**1. Introduction**

Since the Industrial Revolution, fossil fuels have become widespread in the world. For energy stored in fossil fuels, this process requires combustion and therefore cannot prevent emissions and particles in the atmosphere. In addition, the transport and extraction of fossil fuels cause pollution with serious consequences such as air pollution, water deterioration, soil degradation and global warming. Currently, fossil fuels dominate global energy consumption [1].

With global energy shortages and pollution problems, the protection of energy and the environment becomes the main problem for People. The development and application of clean sources of renewable energy such as solar, wind, fuel, tidal and geothermal, etc., are increasingly important. Among them, solar energy will dominate due to its availability and reliability. How As predicted by [2], by the end of this century the sun will provide up to 64% of the total energy, as shown in **Figure 1**.

**Figure 1.**

*Global energy used by a source in the 21st century [2].*

#### **1.1 Overview of photovoltaic cells**

The generation of photovoltaic energy (PV) has become one of the most important ways to use solar energy. And the regenerative energy system based on decentralized generation (DG) is generally connected to the network through inverters or electronic power inverters. Therefore, the development of a photovoltaic inverter system is important to reduce energy and environmental problems.

The first discovery of the effect of photovoltaic energy was made in 1839 by Edmund Becquerel, who demonstrated the production of a device that generates electricity when exposed to sunlight. More than a century later, in 1954, D. Chapin, C.S. Fuller and G. Pearson [2] manufactured the first silicon solar cell at Bell's Laboratories.

#### *1.1.1 Type of photovoltaic panels*

Although there are different types of panels, the most common types of solar panels can be classified into the following categories [3]:

#### *1.1.1.1 Polycrystalline silicon panels*

This type shows that the solar cells in monocrystalline panels are slices cut from pure crystal silicon bars. Where the paintings work best in bright weather with sunlight directly on them. Absorption of sunlight radiation is very high, due to the presence of uniform black color. This type of solar panel is very effective. It is made from the silicon mass obtained from the fusion of pure silicon parts. Efficiency ranges between 15 and 18% and its disadvantages are difficult to manufacture and high cost.

#### *1.1.1.2 Monocrystalline silicon panels*

Also known as polycrystalline plates, these multi-crystalline panels consist of silicon screws, encapsulated to form blocks and create a cell made of pure crystal. This type is not as efficient as this type of monocrystalline silicon (single crystal) tapes. Efficiency of between 12 and 15%. It is difficult to manufacture and costs high but without monocrystalline.

#### *1.1.1.3 Amorphous silicon panels*

The Amorphous Silicon Panel is also known as a thin film board. This plate is made of thin layers of silicon on a layer of glass or metal. They are manufactured by attaching thin layers of silicon to a layer of glass or metal. They also have less than 10% efficiency. Its advantage is easy to manufacture and at a low cost. This is the technique used in this work.

#### *1.1.2 Development of a PV cell*

The solar cell is essentially a semiconductor of two materials known as Type P and Type N semiconductor material. Most frequently Highly purified silicon is a semiconductor material. Through the targeted addition of impurities such as boron and phosphorus, the various types of P and N are produced [4]. Photovoltaic (PV) cells are converted into electrical currents by incident radiation in the solar spectrum. Photovoltaic cells are most commonly made of silicone and are available in two variants, crystalline, and thin film type, as detailed in **Table 1** [5].

In real applications, the light absorbed by a solar cell will be a combination of direct solar radiation and diffused light reflected from the surrounding surfaces. Solar cells are usually coated with anti-reflection material to absorb as much radiation as possible [5–7]. The PV cells may be arranged in a series arrangement to form a panel, and the panels may be connected in parallel row configurations to form arrangements as in **Figure 2**. When cells or plates are connected in series, they must have the same amperage to produce an additive voltage output, and similarly, the plates must have the same nominal voltage when Connected in parallel to produce larger currents.

#### **1.2 Characteristics of photovoltaic cell**

The photovoltaic cell consists of a p-n junction in a semiconductor layer in a slice or slice. In general, the PV cell can be achieved by connecting the parallel DC source to the diode. In addition, the model contains its resistor in parallel and series. A parallel or parallel resistor (Rsh) indicates the relationship between a resistor and a resistor parallel to a working device. The resistor chain switches the current flow through semiconductor materials, metal sheets, communications and power buses. These Umayyad patterns can be combined with the Resistance Series (Rs) [8–10]. The equivalent circuit of the PV cell model is shown in **Figure 3**.

The characteristic equation *I*-*V* of a PV cell is given as [11]:

$$I = I\_{\rm ph} - I\_{\rm D} - (V + \rm IR\_{s})/R\_{\rm sh} \tag{1}$$

Where *I*: is the output current of the cell (A). *I*ph: is the current generated by the light or photocurrent (A).


**Table 1.**

*Crystalline (wafer-based) and photovoltaic thin-film cell.*

**Figure 2.** *Solar array implementation.*

**Figure 3.** *The equivalent circuit of a PV cell.*

ID: is the current of the diode (A).

*V*: is the output voltage of the cell (V).

*R*sh: is the leakage resistance (Ω).

*R*s: is the series resistance (Ω).

The diode current ID is given by the Shockley diode equation [11]:

$$I\_{\rm D} = I\_{\rm o} \left( \mathbf{e}^{\left( (q \,\rm Vol)/K \rm T A \right)} - \mathbf{1} \right) \tag{2}$$

Where *I*o: is the reverse saturation current of the diode (A).

