**5. Equivalent circuit of a solar cell**

To understand the electronic behavior of a solar cell, it is useful to create a model, which is electrically equivalent and is based on discrete electrical components whose behavior is well known. An ideal solar cell may be modeled by a current source in parallel with a diode;

The output power is given by:

**5.3. Fill factor**

(FF) of a solar cell:

**5.4. Efficiency**

*<sup>P</sup>* <sup>=</sup> *<sup>V</sup>*(*<sup>J</sup>*

**5.2. Solar cell characteristics in practice**

characteristic. The solar cell may also contain series (R<sup>s</sup>

*FF* <sup>=</sup> *Vm* . *<sup>J</sup>* \_\_\_\_\_*<sup>m</sup>*

put of the cell to the luminous power falling on it [8]:

*<sup>η</sup>* <sup>=</sup> *Vm* . *<sup>J</sup>* \_\_\_\_\_*<sup>m</sup>*

**Figure 4.** The superposition principle for solar cells.

*ph* − *J*

instances, depend on the voltage, as we have already noted (**Figure 4**) [6].

<sup>0</sup>[*exp*(

*<sup>V</sup>* <sup>+</sup> *<sup>J</sup> <sup>R</sup>* \_\_\_\_\_*<sup>s</sup>*

The J-V characteristic of a solar cell in practice usually differs to some extent from the ideal

leading to a characteristic of the form where the light-generated current Jph may, in some

As always in electrical engineering, optimal power output requires a suitable load resistor that corresponds to the ratio (Vm/Jm). Vm and Jm are, by definition, the voltage and current at the optimal operating point, and Mpp is the maximum achievable power output [7]. We now form the ratio of peak output (Vm. Jm) to the variable (Voc.Jsc) and call this ratio the fill factor

> *Voc* . *J sc*

<sup>=</sup>*FF* . *Voc* . *<sup>J</sup>* \_\_\_\_\_\_\_\_*sc Plight*

The efficiency of a solar cell is defined as the ratio of the photovoltaic-generated electric out-

The silicon solar cells have dominated the PV market for so many years. They have been produced to be used for both research and commercial purposes. They have dominated the

*Plight*

*<sup>n</sup> VT* ) <sup>−</sup> <sup>1</sup>] <sup>−</sup> (*<sup>V</sup>* <sup>+</sup> *<sup>J</sup> Rs*) \_\_\_\_\_\_

*Rsh* )

Introductory Chapter: Introduction to Photovoltaic Effect

http://dx.doi.org/10.5772/intechopen.74389

) and parallel (or shunt, *Rp*

) resistances,

5

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

in practice, no solar cell is ideal, so a shunt resistance and a series resistance component are added to the model (**Figure 3**) [4, 5].

#### **5.1. Characteristic equation**

From the equivalent circuit, it is evident that the current produced by the solar cell is equal to that produced by the current source, minus that which flows through the diode, minus that which flows through the shunt resistor:

$$J = J\_{ph} - J\_s - J\_{sh}$$

where J is the output current, Jph is the photo-generated current, J<sup>s</sup> is the diode current, and Jsh is the shunt current.

The current through these elements is governed by the voltage across them:

$$V\_{\rangle} = V + J\mathcal{R}\_{\text{s}}$$

where Vj is the voltage across both diode and resistor Rsh and V is the voltage across the output terminals.

By the Shockley diode equation, the current diverted through the diode is:

$$J\_s = J\_0 \left[ \exp\left(\frac{V + J\,R\_\*}{n\,V\_T}\right) - 1 \right]^2$$

where J0 is the diode reverse saturation current (A), R<sup>S</sup> is the series resistance (Ω), Rsh is the shunt resistance (Ω) and n is the diode ideality factor. Here, the shunt current is:

$$J\_{sh} = \frac{\langle V+JR\_\circ \rangle}{R\_{sh}}$$

Combining this and above equations results in the complete governing equation for the single-diode model:

$$J = J\_{ph} - J\_0 \left[ \exp\left(\frac{V + J\,R\_\*}{n\,V\_T}\right) - 1\right] - \frac{\left(V + J\,R\_\*\right)}{R\_{sh}}$$

The output power is given by:

$$P = \left| V \left( J\_{ph} - J\_0 \left[ \exp\left( \frac{V + J \, R\_s}{n \, \, V\_T} \right) - 1 \right] - \frac{\left( V + J \, R\_s \right)}{R\_{sh}} \right) \right|$$

#### **5.2. Solar cell characteristics in practice**

The J-V characteristic of a solar cell in practice usually differs to some extent from the ideal characteristic. The solar cell may also contain series (R<sup>s</sup> ) and parallel (or shunt, *Rp* ) resistances, leading to a characteristic of the form where the light-generated current Jph may, in some instances, depend on the voltage, as we have already noted (**Figure 4**) [6].

