This article discusses the problem of accurate and efficient modeling of photovoltaic (PV) panels. It is a highly nonlinear problem. The following models were considered: a single diode model, a double diode model, a triple diode model, a four diode model, a module model (a poly-crystalline Photowatt-PWP201 module and a mono-crystalline STM6-40/36 module). The article presents a mathematical notation of these models, a detailed interpretation of their individual components, and a comparison of obtained results. To increase the effectiveness of modeling, a new population-based algorithm which can handle complex objective functions and a large number of decision variables was developed. This is important for the problem of identifying the parameters of PV cell models because each evaluation of the objective function requires calculating a set of points that determine the current–voltage characteristics. Moreover, in the considered problem a solution is searched with the use of the trial and error method. The proposed algorithm is called Micro Adaptive Fuzzy Cuckoo Search Optimization (μ AFCSO). The μ AFCSO algorithm uses several new mechanisms that were developed based on our experience with population-based algorithms. The use of these mechanisms has produced very good results in simulations. In the scope of simulation studies, the μ AFCSO algorithm was used for parameter extraction in six PV cell models and was also applied to optimize fifteen typical test functions. The test functions were considered in order to demonstrate that our algorithm can be used to solve typical problems processed using population-based algorithms. The results obtained in this study were compared with the results obtained using well-established algorithms. The results obtained in this work are better or comparable to them. [Display omitted] • The article focuses on modeling PV cells by identifying model parameters. • We present a wide collection of PV cell models and compare their accuracy. • We propose a new algorithm for identifying the parameters of the PV models. • Our method uses a population of individuals but has an original working formula. • We have achieved a very high modeling accuracy. [ABSTRACT FROM AUTHOR]