## 1 Introduction
In recent decades, multiple attempts have been made to comprehend, optimize, and estimate the PV parameters derived from various mathematical models of PV systems. Numerous approaches have been put out in scholarly works to address and evaluate the intricacy of non-linearities in PV models, aiming to achieve both precision and efficiency. The simplification of equations has been found to have a detrimental impact on the accuracy and effectiveness of the results. A recent study [4] identified a limitation in the ability of this strategy to accurately extract parameters when compared to the I-V characteristic method. The method that relies on I-V characteristic curves aims to reduce the disparities between the current data obtained from experiments  
Figure 1: The SDM’s equivalent circuit. and the current data generated through simulations in order to identify the PV system parameters. Through the utilization of this methodology, the parameters can be resolved and discerned through diverse means. Within the technical literature, there exist three distinct categories of solutions in which I-V curves are utilized for the purpose of extracting and identifying PV parameters. These include analytical methods, numerical procedures, and solutions utilizing meta-heuristic techniques. Several methodologies can be used to extract PV parameters from experimental data obtained from the characteristics of the I-V curve. The utilization of these techniques is characterized by their relative ease of use, requiring only a single iteration of the computation to successfully accomplish the given task. Analytical solutions for most models can be obtained under Standard Test Conditions (STC) within a specific context through occasional utilization of the Lambert W function [9]. Using the SDM and the DDM, refs. [10; 11] developed an analytical method to precisely determine the PV parameters of various silicon solar cells. This method exhibits a high level of precision, with an error rate of less than 10% for the majority of solar cells. Calculations were conducted for identifying the parameters via key points such as maximum power point (\(M_{PP}\)) (\(V_{MP}\), \(I_{MP}\)) and values resulting from the slops of the measured curves for the short-circuit current Isc and open-circuit voltage \(V_{oc}\) points. Using the values of (\(V_{MP}\), \(I_{MP}\)), and \(V_{oc}\) points on the I-V characteristic curve, subsequently, the ideality factor \(n\) was determined, and the remaining PV parameters were obtained. The analytical approach utilized in study [12] did not consider the effects of series and shunt resistances, although it relied on a comprehensive analysis of many data sheets. Despite the simplicity of this proposed approach, its accuracy is compromised under conditions of low irradiance. Ref. [13] proposed the exclusion of the shunt resistance in various operational scenarios as a method for deriving four PV parameters from the manufacturing data sheet without using all of the characteristics included in the I-V characteristic curve. This lead to a series resistance value that exhibited a non-physically negative characteristic. Ref. [14] extracted the five parameters of the SDM at the STC of irradiance (1000 \(W\)/m\({}^{2}\)) and temperature (25 \({}^{\circ}\)C). This was accomplished by implementing the four-parameter model and fitting the I-V curve with a piecewise linear fit procedure, which required identifying the points corresponding to short-circuit and open-circuit conditions. By establishing a correlation between the diode ideality factor (\(n\)) and the open-circuit voltage (\(V_{oc}\)), ref. [15] proposed a method for deriving the equations of the SDM. This method allowed for access to five PV parameters of the SDM under STC. The analytical solutions for determining the PV parameters have demonstrated notable efficacy and expediency, rendering them readily applicable in practical settings. However, there are assumptions, approximations, exclusions, and simplifications.