The forecasting of the energy conversion effi-ciency for PV systems: Theoretical approach [Y.Soler.C-M.Sahni, 2022], and its notes in the draft from an upcoming paper.

2. Physical and mathematical assumptions of the modeling proposal. Parameters Estimations for the model.

At present days is a fact the accelerated trend on the number of PV installations worldwide, which propels most cost-effective PV modules manufacturing and efficient as well by manufacturers. Those optimizations encompass the antireflective coatings, texturings, controlled-step multilayers and techniques to keep on PV modules as cool as possible (R. Panat and K. K. Varanasi, 2022) [6].

Authors propose a novel approach formulated in normalized fashion facing in that way the difference by several order of magnitude among all kind of PV systems, where the efficiency formulation will be expressed in the relative units to Standard Test Condition (STC).

Semiconductors main parameters responsible for designing the PV cells, in order to reach out its best performance encompass the concentrations of doping atoms as a key factor of the space-charge width region of junction, transport carriers phenomena, i.e., diffusion and drift, recombination-generation processes, and the absorption materials properties for either visible or other solar radiation, this last one as function of the: band gap energy, absorption coefficient and refractive index. Thus, PV devices are designed to maximize its output for which manufactures pay especial attention to key parameters such as: Open-circuit voltage, Short-circuit current, Maximum power curren, Maximum power voltage , Maximum power output, and Fill factor, with the last one featuring how squared I-V curve is. Therefore, authors regarding the model description used in this work, take into account the dynamics behavior of these three manufacturing parameters due to operating conditions, others than the reference ones reported by manufactures in PV modules datasheets, as the main basics for the physical and mathematical formulations depicted throughout it.

On the other hand, voltage and current delivered by a PV system at the maximum power point are mainly a consequence of the operating conditions or environmental parameters changes (O.F. Alrani et.al.,2022) [2], among other factors; which in turn, they are understood as the driving forces that account for the dynamic behavior of the I-V curve. So that, the need of knowing the dynamics limits of the I-V curve to predict its behavior, impels to figure out which are the impacts of solar irradiance and module temperature on the open circuit voltage and short-circuit current, on purpose to sketch the aforementioned dynamics frameworks for this curve. I-V curve limits draw on five major factors as the guidance for speeding up the penetration of photovoltaic technology, and evaluating its feasibility, based on the deeper insight of the physical processes when they are simulated to reproduce the non-linear dynamics, regarding its stochastic fashion. Among these factors to be considered we have the annual irradiance (solar spectrum), and temperature distribution, the variations of the PV module temperature coefficients, the rate of power degradation throughout the time, and the impact in the efficiency variations of these PV devices, which are produced by the mentioned parameters, that will define the behavior of these systems in the specific sites where they be installed (P. K. Dash and N. C. Gupta, 2015) [7].

It is worth noting that PV module parameters reported by manufactures in datasheets do not point out the model used for computing them, so that the given information about open-circuit voltage, short-circuit current and maximum power point is linked to operational reference conditions, but in the real operational ones they changes constantly as function of the environmental variables, and aging effects also. Therefore, the success in the performance forecasting relies on describing the parameters behavior under real conditions, leading to the tracking of I-V curve changes, mainly around its maximum power point, as result of the dynamics in which the I-V curve limits vary, i.e., Open-circuit voltage, Short-circuit current according to the solar irradiance and module temperature (M. Akhsassi et al.,2017) [8]. As reported by (T. Huld and A. M. Gracia, 2015) [9], the energy conversion efficiency of PV modules has in the irradiance and module temperature its major influential factors whose impact spanning depends on systems locations from −20% to +5%.

The model here introduced tracks most of the incidental factors, which affect the PV modules efficiency, like the reflectivity, as function of the angle of the incoming light. The wavelength, regarding the spectral effects, which depending on the PV technology used, it will have influence on the energy yield and performance by the local spectral deviation from standard one that introduces uncertainty in the simulation, thus the effectively absorbed irradiance by the active material has dependence on this effect (J. B. Castro et al.,2020) [10]. The temperature, which accounts for the surrounding air, the intensity of light and the local wind speed. The long-term exposure of PV modules to sunlight and high temperature, they may well be the likely pattern to depict the dynamics involved in those systems.