## 5 Results and Discussion
### Simulation Results for a 7.7 cm\({}^{2}\) Q6-1380 Multi-Crystalline Solar Cell  
In Table 2, estimation of the unknown parameters is listed for the two considered models obtained with the two soft computing algorithms, the CLPSO and EHO algorithms, that are presented in Sections 3 and 4. This table shows the settings of the eight and ten unknown parameters for the MDDM and MTDM, respectively. The fitness functions, that are obtained by CLPSO for the MDDM and MTDM, are 8.7545 \(\times\) 10\({}^{-5}\) and 5.9516 \(\times\) 10\({}^{-5}\), respectively. Thus, a reduction of 32.02% is achieved. The fitness functions that are obtained by EHO for the MDDM and MTDM are 1.823 \(\times\) 10\({}^{-5}\) and 1.4386 \(\times\) 10\({}^{-5}\), respectively, so a reduction of 21.12% is achieved. Therefore, we can conclude that MTDM leads to more accurate parameters compared with MDDM. From the viewpoint of the solution method, the EHO has the lowest fitness functions for both MDDM and MTDD compared with CLPSO, so we can say that the EHO is more reliable for solving the parameter estimation  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cell** & **Irradiance Level (W/m\({}^{2}\))** & \(\mathbf{V_{OC}}\) (V) & \(\mathbf{I_{SC}}\) (A) & \(\mathbf{P_{MP}}\) (W) & FF \\ \hline Q6-1380 & 98.4 & 0.467 & 0.01936 & 0.004883 & 0.5401 \\ \cline{2-6}  & 109.2 & 32.1 & 0.9968 & 23.71 & 0.7410 \\ CS6P-240P & 246.65 & 32.56 & 2.138 & 51.35 & 0.7376 \\ solar module & 347.8 & 32.91 & 3.035 & 76 & 0.7609 \\ \cline{2-6} R.T.C. France & 1000 & 0.5731 & 0.7602 & 0.3115 & 0.7150 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic open circuit and short circuit current for tested solar cells.  
problem than CLPSO. In Table 3, the statistical indices of the studied cases are presented. Also, as shown in Tables 2 and 3, the first rank in the reduction of the calculated RMSE is achieved by using the estimated parameters of the MTDM compared with the MDDM. On the other hand, the EHO method shows more accurate results but slower convergence than the CLPSO, as described in Figures 3-6.  
Moreover, it can be noticed that the EHO algorithm reaches the least level of the RMSE that is achieved for MTDM followed by EHO for MDDM, then MTDM by CLPSO, and at last MDDM by CLPSO. Furthermore, the EHO based estimated (I-V) characteristic is assessed versus experimental ones for MDDM and MTDM in Figures 7 and 8, respectively, under low irradiation and at room temperature.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Model**} & \multirow{2}{*}{**\(I_{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text{\text{\text{\text{ \text{ }}}}}}}}}}}}}}}\) & \multirow{2}{*}{**\(I_{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{{\text{ \text{\text{\text{\text{\text{\text{\text{\text{\text{ }}}}}}}}}}}}}}}}\) }\)**} & \multirow{2}{*}{**\(I_{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{{\text{{ \text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{   }}}}}}}}}}}}}}}}} \)}\)**} & \multirow{2}{*}{**\(I_{\text{\text{\text{\text{\text{\text{\text  
Figure 4: Convergence rate of the MTDM using CLPSO.  
Figure 5: Convergence rate of the MDDM using EHO.  
Figure 6: MTDM convergence rate using EHO.  
The above results prove that the MTDM has a better closeness to the reality compared to MDDM for MCSSC at low illumination. It is also clear that the EHO is a more accurate technique than CLPSO but slower than it. The results, after this research and referring to previous literature [16] for multi-crystalline solar cells, are that the MTDM has the best physical behavior accomplished by EHO algorithm that involves error analysis and (I-V) curves justification.