**2. Modeling of PV Cell**

Ideally, a parallel combination of a current source and a diode represents a solar cell. For practical applications, the model also incorporates shunt and series resistances to take into account manufacturing defects and contact resistances [20], as illustrated in Figure 2a.

(**b**)

**Figure 2.** Solar cell: (**a**) single-diode model and (**b**) double-diode model.

The current generated by the solar cell can be computed by Equation (1).

$$I\_{pv} = I\_{ph} - I\_D - I\_{sh} \tag{1}$$

The Shockley equation and Ohm's law can be used to calculate the current through a diode and shunt resistor, as shown in Equations (2) and (3), respectively.

$$\mathbf{I}\_{\rm D} = \mathbf{I}\_{0} \left[ \exp\left(\frac{q}{N\_{cs}\dot{K}T} \left(V\_{pv} + I\_{pv}R\_{sc}\right) \right) - 1 \right] \tag{2}$$

$$\mathbf{I}\_{\rm sh} = \frac{V\_{\rm pv} + I\_{\rm pv} \ R\_{\rm sc}}{R\_{\rm sh}} \tag{3}$$

Thus, the distinctive Equation of solar cell output current can be written as

$$\mathbf{I}\_{\rm pv} = \mathbf{I}\_{\rm ph} - \mathbf{I}\_0 \left[ \exp\left(\frac{q}{nkT} \left(V\_{\rm pv} + I\_{\rm pv} R\_{\rm sc}\right)\right) - 1\right] - \frac{V\_{\rm pv} + I\_{\rm pv} R\_{\rm sc}}{R\_{\rm sh}} \tag{4}$$

The ideality factor "n" is assumed to be constant in single-diode model, but this factor is a function of voltage at the device terminals. Its value is close to one at high voltages and becomes two at low voltages because of recombination in junction. This effect can be modelled by connecting another diode in parallel with the first diode, giving rise to the double-diode model, as shown in Figure 2b. The ideality factor is set to "2" for the double-diode model.

Figure 3 shows the PV module (I–V) and (P–V) characteristic curves. It details the solar energy conversion capability and efficiency for a particular atmospheric condition. Since short- and open-circuit circumstances have no effect on power generation, there must be a point somewhere in the middle where the solar module produces most power and is located close to the bend in the characteristic curves. Pmax is generated by a specific combination of voltage and current, and the combination's coordinates represent the MPP.

**Figure 3.** PV module characteristic curves (I–V) and (P–V).

A slight change in atmospheric temperature and irradiance affects the module's performance. Since module Voc decreases as temperature rises [21], the power output yield of the PV system will decrease. Figure 4a,b show the temperature variation effect on PV module (I–V) and (P–V) curves.

**Figure 4.** Temperature variations effect on PV module: (**a**) I–V curve and (**b**) P–V Similarly, the output of PV modules is also affected by the change in solar irradiance "W w/m2", as the output current of PV module depends on irradiance. As irradiance increases, the PV module output current also increases. Thus, the PV module can generate more output power. Figure 5a,b show the effect of irradiance change on PV module (I–V) and (P–V) curves.

**Figure 5.** Irradiance variation effect on PV module: (**a**) I–V curve and (**b**) P–V curve.
