2.1.2. DDM

Figure 1b mentions the equivalent schematic of the DDM. After adding a diode, below is the electrical expression of *I* [36,37].

$$I = I\_{\rm ph} - I\_{\rm sh} - I\_{\rm s\rm d1} - I\_{\rm s\rm d2} = I\_{\rm ph} - \frac{V + IR\_{\rm s}}{R\_{\rm sh}} - I\_{\rm s\rm s\rm d1} \left[ \exp\left(\frac{q(V + IR\_{\rm s})}{n\_1 kT}\right) - 1\right] - I\_{\rm s\rm s\rm d2} \left[ \exp\left(\frac{q(V + IR\_{\rm s})}{n\_2 kT}\right) - 1\right] \tag{2}$$

where *Isd*<sup>1</sup> and *Isd*<sup>2</sup> represent the first and second diode line currents, respectively, *Issd*<sup>1</sup> and *Issd*<sup>2</sup> represent the corresponding diode saturation currents, and *n*<sup>1</sup> and *n*<sup>2</sup> represent the corresponding ideal factors.

This model needs to estimate the values of *Iph*, *Issd*1, *Issd*2, *n*1, *n*2, *Rs*, and *Rsh*.

### 2.1.3. TDM

Figure 1c mentions the equivalent schematic of the TDM. Below is the electrical expression of *I* [38–40].

$$I = I\_{ph} - I\_{sh} - \sum\_{j=1 \to 3} I\_{sdj} = I\_{ph} - \frac{V + IR\_s}{R\_{sh}} - \sum\_{j=1 \to 3} I\_{ssdj} \left[ \exp\left(\frac{q(V + IR\_s)}{n\_j kT}\right) - 1 \right] \tag{3}$$

where *Isdj*, *Issdj*, and *nj* represent the *j*th diode line current, the saturation current, and the ideal factor, respectively.

The TDM requires estimating the values of *Iph*, *Issd*1, *Issd*2, *Issd*3, *n*1, *n*2, *n*3, *Rs*, and *Rsh*.

#### 2.1.4. PV Module

Figure 1d mentions the equivalent schematic of the PV module based on the SDM. A PV module composed of *Ns* × *Np* cells inherently has a high complexity. Therefore, using the SDM to construct PV modules is the first choice for most researchers. Equation (4) is the electrical expression of the PV module's current [4,41].

$$I = I\_{ph}N\_p - \frac{V + IR\_sN\_s/N\_p}{R\_{sl}N\_s/N\_p} - I\_{ssd}N\_p \left[ \exp\left(\frac{q\left(V + IR\_sN\_s/N\_p\right)}{nN\_skT}\right) - 1\right] \tag{4}$$

The PV module has the same parameters as the SDM (*Iph*, *Issd*, *n*, *Rs*, and *Rsh*).
