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• An enhanced political optimizer (QNMPO) is proposed to realize the extraction of photovoltaic models parameters. • The performance of the proposed QNMPO algorithm is compared with some well-known competing algorithms. • The stability performance of QNMPO was tested on three commercial PV models at different temperature levels and irradiation levels. • QNMPO exhibits better convergence speed and accuracy. Evaluating the PV system parameters is crucial for the more efficient utilization of sustainable solar energy. Due to PV systems' nonlinear and multimodal nature, efficient evaluation of PV system parameters is still a very challenging task. This paper proposes an improved political optimization algorithm, namely the QNMPO algorithm, which combines quantum rotation gate and Nelder-Mead simplex (NMs). It can be used to evaluate unknown parameters of PV systems and solar cells efficiently. In QNMPO, the quantum rotation gate method can rotate the population of agents to a more favorable position for finding the optimal solution, making the individuals in the middle of the population communicate more frequently and enhancing the population's diversity. In addition, the NMs method can improve the solution quality by better searching the neighborhoods near the optimal solution and then strengthen the advantage of local development of the algorithm so that it can converge to the global optimal solution faster. The developed QNMPO algorithm extracts the unknown parameters for single diode, double diode, triple diode and photovoltaic modules in this study. It is compared with some other representative algorithms. The experimental results show that QNMPO outperforms similar algorithms in convergence speed, solution accuracy, and better solution performance. QNMPO was then used to successfully extract the best parameter values for three real PV models (three commercial PV models (thin-film ST40, monocrystalline SM55, and multi crystalline KC200GT)) at different temperatures and different irradiance levels. The results also show that QNMPO performs consistently and accurately enough under varying temperatures and irradiation. Therefore, the QNMPO algorithm proposed in this paper can be a promising parameter extraction method for solar PV systems with good performance. [ABSTRACT FROM AUTHOR]