Solar Photovoltaic (PV) system is one of the most significant forms of renewable energy resources, and it requires accuracy to assess, design, and extraction of its parameters. Several methods have been extensively applied to mimic the nonlinearity and multi-model behavior of the PV system. However, there is no method to date that can guarantee the extracted parameter of the PV model is the most accurate one. Therefore, this paper presents a unique approach known as Hybridized Arithmetic Operation Algorithm based on Efficient Newton Raphson (HAOAENR) to experimentally extract the parameters of the single-diode and double-diode PV models at the variability of the climatic changes. Firstly, the objective function is efficiently designed to roughly predict the initial root values of the PV equation. Secondly, the Lévy flight and Brownian strategies are integrated in the four operators of AOA to thoroughly analyze the feature space of this problem. Additionally, the four operators of the AOA is divided into two phases to equilibrium between the exploration and exploitation tendencies. Furthermore, the chaotic map and robust mutation techniques are systematically employed in the beginning and halves of generations to ensure the algorithm can reach globally at few numbers iterations. Finally, a nonlinearly adjustable damping parameter of the Levenberg-Marquardt technique is linked with the NR method to replicate the fluctuation behaviours of the PV models. The experimental findings revealed that the proposed HAOAENR outperformed all other methods found in the literature, with average RMSE values close to zero values for both PV models.