###### Abstract  
In this paper, we propose very simple analytical methodologies for modeling the behavior of photovoltaic (solar cells/panels) using a one-diode/two-resistor (I-D/2-R) equivalent circuit. A value of \(a=1\) for the ideality factor is shown to be very reasonable for the different photovoltaic technologies studied here. The solutions to the analytical equations of this model are simplified using easy mathematical expressions defined for the Lambert W-function. The definition of these mathematical expressions was based on a large dataset related to solar cells and panels obtained from the available academic literature. These simplified approaches were successfully used to extract the parameters from explicit methods for analyzing the behavior of solar cells/panels, where the exact solutions depend on the Lambert W-function. Finally, a case study was carried out that consisted of fitting the aforementioned models to the behavior (that is, the _I-V_ curve) of two solar panels from the UPMSat-1 satellite. The results show a fairly high level of accuracy for the proposed methodologies. solar cell; solar panel; parameter extraction; analytical; Lambert W-function; spacecraft solar panels; _I-V_ curve; modeling +
Footnote †: journal: _Sci. in the early predesign phase of space missions. It is based on the parallelization of processes associated with different sub-systems and is carried out in a special working environment organized into Concurrent Design Facilities (CDFs), where design parameters are shared, and the information flow is organized thus that stable solutions can be reached as quickly as possible [13; 14; 15; 16; 17]. Research carried out at the IDR/UPM Institute on solar panels has been driven by the need for simple procedures to calculate the performance of these panels. This need has arisen in the context of mission predesign at the CDF [18; 19], and particularly in relation to sub-system coupling effects, such as those that can be found when analyzing thermal control and power distribution in spacecraft. The simulation of photovoltaic devices (solar cells/panels) is normally carried out by means of equivalent circuit models, which are defined by implicit mathematical expressions. However, problems arise in terms of:  
* The extraction of the parameters appearing in this equation, which define the performance of the photovoltaic device at a certain temperature and irradiance level, and;
* The calculation of the output current as a function of the output voltage, or vice versa, since this equation is implicit. There are multiple ways to fit the equation for the photovoltaic equivalent circuit models to experimental data [20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. All of these approaches can essentially be grouped into two different types: Numerical (in which the equation is fitted to a large dataset that represents the \(I\)-\(V\) curve of the photovoltaic device) and analytical (in which the parameters of the equation are extracted based on three points of the \(I\)-\(V\) curve: short circuit, maximum power, and open voltage). The second issue described above, i.e., the calculation of the output current as a function of the output voltage once the parameters of the equation have been extracted, can only be solved by numerical approaches [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46] (which include iterative solutions [47; 48; 49]), or by using of the Lambert W-function [50; 51; 52; 53; 54; 55] (whose exact calculation requires a numerical approach). Possible solutions to the aforementioned problems include explicit methods of photovoltaic modeling, which are based on explicit equations with parameters defined based on the characteristic points of the \(I\)-\(V\) curve. Some of these methods also require the use of the Lambert W-function to define the parameters [56].