 & \textgreater{}50 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between the proposed observer, open-loop observer, and the classical observer. Figure 7: Comparison of SOC estimation performance during dynamic charging with capacitance variations. (**a**) SOC estimation with 10% capacitance variations. (**b**) Changes in the switch. The initial voltages of the second and third cells were set to 0.1 V and 0.9 V, respectively, while maintaining a constant charging current of 2 A. A 10% capacitance error was introduced to assess the observers' robustness. Both the proposed and classical observers were initialized at 15% SOC. We started charging at t = 8 s and stopped at t = 242 s.  
Figure 8a shows the SOC of two supercapacitors. Due to the presence of the active balancing system, the third supercapacitor, which initially has a higher SOC, will wait until the SOC of the second supercapacitor matches its own before switching on to start charging, as illustrated in Figure 8b. It begins charging only after t = 125 s. Figure 9a,b, respectively, show the SOC estimation of the second and third supercapacitors. Figure 8: The charging process with active balancing strategy. (**a**) SOC evolution of the cells during active balancing. (**b**) Switching sequence during active balancing. Figure 9: _Cont._  
Focusing on the second supercapacitor, according to Tables 4 and 5, the proposed observer demonstrates a significantly superior performance, achieving a tracking error below 1% within 3 s. While the classical observer eventually approaches the true SOC, its convergence speed and accuracy lag behind the proposed observer, particularly after switching events. Specifically, after the switching moment, the classical observer's tracking error rises to 2.7%, whereas the proposed observer maintains an error below 0.5%. Similar trends are observed for the third supercapacitor, with the proposed observer exhibiting stable and accurate tracking performance despite the extended initial charging time, which negatively impacts the classical observer's performance. In this experiment, the open-loop observer still performed poorly, failing to converge in estimating the SOC for both supercapacitors, highlighting its inadequacy in complex scenarios. These findings underscore the robustness and accuracy of the proposed switching observer in handling the complexities of active balancing, further solidifying its suitability for demanding supercapacitor applications. _(4) Case 4:_ In this case, we introduce the Kalman Filter, a widely used tool for state estimation, to estimate the State of Charge (SOC) of the supercapacitor. We employ the same switching scheme as in case 1 and also consider a 10% parameter deviation. However, unlike before, we separately consider the cases where the capacitance \(C_{eq}\) and ESR in the RC model have fluctuations.