###### Abstract  
Recently, the use of multi-crystalline silicon solar cells (MCSSCs) has been increasing worldwide. This work proposes a novel MCSSC pattern for achieving a more accurate emulation of the electrical behavior of solar cells. Specifically, this pattern is dependent on the modification of the double diode model of MCSSCs. Importantly, the proposed pattern has an extra diode compared to the previously modified double-diode model (MDDM) described in the literature for considering the defect region of MCSSC to form a modified three diode model (MTDM). For estimating the parameters of the proposed MTDM, two metaheuristic algorithms called closed-loop particle swarm optimization (CLPSO) and elephant herd optimization (EHO) are developed, which have superior convergence rates. The competitive algorithms are executed on experimental data based on a MCSSC of area 7.7 cm\({}^{2}\) from Q6-1380 and CS6P-240P solar modules under different irradiance and temperature levels for both MDDM and MTDM. Also, the proposed elephant herd optimization soft paradigm is extended for a high irradiance level at 1000 W/m\({}^{2}\) on an R.T.C. France Solar cell. The proposed new optimization models are more efficient in dealing with the natural characteristics of the MCSSC. The simulation results show that the MTDM gives more accurate solutions as a model to the MCSSC compared with the results reported in the literature. From the viewpoint of soft computing paradigms, the EHO outperforms CLPSO in terms of the solution quality and convergence rates. s 2021 21 January 2021 25 January 20  
The current leakage in the MCS solar cells is correlated to their grain bounds and it is most probable that recombination will occur [5]. Thus, it is possible to say that an important issue of research in MCS solar cells is the necessity of introducing these effects in an accurate model to describe the physical effects of the grain boundaries [6]. In the related literature, it is possible to find several models of PV cells; the basics are the single-, double-, and three-diode models that are abbreviated as SDM, DDM, and TDM, respectively. Each model has a certain increasing degree of complexity as the number of parameters to be estimated increases [7]. The simple construction of the PV cell ensures two differently doped semiconductor layers forming a PN junction when the irradiation exists; the cell absorbs the photons from incident light and yields carriers (or electron-hole pairs). This produces a potential difference across the junction. Then, the charge carriers jump to flow through the outer circuit. An ideal PV cell model is constituted by a photo current source connected with a diode in parallel. This is the simplest model that only has three unknown parameters to be estimated: the photocurrent \(I_{pv}\), the ideality factor \(\eta\), and the diode reverse saturation current \(I_{s}\). However, the previous ideal model is not commonly used in PV simulations to explain the physical concepts of PV cells. A series resistance (\(R_{s}\)) added to the ideal model makes it more realistic. This resistance represents the contact resistance between the silicon and electrode surfaces [7]. A parallel resistance is also added to the diode \(R_{p}\) to consider the leakage current in the PN junction. This model is known as SDM and has five parameters to be estimated (\(I_{pv}\), \(\eta\), \(I_{s}\), \(R_{s}\), and \(R_{p}\)) [8]. The DDM can be considered as a more accurate way of modeling PV cells. It considers the depletion region current loss recombination. With an additional parallel diode, the resulting model now has seven parameters to be estimated (\(I_{pv}\), \(\eta_{1}\), \(I_{s1}\), \(\eta_{2}\), \(I_{s2}\), \(R_{p}\), and \(R_{s}\)) [9]. Although the models mentioned above are the ones most used in the literature, there are other PV cell models.