**4. Electrical modeling of PV panel under dust**

In the literature, there are several models describing the electrical behavior of a PV cell. The one-diode and two-diode models are widely used to obtain the I–V characteristic of the PV cell or panel output [17]. However, as shown in **Figure 4**, the onediode model is the simplest one, moreover it is improved by incorporating a series resistor Rs [18, 19] and an additional shunt resistor Rsh [20].

The electrical current of the PV panel for the one diode model is given by:

$$I\_{pv} = I\_{ph} - I\_0 \left[ \exp\left(\frac{V\_{pv} + R\_s I\_{pv}}{n\_1 V\_{th}}\right) - 1\right] - \frac{V\_{pv} + R\_s I\_{pv}}{R\_{sh}} \tag{1}$$

Where *Iph* is the photo-generated current dependent on *G* solar radiation, and temperature according to the relationship:

$$I\_{ph} = \left(I\_{ph,ref} + \alpha\_0 \Delta T\right) \frac{G\_l}{G\_{ref}} \tag{2}$$

**Figure 4.** *One diode equivalent circuit of a PV cell.*

With:

*a*<sup>0</sup> temperature correction coefficient for current (°C�<sup>1</sup> ). Δ*T* = (*T* � *Ta*). *G* solar irradiance on module plane (W/m<sup>2</sup> ). *Gref* = 1000 W/m2 . *Iph,ref* photo-generated current (A). *Ipv* solar cell terminal current (A). *I*<sup>0</sup> reverse saturation current (A). *RS* series resistance (W). *Rsh* shunt resistance (W). STC standard test conditions (*Gref* = 1000 W/m2 ,*T* = 25°C and *AM* = 1.5). *T* cell or module operating temperature (°C). *T*<sup>a</sup> ambient temperature (°C). *Vpv* solar cell output voltage (V). *Vth* <sup>¼</sup> *kT <sup>q</sup>* thermal voltage (V).

**Figure 5** shows the block diagram of the experimental I–V curve plotter for PV modules using the IRF740 MOSFET transistor as electronic method. When the control voltage VGS is applied to its grid, it generates an output current Ipv variable quickly from 0 to Isc as well as a variable output voltage Vpv from Voc to 0 [21].

The Arduino board generates a continuous signal by the pin Vcc = 5 V, then amplified with a DC/DC converter type Boost XL6009E1, then this signal is injected into an RC filter (R = 440 Ω, C = 4700 mF). This also requires the resistance RDS to evolve gradually [14]. The three MOSFET operating regimes that describe the relationship between ID as a function of VGS and VDS are [16]:

Blocking regime ID = 0 A, if:

$$V\_{\rm GS} < V\_{th} \tag{3}$$

Ohmic regime, *ID* <sup>¼</sup> *<sup>K</sup>* <sup>2</sup>ð Þ *VGS* � *Vth VDS* � *<sup>V</sup>*<sup>2</sup> *DS* , if

$$V\_{\rm GS} - Vth > 0 \& \ V\_{\rm GS} - Vth > V\_{\rm DS} \tag{4}$$

**Figure 5.**

*Synoptic diagram of electronic charging technology.*

*Utilization of MOSFET Transistor to Characterize PV Panels under Dust: Study Area… DOI: http://dx.doi.org/10.5772/intechopen.109731*

Saturation regime, *ID* <sup>¼</sup> *K V*ð Þ *GS* � *Vth* <sup>2</sup> , if *VGS*–*Vth* >0&*VGS*–*Vth*<*VDS* (5)

Where K is the constant of the device and Vth the control threshold voltage of the transistor. By changing the value of VGS within an appropriate range, the measurement points can vary between 0 and VOC.

with:

$$I\_D = I\_{pv} \tag{6}$$

Arduino UNO is an open-source module based on a microcontroller, used to generate the PWM (Pulse Width Modulation) control signal. (PWM) is a technique used to control an analog circuit via a digital output, using the AnalogWrite function. This PWM signal is an electrical signal of maximum amplitude 5 V and constant frequency but with a variable duty cycle (**Figure 6**) [23].

The signal at the output of the DC/DC converter type Boost is injected into an RC filter, resistance R ≈ 110 W [24] and capacity of C ≈ 4700 mF [24], installed in series to vary the VGS control voltage of the MOSFET, and finally trace the I-V & P-V characteristics of the solar PV panel.

According to **Figure 7**, the expression of the control voltage VGS(t) of the MOSFET is given by:

$$V\_{GS}(t) = V\_{PWM} \cdot \left(1 - e^{-\frac{t}{RC}}\right) \tag{7}$$

**Figure 6.** *Boost DC/DC converter XL6009E1 [22].*

**Figure 7.** *RC filter circuit.*
