Currently, the incorporation of solar panels in many applications is a booming trend, which necessitates accurate simulations and analysis of their performance under different operating conditions for further decision making. In this paper, various optimization algorithms are addressed comprehensively through a comparative study and further discussions for extracting the unknown parameters. Efficient use of the iterations within the optimization process may help meta-heuristic algorithms in accelerating convergence plus attaining better accuracy for the final outcome. In this paper, a method, namely, the premature convergence method (PCM), is proposed to boost the convergence of meta-heuristic algorithms with significant improvement in their accuracies. PCM is based on updating the current position around the best-so-far solution with two-step sizes: the first is based on the distance between two individuals selected randomly from the population to encourage the exploration capability, and the second is based on the distance between the current position and the best-so-far solution to promote exploitation. In addition, PCM uses a weight variable, known also as a controlling factor, as a trade-off between the two-step sizes. The proposed method is integrated with three well-known meta-heuristic algorithms to observe its efficacy for estimating efficiently and effectively the unknown parameters of the single diode model (SDM). In addition, an RTC France Si solar cell, and three PV modules, namely, Photowatt-PWP201, Ultra 85-P, and STM6-40/36, are investigated with the improved algorithms and selected standard approaches to compare their performances in estimating the unknown parameters for those different types of PV cells and modules. The experimental results point out the efficacy of the PCM in accelerating the convergence speed with improved final outcomes.