In this article, the triple diode model (TDM) is studied for modeling the Canadian-Solar-CS6P-240P poly-crystalline PV module, Kyocera Solar KC200GT multi-crystalline PV module, Sharp NU-(Q250W2) mono-crystalline PV module, and Pythagoras Solar Large PVGU Window mono-crystalline PV module. A novel hybrid algorithm of the marine predator’s algorithm (MPA) and slime mould algorithm (SMA) (HMPA) is proposed to enhance the MPA exploitation phase while identifying the TDM parameters. The HMPA results are compared to several recent algorithms that are equilibrium optimizer (EO), manta ray foraging optimization (MRFO), transient search optimization (TSO), jellyfish optimizer (JS), and forensic-based optimizer (FBI), besides the basic versions of MPA and SMA. For unbiased comparison, several statistical analyses and non-parametric tests are applied. The convergence curves are used to evaluate the convergence property of the proposed algorithm compared to their counterparts. The HMPA confirms its efficiency in handling the complex multi-modal and multi-dimensional optimization process of identifying the TDM parameters. HMPA provides the least root mean square error (RMSE) between the measured and estimated datasets with the least standard deviation (STD). For Canadian Solar (CS6P-240P) module, the proposed HMPA achieves the minimum RMSE of 0.00037313 with STD of 0.0030488; for Kyocera Solar (KC200GT) module, HMPA attains RMSE ± STD of 0.0033042± 0.0061813. For SharpNU-(Q250W2) PV module and Pythagoras Solar Large PVGU Window, HMPA outperforms the other counterparts with RMSEs ± STDs of 0.00027661± 0.0053002 and 0.00285± 0.0020075, respectively. Accordingly, the HMPA provides the slightest deviation between the estimated datasets and the experimental ones with high consistency over several independent runs. The convergence curves of the proposed HMPA affirm its fast response while handling the optimization problem of TDM. The reliability of the identified parameters is tested to emulate the PV modules’ characteristics at different irradiation levels. Furthermore, the robustness of the identified parameters is examined for integrated systems of series string and series–parallel arrays under partial shading conditions. The PV solar modules/strings/arrays characteristics confirm the accuracy of the identified parameters as the attained main points on the characteristics are defined with high quality.