This paper presents a new methodology to extract the unknown parameters of a single-diode photovoltaic (PV) cell model. The first contribution of this paper is the development and implementation of a new version of the wind-driven optimization algorithm, called an adaptive wind-driven optimization (AWDO) algorithm. The advantages of the AWDO algorithm are: 1) accurate extraction of the global values of the optimized PV parameters in changing weather conditions, which is achieved by building solutions from random operations; and 2) capability of handling the given complex multi-modal and multi-dimensional optimization problems. The second contribution is the identification of a generalization model to generalize the extracted parameters of a single-diode PV cell model. That provides an ability of the proposed methodology to work with any I-V characteristic curve of PV cells and at any weather condition on a 15-min basis. To validate the proposed methodology, it has been tested for 1307 I-V characteristic curves of a PV module at various weather conditions on a 15-min basis. Additionally, its accuracy and computational efficiency are verified and compared with five well-known existing extraction methods: Villalva's model, particle swarm optimization, biogeography-based optimization, Gang's model, and bacterial foraging optimization by both simulation and outdoor measurements. The results show that the AWDO algorithm can provide the extracted five parameters with an acceptable range of accuracy and faster than the aforementioned models. Therefore, the proposed methodology (AWDO based on Chenlo's model) can be confidently recommended as a reliable, feasible, valuable, and fast optimization algorithm for parameter extraction of a single-diode PV cell model.