*4.4. Analysis of Dynamic Models' Works*

The above results are for static models. This subsection starts with several representative metaheuristics for solving dynamic models to analyze their parameter extraction results.

Yousri et al. [52] developed CHCLPSO by combining heterogeneous integrated learning PSO with chaotic optimization techniques. HROA was developed along similar lines to CHCLPSO, a hybrid of the chaotic mapping mechanism with the Rao\_1 algorithm by Wang et al. [53]. Elaziz et al. [51] developed EMPA by an effective combination of DE and the Marine Predator algorithm.

For the results of the dynamic model, CHCLPSO provides parameters of *RC* = 7.3149 Ω, *<sup>C</sup>* = 3.81307 × <sup>10</sup>−<sup>7</sup> F, and *<sup>L</sup>* = 7.3251 × <sup>10</sup>−<sup>6</sup> H. EMPA provides parameters of *RC* = 7.315 <sup>Ω</sup>, *<sup>C</sup>* = 3.1831 × <sup>10</sup>−<sup>7</sup> F, and *<sup>L</sup>* = 7.3251 × <sup>10</sup>−<sup>6</sup> H. Their difference is insignificant, indicating that both methods have similar solving power. The MIN and Mean RMSEs for CHCLPSO are 8.45045 × <sup>10</sup><sup>−</sup>3, and the STD is 1.13566 × <sup>10</sup><sup>−</sup>12. The MIN, Mean, and MAX RMSEs for HROA are 6.709393 × <sup>10</sup>−3, and the STD is 5.209153 × <sup>10</sup>−18. The Mean RMSE for EMPA makes it clear that HROA has the best accuracy and robustness, followed by EMPA and CHCLPSO. However, CHCLPSO is at the same level of accuracy as EMPA, and both have a minor STD. This indicates that EMPA and CHCLPSO have converged early, and their further improvement needs to start from exploration. For HROA, it achieves the optimal

RMSE value, but 6.709393 × <sup>10</sup>−<sup>3</sup> is still a significant error and there is room for further optimization of the accuracy of the solution.

It is worth mentioning that the model of dynamics is suitable for grid-connected operation. However, there has been little research related to it since its introduction, and especially little research on metaheuristic methods to optimize the dynamic model. Therefore, it has broad application and research prospects and is a crucial research direction for the future.
