## 1 Introduction
Photovoltaic systems often rely on implicit, nonlinear, multi-variable, and multi-modal equations in their mathematical models [7]. Figure 1: SDiM of (**a**) ideal solar PV cell, (**b**) practical solar PV cell. Figure 2: DDiM of solar PV cell. As per the researchers' findings, solving PV models remains a difficult problem. They have proposed many methods to solve this, with the goals of timeliness, precision, and reliability, for extracting, evaluating, and simulating PV parameters [4; 5; 8]. Over the past few decades, there have been numerous efforts to understand, optimize, and estimate the photovoltaic parameters derived from various mathematical models of PV systems. The complexity of non-linearities in PV models has been addressed and evaluated using various techniques published in academic works with the goals of efficiency and accuracy. It has been discovered that simplifying equations negatively affects the precision and usefulness of the outcomes. Recent research [4] found that, in comparison to the _I-V_ characteristic technique, this strategy's capacity to reliably extract parameters was limited. In order to determine the characteristics of the PV system, the technique that uses _I-V_ characteristic curves seeks to lessen the differences between the current data produced by simulations and the current data acquired through tests. By applying this process, the parameters can be determined and resolved in a variety of ways. Numerous scholars have created a range of models of PV systems in the existing literature, such as the SDiM and DDiM. Furthermore, the efficiency of the photovoltaic model relies on undisclosed internal traits. It is difficult to maintain and assess all the unknown factors because of deterioration, aging, and erratic operating states. It is impossible to design, estimate, simulate, and optimize PV modules without first determining the relevant electrical parameters. Consequently, research is being conducted to determine how well swarm optimization techniques work for measuring PV system characteristics. Analytical methods [9] produce specific approximations or oversimplified assumptions while disregarding accuracy compromises. However, to compute the current and voltage corresponding to the maximum power output, this analytical model has been streamlined by disregarding the effects of parallel and series resistances. The Lagrange multiplier method was proposed in [10] for the SDiM/DDiM to optimize the power outputs of PV solar cells. The essential details were taken from the datasheet provided by the manufacturer and reduced in [11], where the power first derivative was used to produce a boundary need for a zero-voltage state. In addition, the I-V curve's four random locations and their slopes are shown in [12] in order to precisely extract the SDiM parameters without analytical approximations or simplifications. Nevertheless, such an analytical method is constrained to standard testing situations. This fails when they change and contain many calculations [13]. Conversely, numerical methods have been introduced, such as deterministic and metaheuristic algorithms. The deterministic approach may produce local optima if the beginning values are inaccurate, and the real model may struggle to meet the constraints of the objective function equation [14]. On the other hand, the PV model parameters can be found efficiently and straightforwardly using metaheuristic methods. Consequently, metaheuristic techniques have been studied to address parameter extraction. For electric solar PV systems, the gorilla troops optimizer [GTO] [15], dandelion OA [DOA] [16], and artificial hummingbird optimizer [AHBO] [17] have been developed. Gradient-based optimization using a rank-based strategy and logistic map has been expanded to SM55 and KC200 GT using the SDiM and DDiM [18]. Differential Evolution (DE) has been used in numerous studies [19; 20] to address the challenge of identifying parameters in the PV model.