## 1 Introduction
There have been many successful algorithms for adjusting parameters of PV cells in SDM and DDM, but few works in TDM have been published in this area. Reference [29] proposed a solar PV parameter extraction method based on the Flower Pollination Algorithm (FPA). Two diode models are chosen to understand the precision of the computation. The authors experimented with the effectiveness of FPA using RTC France info. Simulated Annealing (SA), Pattern Search (PS), Harmony Search (HS), and Artificial Bee Swarm Optimization (ABSO) techniques are often used to compare the measured root mean square error and relative error for the built model. Researchers [30] proposed a hybridized optimization algorithm (HISA) for accurately estimating the parameters of the PV cells and modules. From the experimental data obtained from five case studies consisting of two cells and three modules for monocrystalline, multi-crystalline, and thin-film PV technologies, single- and double-diode models of PV cells/modules were developed with their respective single I V nonlinear characteristics. The authors [31] propose two simple metaphor-free algorithms called Rao-2 (R-II) and Rao-3 (R-III) to estimate the parameters of PV cells. Several well-known optimization algorithms are compared to the efficiency of the proposed algorithms. The comparison helps show the merit of the algorithms. Finally, an analysis of statistical data is combined with experimental findings to verify the efficiency of the proposed algorithms. The Grasshopper Optimization Algorithm (GOA) is proposed [32] for parameter extraction of a PV module's three-diode PV model. This GOA-based PV model uses two popular commercial modules: Kyocera KC200 GT and Solarex MSX-60. The single-, double-, and three-diode models have different solar cell parameters. These models have five parameters for the single-diode model and seven parameters for the double- and three-diode models. Each parameter must be obtained accurately based on the objective function to reach the global optimum. In this study, the EHO algorithms have been chosen to solve this problem because they have a few control parameters and smooth implementation. In addition, EHO's simplicity and few parameters made it a suitable choice for achieving such enhancements. Furthermore, by dividing the population into clans, we could avoid becoming trapped in a local optimum and instead converge on reaching a global minimum. Finally, after getting experimental results for this problem, a comparison with other well-known algorithms was presented to prove the result's quality. This comparison is important to ensure that the new variants can solve this problem and compete with other algorithms. Table 1 reports some of the recent solvers that were applied for PV parameter estimation problems in the recent years  
The RMSE and the relative error are used as the most performance measures developed in the previous methods. The proposed variants of EHO are compared against most of the new well-known algorithms on the parameter identification of different photovoltaics. The performance of these proposed algorithms can be judged according to convergence speed, high estimation of parameters, and low computation time. The main contributions of this paper can be summarized as follows:  
* Proposing three variants of the EHO algorithms for solar cell parameters estimation. * The EHO and the proposed EHO variants are tested on single-, double-, and three-diode models. * Verifying the performance of each algorithm by comparing results with those of competitors.