**2. Optimization of the operation of photovoltaic (PV) panels**

#### **2.1 Electrical model of a PV panel cell**

**Figure 1** shows the equivalent electrical circuit of a cell (Junction P/N) of a PV panel, illuminated by radiation of intensity "Le" [25]. This circuit is formed by a diode (D), a current source (*I*CC), a contact series resistance (*R*s), and a parallel resistance (*R*sh), which represents the leakage current of the cell. From this diagram, the current of the PV cell (*I*) is expressed as a function of the voltage V according to the expression [25–29]:

$$I = I\_{\rm CC} - I\_s \left\{ \exp\left[\frac{q(\rm V + IR\_s)}{A \cdot K \cdot T}\right] - 1 \right\} - \left(\frac{V + IR\_s}{R\_{\rm sh}}\right) \tag{1}$$

where


**Figure 1.**

*The diagram of the electrical circuit of a cell of a PV panel.*

In this expression, the current ICC depends very little on the temperature and varies with the intensity of the illumination according to the equation [30, 31]:

$$\mathbf{Icc} = \mathbf{A.Le} + \mathbf{B} \tag{2}$$

where

A and B are two constant factors [30, 31].

As part of our application, we used PV panels that have cells, where A = 0.00932; B = 0.0055; very low contact resistance and very high parallel resistance. Under these conditions, the current I is written as a function of the voltage V according to the expression:

$$I = \text{A.Le} + \text{B} - I\_s \left\{ \exp\left[\frac{q(\text{V})}{A \cdot K \cdot T}\right] - 1 \right\} \tag{3}$$

#### **2.2 Electrical characteristics of PV panels**

As part of our experiment, we used PV panels (**Figure 2**), 300 Wp, formed by *Ns* ¼ 80 identical cells in series. The expression of the current of the *IPV* panels is written according to the intensity of the illumination (*Le*) and the voltage *VPV* according to the equations:

$$I\_{PV} = 0.00932 \ast L\_{\epsilon} + 0.0055 - I\_{\text{s}} \left\{ \exp \left[ \frac{q(V\_{PV})}{80.A \cdot K \cdot T} \right] - 1 \right\} \tag{4}$$

The typical experimental electrical characteristics (current–voltage and power voltage) of the PV panels (**Figure 2**), each with a power of 300 Wp, for illuminations ranging from 300 W/m<sup>2</sup> to 900 W/m<sup>2</sup> , are shown in **Figure 3**. From these characteristics, we have determined and represented in **Table 1** the optimal electrical values:

#### **Figure 2.**

*Photos of 600 Wp photovoltaic panels (Type 1) installed in the laboratory.*


**Table 1.**

*Optimal electrical values of a PV panel, from Figure 2, as a function of illuminations. Temperature = 25°C.*

#### **Figure 3.**

*Current–voltage-power characteristics of the photovoltaic panel used (Type 1), for three illuminations (300, 500, and 900 W/m<sup>2</sup> ). Ambient temperature = 25°C.*

voltage, current, maximum power point (MPP), and optimal resistance. Therefore, we can deduce, when the illuminance varies from 300 to 900 W/m2 , the optimal power and resistance vary from 72.9 to 218.7 W and from 8.85 to 95 Ω, respectively. In a PV application, to ensure the production of optimal electrical energy and reduce the cost of kWh, the operation of PV panels, over the sun, must follow these variations.

Moreover, in the design of PV system blocks, these optimal values allow for determining the size of each electrical component of the power, and the nature of the MPPT control that optimizes the operation of the PV panels, during the operation of the applications throughout the day.

#### **2.3 MPPT command: perturb and observe**

In this section, we describe the basic functioning of the MPPT command type perturb and observe that we used in all the applications developed in the laboratory. To do this, the PV panel adaptation block (**Figure 3**) generates a PWM signal of frequency f and duty cycle α, following the execution of an MPPT algorithm (**Figure 4**), which controls the DC/DC converters. The basic principle of the P&O method consists in disturbing the voltage of the PV panels (Vpv) and observing its impact on the variation of the output power of the PV panel, following the steps:

*Operation of Photovoltaic Panels in Stand-alone Applications DOI: http://dx.doi.org/10.5772/intechopen.110326*

**Figure 4.**

*PV panel adaptation system.*

