This study focuses on accurate parameter identification for solar cells and photovoltaic module simulation using experimental data. To tackle the challenge of modelling these highly nonlinear systems, we propose the novel use of the Cheetah Optimizer (CO) algorithm, inspired by cheetah hunting strategies. The CO algorithm employs mathematical models and randomization parameters to balance exploration and exploitation, avoiding local optima by considering energy limitations. We demonstrate the CO algorithm's effectiveness by applying it to the three-diode model in solar photovoltaic systems, specifically the STP6-120/36 and Photowatt-PWP201 PV modules. Impressively, the CO algorithm achieves remarkably low root mean square error values of 0.0145 A and 0.0019 A, outperforming state-of-the-art methods and ensuring high accuracy. Additionally, it delivers the lowest power errors of 0.16054 W and 0.01484 W for the respective modules, highlighting its exceptional performance. The CO algorithm proves to be a promising tool for precise parameter extraction and optimization, leading to improved modelling and performance of solar photovoltaic systems.