*4.3. Analysis of Modified Diode Models' Works*

The MSDM, MDDM, and MTDM all consider the quasi-neutral zone's losses. It is reflected in the circuit diagram by selecting a diode branch and adding a series resistor *Rsm*. The improved model adds an unknown parameter compared to the pre-improved model. Their circuit diagram is shown in Figure 9.

**Figure 9.** Modified diode models' circuits.

Their output current changes to [48,49]:

$$I = I\_{ph} - \frac{V + IR\_s}{R\_{sl}} - \sum\_{j=1-(nD-1)} I\_{sdj} \left[ \exp\left(\frac{q(V + IR\_s)}{n\_j kT}\right) - 1 \right] - I\_{sdnD} \left[ \exp\left(\frac{q(V + IR\_s - I\_{sdnD}R\_{sw})}{n\_{nD} kT}\right) - 1 \right] \tag{14}$$

where *nD* represents the number of diodes in the cell model.

In this subsection, two papers from the last three years are chosen to present the results of metaheuristic approaches to solving the above models. Ramadan et al. [48] improved the Bald Eagle Search algorithm (IBES), employing decay equations to achieve adaptive learning factors. Abdelminaam et al. [49] pioneered the use of Turbulent Flow Optimization of Water (TFWO) for the parameter extraction of PV cells with a new objective function (PE5DSSE). Their extraction results are illustrated in Table 24.

**Table 24.** Results of the modified diode models.


In Table 24, for MSDM, the parameter that differs most between IBES and TFWO is *Rsm*. For MDDM, IBES and TFWO are similar in *Iph* and *Rsh*, and the other parameters differ more. For MTDM, IBES and TFWO are almost identical in *Iph* and *Rsh*, and the other parameters differ more. As they use different objective functions, it is impossible to compare the accuracy of the two.

In IBES, the MIN RMSE is 9.88 × <sup>10</sup>−<sup>4</sup> for TDM and 9.86 × <sup>10</sup>−<sup>4</sup> for SDM and DDM. In TFWO, the PE5DSSE is 2.5278 × <sup>10</sup>−<sup>5</sup> for SDM, 2.51 × <sup>10</sup>−<sup>5</sup> for DDM and 2.51 × <sup>10</sup>−<sup>5</sup> for TDM. It indicates that the addition of Rsh did improve the accuracy by a small margin. Therefore, applying MSDM, MDDM, MTDM, and the PV module models constructed from them to future studies will be an effective way to improve the accuracy further.
