•A novel application of SFO algorithm to extract PV model parameters is presented.•Three-diode PV model is used in this paper.•Parameters of SFO-TDPV model are compared with other optimization based models.•The SFO-TDPV model is verified by comparing its results with measured data.•The error among these results records a value less than 0.5%. This article proposes an accurate and straightforward method for modeling and simulation of photovoltaic (PV) modules. The main target is to find the nine-parameter of a three-diode (TD) model based on the datasheet parameters, which are given by all commercial PV modules. The objective function is formulated based on short circuit, open circuit, power derivative, and maximum power equations. Two parameters (parallel resistance and photo-generated current) are calculated analytically and rest parameters are optimally designed using the sunflower optimization (SFO) algorithm. The presented method is applied to model three types of commercial PV modules (multicrystal KC200GT, poly-crystalline MSX-60, and mono-crystalline CS6K-280M). The optimal nine-parameters obtained in this paper are paralleled with that attained by other approaches. In order to assess the efficiency of the offered approach, I-V and P-V characteristics are validated with measured data under various temperatures and solar irradiations. The error among these results records a value less than 0.5%. Therefore, the simulation results indicate an excellent agreement with the measured data. This proposed approach can be utilized to model any marketable PV module based on given datasheet parameters only.