**2. PV Configuration**

The five-parameter electric circuit model of a PV cell is shown in Figure 1 [94–96]. It consists of a light-dependent current source, a p-n junction diode, and two resistances, one in series and the other in parallel.

**Figure 1.** Five-parameter equivalent electric circuit model of a PV cell.

Using simple Kirchhoff's current law:

$$I\_{PV} = I\_L - I\_D - I\_{SH} \tag{1}$$

where *ID* and *ISH* depict the diode and shunt branch currents, respectively, and are given by:

$$I\_D = I\_0 \{ \exp[\frac{V\_{PV} + I\_{PV}R\_S}{a}] - 1 \} \tag{2}$$

$$I\_{SH} = \frac{V\_{PV} + I\_{PV}R\_S}{R\_{SH}}\tag{3}$$

Putting these expressions of *ID* and *ISH* into Equation (1) gives the complete I-V characteristics of a PV panel:

$$I\_D = I\_L - I\_0 \{ \exp[\frac{V\_{PV} + I\_{PV}R\_S}{a}] - 1 \} - \frac{V\_{PV} + I\_{PV}R\_S}{R\_{SH}} \tag{4}$$

where *IPV* and *VPV* represent the current and voltage generated from the PV panel. *IL* is the light-generated current, *I0* is the diode saturation current, *RS* and *RSH* are the series and parallel resistance, respectively, and factor *a* is the diode-modified ideality factor, which is given by:

$$a = \frac{\text{N} \text{s} \text{nKT}}{q} \tag{5}$$

where *Ns* is the number of cells in the PV panel, *n* is the ideality factor (it has a value between one and two for the real diode), *K* is Boltzmann's constant, *T* is the cell temperature, and *q* is the electronic charge.

A standard PV cell generates a relatively low voltage (around 0.6 V); hence, PV cells are connected in series and parallel to raise the appropriate voltage level for the required application. PV modules are built using the PV cells' series and parallel connections; a PV array consists of PV modules connected in series or parallel [97]. Equation (4) can be modified to represent the I-V relationship of the series and parallel array and written as:

$$I\_{PV} = N\_{pp} \* I\_L - N\_{pp} \* I\_0 \{ \exp[\frac{V\_{PV} + I\_{PV}R\_S \* N}{N\_{ss} \* a}] - 1 \} - (\frac{V\_{PV} + I\_{PV}R\_S \* N}{R\_{SH} \* N}) \tag{6}$$

$$N = \frac{N\_{ss}}{N\_{pp}}\tag{7}$$

where *NSS* and *NPP* represent the number of panels connected in series and parallel, respectively. Figure 2 depicts the current–voltage characteristics of PV panels for different irradiation levels from 200 W/m<sup>2</sup> to 1000 W/m2 and a constant temperature of 25 ◦C.

**Figure 2.** Current–voltage characteristics of a PV panel under different irradiation levels.
