*4.3. Convergence Analysis*

℃ Figures 5 and 6 depict the convergence curves of the R.T.C France solar cell and the SSS2018 polycrystalline PV cell for examining the computational competency of the STO. The convergence rate analysis shows that the STO algorithm is more accurate than the GSA, SCA, GWO, and WOA algorithms. Thus, the STO algorithm produces a realistic answer for the same amount of evaluation functions (i.e., 50,000).

### ௦ௗ <sup>௦</sup> ௦ *4.4. Statistical and Robustness Analysis*

This subsection offers statistical assessments of the mean, minimum, maximum, and standard deviation (SD) of RMSE for all recently created strategies. The accuracy and reliability comparison of the various algorithms in 30 runs is summarized in Table 6. The RMSE mean and standard deviation were calculated to investigate the durability of the parameter estimation algorithms. According to the statistical data presented in Table 6, the STO is found to be the most precise and trustworthy parameter optimization technique.


**Table 4.** The simulated current and absolute error results of the STO for SDM of the SS2018 PV module.

**Table 5.** Comparison of the STO with other parameter estimation methods for the SS2018 PV module.


In addition to the conventional statistical analysis, we also applied the Friedman rank test [47] to determine the relevance of the presented study. It is a nonparametric test which is employed to decide the rank of algorithms for the analysis of PV modules; lower the rank, better the algorithm. Table 7 illustrates the Friedman ranking test results of different algorithms. The Friedman ranking test results show that the STO has the highest ranking compared to WOA, SCA, GWO and GSA. In the Friedman test, the null hypothesis *H*<sup>0</sup> (*p*-value > 5%) suggests that there are no noteworthy alterations among the compared algorithms. For all 30 runs, the contrary hypothesis *H*<sup>1</sup> indicates a significant difference between the compared methods. Each algorithm is ranked in this test depending on its efficiency.

**Figure 4.** I-V and P-V characteristics curves for anticipated and experimental values for the SS2018 PV module. Symbols indicate measured data, while solid lines indicate optimized data.

**Ω Ω μ**

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**Figure 5.** Convergence plot for the RTC France solar cell.

**Figure 6.** Convergence plot for the SS2018 PV module.

**Table 6.** Statistical RMSE results for various techniques for the R.T.C France solar cell and the SS2018 PV module.


**Table 7.** Friedman ranking of different algorithms for all modules.

