## 1 Introduction  
Owing to the urgent need to protect the environment from pollution, scientists have been working hard to build a wide variety of accurate models that are intended to provide efficient Renewable Energy (RE) substitutes for traditional energy obtained from fossil fuels [1; 2]. One of the main issues in environmental difficulties is the emergence of environmental pollution due to the use of traditional energy sources. As a potential remedy for this issue, using alternative RE sources has attracted much attention lately. Nuclear power, wind, solar, tidal, wave, and other RE sources are commercially feasible. The sources indicated above offer a wide range of practical applications in areas including agriculture, hot water distribution, wireless sensors, and photovoltaic (PV) systems. In contrast to the consequences of fossil fuels, solar power has gained substantial attention recently from institutions, governments, and academics for its long-lasting benefits in producing electricity via photovoltaic energy while avoiding environmental harm [1; 2; 3]. PV technology is of great significance in technology and scientific research since it provides a comprehensive future vision. The significance of its contribution to RE, energy independence, climate change mitigation, and economic prosperity cannot be exaggerated. Through the inclusion of PV in scientific research, researchers and statisticians may actively contribute to the development of solar cell technology, therefore facilitating further advancements in the sector and promoting a future that relies on sustainable and environmentally friendly energy sources. In order to fully harness the potential of solar energy, reduce prices, and establish a sustainable and resilient energy future, it is imperative to maintain ongoing scientific research and innovation in PV technology. PV systems efficiently convert solar energy into electrical power, which is essential for the global growth of RE [4; 5]. However, the effective energy delivery of PV systems is hampered by external factors, such as dust deposition in the vast networks of the PV grid. Airborne particles, erratic weather patterns, and temperature fluctuations all negatively impact solar cell performance and reduce their overall efficiency. One way to potentially address these issues is to find precise PV models that maximize the efficiency of solar cell energy output. In order to use a PV system efficiently, it is first necessary to know the system's current-voltage (_I-V_) characteristics, in both theory and practice. This requires accurate mathematical modeling of the system. The most common versions of solar photovoltaic systems may be described as follows: a current source paralleled with a diode and two resistors, one of which is linked in series and the other in shunt [6]. To create a Single-Diode Model (SDiM) for PV parallel circuits, as seen in Figure 1, one must combine a single diode with two resistors. The addition of more diodes to the PV models increases the number of unknown factors, which raises the complexity of the model itself. Within a PV-comparable circuit, the SDiM includes five unknown features associated with PV behavior. In contrast, the Double-Diode Model (DDiM), which is created by pairing two diodes as seen in Figure 2, has seven unknown parameters. Subsequent models also adhere to a similar pattern. Numerous factors, such as saturation current, series/parallel resistance, shunt-resistant current, and shunt resistor, are included in diode models. It is necessary to compute and extract these unknown parameters from the information provided by the _I-V_ curve. Since inaccurate predictions of these factors might result in significant differences in the manufacturing process, careful consideration of these components is necessary for solar cell process models to be effective. As a result, estimating these properties is an important task that improves PV system optimization.