**7. Conclusions**

A new hybrid multi-population gorilla troops optimizer and beluga whale optimization (HGTO-BWO) was proposed to assign the PV cell/panel equivalent circuit by estimating its optimal parameters. In the proposed approach, a multi-population methodology was employed to improve the performance of the algorithm and to prevent it from falling into the local optima. The classical and CEC-C06 2019 benchmark functions were solved via the proposed approach to assess its performance. Two models, the double and triple diode models (DDM and TDM), were constructed for the PV cell/panel via minimizing the root mean square error (RMSE) between the simulated and measured currents. Various PV cells and panels operating in stable and variable weather situations were analyzed. Also, excessive comparison with TSA, SCA, GWO, WOA, HS, BWO, and GTO was conducted. The proposed approach findings can be summarized as follows:


The results revealed that the proposed approach can be recommended as an efficient optimizer when constructing the PV unit equivalent circuit via identifying its parameters. The proposed method requires a great effort to implement and program, which is considered a major obstacle during implementation; in addition, a lot of time is needed. Therefore, simplifying this method and reducing the time required will be of interest to the authors of the future works. Moreover, the validation of the proposed methodology in estimating the parameters of the PV array when operated under different conditions will be considered in the next work.

**Supplementary Materials:** The following supporting information can be downloaded at: https://www. mdpi.com/article/10.3390/su151411089/s1, Figure S1: The convergence curves of some traditional benchmark functions achieved by the proposed hybrid approach and others; Figure S2: The boxplots curves of some traditional benchmark functions obtained via the proposed hybrid approach and others; Figure S3: The convergence of some CEC-2019 functions achieved by the proposed hybrid method and others; Figure S4: The boxplots curves of some CEC-2019 functions obtained via the proposed hybrid approach and others; Figure S5: Performance of RMSE through iteration process for DDM (a) PWP-201 and (b) STM6-40/36; Figure S6: RMSE with numeral of iteration for TDM (a) STM6-40/36 panels and (b) PWP-201.

**Author Contributions:** Conceptualization, H.H.A. and A.F.; methodology, A.A.M. and H.H.A.; software, M.E. and F.J.; validation, A.F., T.S.B., and F.J.; formal analysis, H.H.A. and A.F.; investigation, M.E. and H.H.A.; data curation, M.E., F.J., and T.S.B.; writing—original draft preparation, A.A.M. and A.F.; writing—review and editing, A.F.; supervision, T.S.B. and F.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
