# Parameter Identification Method of a Double-Layer Supercapacitor by Using a Real Voltage Source
## 5 Conclusions  
The methods developed have been employed to analyze several SCs from different manufacturers, with capacities ranging from 150 F to 600 F. The variable capacity model parameters have been obtained and the experimentally recorded measurements have been compared with the theoretical curve, \(\mathrm{u_{co}(t)}\), which would be obtained with the calculated variables. The results show an almost perfect coincidence between both. The estimated values of series resistance and rated capacitances present a good agreement with the values specified by the manufacturers as well. The only differences with respect to the data given in the datasheets of the SCs are that, in the case of the 600 F cell, the measured value of internal resistance is 1 m\(\Omega\) higher, while in the 400 F cell, the capacitance value measured in the test is 1% higher than the expected maximum value. However, it should be noted that the values provided by the manufacturers are measured considering the cells as an RC load of constant values, rather than considering the variable capacitance model, so it is reasonable to find slight discrepancies. The proposed methods have been demonstrated to be an alternative, and fairly accurate tool, for estimating the parameters of the main branch. They are capable of being calculated using a real voltage source or simply a constant resistance, in contrast to the current source that has been proposed by other authors to date.  
Conceptualization, J.F.P.; methodology, J.F.P. and M.F.Q.; software, M.F.Q., M.F.C. and E.E.Z.; validation, M.F.Q., G.A.O. and M.F.C.; formal analysis, J.F.P. and M.F.C.; investigation, M.F.Q., J.F.P. and G.A.O.; writing--original draft preparation, J.F.P.; writing--review and editing, E.E.Z., G.A.O., J.C.V. and M.F.C.; supervision, E.E.Z. and J.C.V.; project administration, J.C.V. and M.F.Q.; funding acquisition, J.C.V. and G.A.O. All authors have read and agreed to the published version of the manuscript.  
Figure 10: Voltage \(\mathrm{uco(t)}\) measured and estimated from the values in Table 3 using the parameters obtained with the LSM method, for all the tested SCs.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{C_{N}}\) [F] & \(\mathbf{\epsilon_{min}}\) [mV] & \(\mathbf{\epsilon_{mean}}\) [mV] & \(\mathbf{\epsilon_{max}}\) [mV] & \(\mathbf{\sigma}\) [mV\({}^{2}\)] &
\begin{tabular}{c} **Correlation** \\ **Coefficient, \(\mathbf{R}^{2}\)** \\ \end{tabular} \\ \hline
150 & 2.572 \(\times\) 10\({}^{-6}\) & 1.565 & 14.515 & 2.045 & 0.999977 \\
310 & 30.532 \(\times\) 10\({}^{-6}\) & 1.361 & 8.913 & 1.382 & 0.999955 \\
400 & 1.392 \(\times\) 10\({}^{-6}\) & 2.108 & 11.184 & 3.217 & 0.999872 \\
600 & 35.268 \(\times\) 10\({}^{-6}\) & 1.532 & 12.208 & 2.008 & 0.999866 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Main fit data. Errors and correlation coefficient.  
**Funding:** This work has been partially funded by the Spanish Government, MCIN/AEI/FEDER, and the EU, under grants PID2021-122704 OB-I00 and TED2021-131498B-I00.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.