#### **5.3. Fill factor**

in practice, no solar cell is ideal, so a shunt resistance and a series resistance component are

From the equivalent circuit, it is evident that the current produced by the solar cell is equal to that produced by the current source, minus that which flows through the diode, minus that

> *ph* − *J <sup>s</sup>* − *J sh*

*V*<sup>j</sup> *= V + JRS*

is the voltage across both diode and resistor Rsh and V is the voltage across the out-

*<sup>V</sup>* <sup>+</sup> *<sup>J</sup> <sup>R</sup>* \_\_\_\_\_*<sup>s</sup> <sup>n</sup> VT* ) <sup>−</sup> <sup>1</sup>]

*sh* <sup>=</sup> (*<sup>V</sup>* <sup>+</sup> *<sup>J</sup> Rs*) \_\_\_\_\_\_ *Rsh*

Combining this and above equations results in the complete governing equation for the sin-

*<sup>V</sup>* <sup>+</sup> *<sup>J</sup> <sup>R</sup>* \_\_\_\_\_*<sup>s</sup>*

*<sup>n</sup> VT* ) <sup>−</sup> <sup>1</sup>] <sup>−</sup> (*<sup>V</sup>* <sup>+</sup> *<sup>J</sup> Rs*) \_\_\_\_\_\_

*Rsh*

is the diode current, and Jsh

is the series resistance (Ω), Rsh is the

added to the model (**Figure 3**) [4, 5].

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

which flows through the shunt resistor:

*J*

*J*

*J* = *J*

*J* = *J*

where J is the output current, Jph is the photo-generated current, J<sup>s</sup>

The current through these elements is governed by the voltage across them:

By the Shockley diode equation, the current diverted through the diode is:

*<sup>s</sup>* = *J*

shunt resistance (Ω) and n is the diode ideality factor. Here, the shunt current is:

is the diode reverse saturation current (A), R<sup>S</sup>

*ph* − *J*

<sup>0</sup>[*exp*(

<sup>0</sup>[*exp*(

**5.1. Characteristic equation**

4 Solar Panels and Photovoltaic Materials

is the shunt current.

where Vj

where J0

gle-diode model:

put terminals.

As always in electrical engineering, optimal power output requires a suitable load resistor that corresponds to the ratio (Vm/Jm). Vm and Jm are, by definition, the voltage and current at the optimal operating point, and Mpp is the maximum achievable power output [7]. We now form the ratio of peak output (Vm. Jm) to the variable (Voc.Jsc) and call this ratio the fill factor (FF) of a solar cell:

$$FF = \frac{V\_m \cdot J\_m}{V\_{oc} \cdot J\_{oc}}$$

#### **5.4. Efficiency**

The efficiency of a solar cell is defined as the ratio of the photovoltaic-generated electric output of the cell to the luminous power falling on it [8]:

$$\eta = \frac{V\_m \cdot J\_m}{P\_{light}} = \frac{FF \cdot V\_{\kappa} \cdot J\_{\kappa}}{P\_{light}}$$

The silicon solar cells have dominated the PV market for so many years. They have been produced to be used for both research and commercial purposes. They have dominated the

**Figure 4.** The superposition principle for solar cells.


[6] Zaidi B et al. Matlab/Simulink based simulation of monocrystalline silicon solar cells.

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7

[7] Honsberg C et al. Photovoltaics: Devices, Systems and Applications [CDROM]. Sydney

[10] Zaidi B et al. Hydrogenation effect on electrical behavior of polysilicon thin films. Silicon.

[11] Zaidi B et al. Effet des Traitements Thermiques sur le Comportement Électrique des Couches de Silicium Polycristallin pour des Applications Photovoltaïques. Revue de Métallurgie.

[12] Zaidi B et al. Influence of doping and heat treatments on carriers mobility in polycrystalline silicon thin films for photovoltaic application. Turkish Journal of Physics. 2011;

[13] Zaidi B et al. Optimum parameters for obtaining polycrystalline silicon for photovoltaic

[14] Zaidi B et al. Electrical energy generated by amorphous silicon solar panels. Silicon.

International Journal of Materials Science and Applications. 2016;**5**:11-15

[9] Beaucarne G. Silicon thin-film solar cells. Advances in Optoelectronics. 2007

[8] Zaidi B. Cellules Solaires Éditions Universitaire Européennes. 2016

application. American Journal of Nanosciences. 2015;**1**:1-4

(Aus): University of New South Wales; 1998

2015;**7**:275-278

2011;**108**:443-446

DOI: 10.1007/s12633-017-9555-8

**35**:185-188

**Table 1.** Current operational data of compared technologies based on modules.

market because of the abundance of silicon, nontoxicity, module efficiency, and excellent cell stability. There are various levels of skills for production of the evaluated technologies (monocrystalline [9], polycrystalline [10–13], amorphous [14], and inorganic and organics cells). The current operating data of the evaluated cells in their module state are compared in **Table 1**. These data were measured under the global AM1.5 spectrum (1000 W/m<sup>2</sup> ) at 25°C.