*q*: is the charge of the electron (*q* = 1.6 � 10(�19) Coulomb).

VD: is the voltage of the diode (V).

*K*: is the Boltzmann constant (*K* = 1.38 � 10(�23) J/K).

*T*: is the temperature of the cell (K).

*A*: It's the ideality of the constant-current diode, it depends on the PV technology and it takes the value between one and two.

Replacing *I*<sup>D</sup> of the Eq. (1) by the Eq. (2) gives the *I*-*V* relation of the PV cell:

$$I\_{\rm D} = I\_{\rm ph} - I\_{\rm o} \left( e^{\left(\frac{(\rm qVd)}{RT\lambda}\right)} - 1 \right) - \frac{V + IR\_{\rm s}}{R\_{\rm sh}} \tag{3}$$

The photocurrent (*I*ph) depends mainly on the solar radiation and the working temperature of the cell, which is given as [11, 12]:

$$I\_{\rm ph} = \frac{\mathcal{S}}{\mathcal{S}\_{\rm R}} (I\_{\rm SC} + K\_I (T - T\_{\rm r}) \tag{4}$$

Where ISC: is the cell's short-circuit current at 25°C and 1 kW/m<sup>2</sup> .

*K*I: is the short-circuit current/temperature coefficient.

*Tr*: is the cell reference temperature (K).

*S*: is the solar insolation in W/m2 .

*S*r: is the solar reference insolation which is normally (1000 W/m2 ).

The inverse saturation current of the diode (*I*o) depends on the ambient temperature. The inverse saturation current of the diode at the set point temperature (*I*o,n) can be determined as follows by setting the no-load condition (without output current) as follows:

Using the Eqs. (4) & (3), let *I* = 0 and *T* = 25°C and solve for *I*<sup>o</sup> = *I*o,n, *I*ph = *I*sc and *R*sh = ∞

$$\mathbf{0} = I\_{\rm sc} - I\_{\rm o,n} \left( \mathbf{e}^{\frac{\mathbf{q} \mathbf{V}\_d}{\mathbf{e} \times \mathbf{A}}} - \mathbf{1} \right)$$

$$I\_{\rm sc} = I\_{\rm o,n} \left( \mathbf{e}^{\frac{\mathbf{q} \mathbf{V}\_d}{\mathbf{e} \times \mathbf{A}}} - \mathbf{1} \right)$$

$$\therefore \; I\_{\rm o,n} = \frac{I\_{\rm sc}}{\left( \mathbf{e}^{\frac{\mathbf{q} \mathbf{V}\_d}{\mathbf{e} \times \mathbf{A}}} - \mathbf{1} \right)} \tag{5}$$

Where *I*o,n is the nominal diode saturation current at the nominal condition (25°C and 1 kW/m<sup>2</sup> ).

The reverse saturation current of the diode (*I*o) at any temperature (*T*) can be calculated as [11, 12]:

$$I\_{\rm o} = I\_{\rm o,n} \left(\frac{T}{T\_{\rm r}}\right)^{\rm 3} \exp\left[\frac{qE\_{\rm g}}{\rm KA} \left(\frac{1}{T\_{\rm r}} - \frac{1}{T}\right)\right] \tag{6}$$

Where *E*<sup>g</sup> is the band-gap energy of the semiconductor used in the cell and equal (1.12 electron-volt) for the silicon.

#### **1.3 PV panel model**

Since the energy generated by a PV cell is very low (**Figure 4**). Therefore, to generate enough energy, the cells should be assembled in a parallel-serial configuration of a module. As mentioned above, the photovoltaic panel is a set of photovoltaic modules that are connected in parallel and in series to produce a required current and voltage and therefore current. The equivalent circuit for a PV array formed in the row N\_S and in the parallel cells N\_P is shown in **Figure 4** [11].

#### **Figure 4.**

*Equivalent circuit model of the generalized PV panel.*

#### **Figure 5.**

*Characteristics of a photovoltaic panel for different values of solar irradiance (*S*) at constant temperature (25°C) [13] (a)* I*-*V *characteristics (b)* P*-*V *characteristics.*

The terminal equation for the current and voltage of the panel becomes as follows [13]:

$$I = N\_\text{P} I\_{\text{ph}} - N\_\text{P} I\_\text{O} \left( \exp \left[ \frac{q}{\text{KTA}} \left( \frac{V}{N\_\text{S}} + \frac{\text{IR}\_\text{s}}{N\_\text{P}} \right) - 1 \right] - \frac{\frac{\text{Np}}{N\_\text{s}} V + \text{IR}\_\text{s}}{R\_\text{sh}} \right) \tag{7}$$

Where NP: is the number of cells connected in parallel.

NS: is the number of cells connected in series.

Therefore, the *I*-*V* characteristics, as illustrated in Eq. (7), are nonlinear and varied by varying the radiation intensity and temperature. **Figures 5** and **6** illustrates these characteristics of PV panel under different conditions of radiation intensity and temperature [13].

#### **Figure 6.**

*Characteristics of a photovoltaic panel for different values of temperature (C) at a constant solar irradiance (1000 W/m<sup>2</sup> ) [13] (a)* I*-*V *characteristics (b)* P*-*V *characteristics.*
