# Enhancing Supercapacitor Simulation Accuracy Through a Novel Hybrid Modeling Approach
## 4 Results and Discussions
### Experimental and Numerical Results  
The experiments aimed to validate and showcase the improvements provided by the proposed method in comparison to already existing methods. The implemented experiments were conducted for 300 F and 400 F SCs using the experimental setup presented above. As part of the experiment, the charging and relaxation cycles were measured and used to determine the models for the two SCs using the Zubieta and HyMASC methods. In the charging process, the SC is charged from 0 V to its nominal voltage. A 3.2 A current for the 300 F SC and 4.2 A current for the 400 SC were used. After the charging phase, the relaxation period is evaluated for a 30 min period. The experimental data obtained are presented in Figure 9. The blue line represents the V\({}_{\text{sc}}\) voltage variation, and the red line represents the I\({}_{\text{sc}}\) current variation. The obtained parameter values for the equivalent model are presented in Table 1. The HyMASC method used the initial parameters determined with [PERSON] for further optimization to fit the experimental data better. It can be observed that, using the HyMASC method, the initial parameters are slightly adjusted. In both experiments, a higher adjustment for R\({}_{1}\) and C\({}_{3}\) was observed as an exception The situation can be explained due to the difficulty in evaluating the two parameters from the experimental results, which leads to values that are initially not correctly calculated. These parameters, together with the MATLAB/Simscape model (Figure 7), are further used to simulate the SC behavior in different scenarios. In the developed simulations, the input is the I\({}_{\text{sc}}\) current. The output of the model is voltage V\({}_{\text{sc}}\), which is obtained using the two models: one that uses the [PERSON] and [PERSON]'s parameters, and another that uses the HyMASC method parameters. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**300 F**} & \multicolumn{2}{c}{**400 F**} \\ \hline
**Parameter** & **Zubieta** & **HyMASC** & **Zubieta** & **HyMASC** \\ \hline R\({}_{1}\) [\(\Omega\)] & 0.00416 & 0.0005014 & 0.00467 & 0.0014 \\ \hline C\({}_{0}\) [F] & 235.5584 & 216.7132 & 317.512 & 279.0738 \\ \hline C\({}_{\text{v}}\) [F/V] & 59.5933 & 55.9182 & 43.811 & 58.0748 \\ \hline R\({}_{2}\) [\(\Omega\)] & 4.9866 & 2.8508 & 5.459 & 2.7701 \\ \hline C\({}_{2}\) [F] & 30.3932 & 48.5249 & 28.0581 & 41.1251 \\ \hline R\({}_{3}\) [\(\Omega\)] & 30.9249 & 20.3804 & 28.943 & 18.9504 \\ \hline C\({}_{3}\) [F] & 31.187 & 60.2140 & 29.4708 & 61.8217 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Determined parameters for the 300 F and 400 F supercapacitor. Figure 9: Experimental data for (a) the 300 F SC; (b) the 400 F SC. First, the accuracy of the two models is evaluated. For this, a simulation is developed for a charge and relaxation phase using the same input \(\mathrm{I_{sc}}\) current as the experimental data presented in Figure 9. The simulation results are presented in Figures 10a and 11a. In the second experiment, the 300 F SC model was used to fully charge and discharge several times. In the experiment, the SC was charged with a current of 3.2 A for 268 s until it reached its nominal voltage, followed by a relaxation period of 600 s, and then it was discharged with \(-3.2\) A for 224 s, followed by a relaxation period of 600 s. After the relaxation period, the voltage inside the SC increased. Therefore, the charging time to reach the nominal voltage is smaller than 230 s. The pattern of 224 s discharge, 600 s relaxation, and 230 s charge is repeated five times. The obtained results are presented in Figure 12.  
Figure 11: Experimental results for the 400 F SC (**a**) simulation results; (**b**) simulation errors. Figure 12: Charge/discharge test simulation results for 300 F SC. Figure 10: Experimental results for the 300 F SC (**a**) simulation results; (**b**) simulation errors. In the third experiment, a random pulse charge and discharge setup was implemented.