# Experimental validation of a photovoltaic panel model

Y Boukili, R El Bachtiri, Houcine Chafouk, I Idrissi, M Khanfara

► To cite this version:

Y Boukili, R El Bachtiri, Houcine Chafouk, I Idrissi, M Khanfara. Experimental validation of a photovoltaic panel model. IOP Conference Series: Earth and Environmental Science, 2018, 161, pp.012013. 10.1088/1755-1315/161/1/012013 . hal-02302299

HAL Id: hal-02302299

https://normandie-univ.hal.science/hal-02302299

Submitted on 31 May 2024

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PAPER • OPEN ACCESS

# Experimental validation of a photovoltaic panel model

To cite this article: Y Boukili et al 2018 IOP Conf. Ser.: Earth Environ. Sci. 161 012013

View the article online for updates and enhancements.

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PAPER • OPEN ACCESS

# Experimental validation of a photovoltaic panel model

To cite this article: Y Boukili et al 2018 IOP Conf. Ser.: Earth Environ. Sci. 161 012013

View the article online for updates and enhancements.

You may also like

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Advancing solid state &
electrochemical science & technology

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DISCOVER
how sustainability
intersects with
electrochemistry & solid
state science research

<figure><img src="image_4.png" /></figure>
# Experimental validation of a photovoltaic panel model

Y Boukili<fnref n="1" />, R El Bachtiri<fnref n="1" />, H Chafouk<fnref n="2" />, I Idrissi<fnref n="1" />,<fnref n="2" /> and M Khanfara<fnref n="1" />

Email: yassine.boukili@usmba.ac.ma; rachid.elbachtiri@usmba.ac.ma

**Abstract.** For operation optimizing, it's important to have internal parameters of a photovoltaic (PV) panel. Experimental measurements were carried out, in order to determine a PV panel internal parameters. From simple measurements, two resistances values: series R<sub>s</sub> and shunt R<sub>sh</sub> have been determined. The two experimental characteristics I-V and P-V have been plotted. And afterward, the system operation has been simulated in Matlab Simulink, to validate the model. Otherwise, PV current equation resulting from the PV cell model has been used to determine 5 parameters. A Matlab program has been developed with the function "fsolve" for solving the system of five equations with five unknowns. Theoretical values were compared with experimental results.

## 1. Introduction

Electricity needs in the world are constantly increasing at the rate of industrialization and the improvement of people's level of living. In face of this, the climate issue implies an increasingly clean electricity production.

However, the solution can no longer go only through the centralized production of electricity. It must also concern the decentralized production of renewable energy. Photovoltaic has a great potential, among the sources of renewable energy. In fact, the demand for solar energy has increased by 20% to 25% over the past 20 years [1].

In order to improve the use of photovoltaic systems, there are research activities to reduce their costs and improve their efficiency and reliability.

A PV panel in our laboratory will be used to determine by measurements the internal parameters. After that, theoretical characteristics will be validated.

Starting with experimental measurements to determine two resistances values: R<sub>s</sub> and R<sub>sh</sub> of the equivalent electrical circuit. Then, two theoretical characteristics P-V and I-V will be plotted in Matlab Simulink environment using values found in the experimentation. Afterward, the experimental characteristics P-V and I-V will be plotted to validate simulation results.

To be sure of experimental results, a program on Matlab with "fsolve" function will be created, to solve PV current equation for determining the PV panel parameters [11]. The equation has been obtained from the equivalent electrical circuit of a PV cell model, it's a nonlinear equation. A system will be created by repeating this equation five times according to voltage and current measurements. With the "fsolve" function, we will determine five parameters (R<sub>s</sub>, R<sub>sh</sub>, A, T, and I<sub>sat</sub>) from the system. Finally, a comparison between theoretical and experimental results will be presented.

<figure><img src="image_4.png" /></figure>

<footnote n="1">¹CED STI, FST, PERE Laboratory EST-USMBA, Fez, Morocco</footnote>

<footnote n="2">²IRSEEM, ESIGELEC, Normandie University / UNIRouen, Rouen, France</footnote>
# Experimental validation of a photovoltaic panel model

Y Boukili<fnref n="1" />, R El Bachtiri<fnref n="1" />, H Chafouk<fnref n="2" />, I Idrissi<fnref n="1" />,<fnref n="2" /> and M Khanfara<fnref n="1" />

Email: yassine.boukili@usmba.ac.ma; rachid.elbachtiri@usmba.ac.ma

**Abstract.** For operation optimizing, it's important to have internal parameters of a photovoltaic (PV) panel. Experimental measurements were carried out, in order to determine a PV panel internal parameters. From simple measurements, two resistances values: series R<sub>s</sub> and shunt R<sub>sh</sub> have been determined. The two experimental characteristics I-V and P-V have been plotted. And afterward, the system operation has been simulated in Matlab Simulink, to validate the model. Otherwise, PV current equation resulting from the PV cell model has been used to determine 5 parameters. A Matlab program has been developed with the function "fsolve" for solving the system of five equations with five unknowns. Theoretical values were compared with experimental results.

## 1. Introduction

Electricity needs in the world are constantly increasing at the rate of industrialization and the improvement of people's level of living. In face of this, the climate issue implies an increasingly clean electricity production.

However, the solution can no longer go only through the centralized production of electricity. It must also concern the decentralized production of renewable energy. Photovoltaic has a great potential, among the sources of renewable energy. In fact, the demand for solar energy has increased by 20% to 25% over the past 20 years [1].

In order to improve the use of photovoltaic systems, there are research activities to reduce their costs and improve their efficiency and reliability.

A PV panel in our laboratory will be used to determine by measurements the internal parameters. After that, theoretical characteristics will be validated.

Starting with experimental measurements to determine two resistances values: R<sub>s</sub> and R<sub>sh</sub> of the equivalent electrical circuit. Then, two theoretical characteristics P-V and I-V will be plotted in Matlab Simulink environment using values found in the experimentation. Afterward, the experimental characteristics P-V and I-V will be plotted to validate simulation results.

To be sure of experimental results, a program on Matlab with "fsolve" function will be created, to solve PV current equation for determining the PV panel parameters [11]. The equation has been obtained from the equivalent electrical circuit of a PV cell model, it's a nonlinear equation. A system will be created by repeating this equation five times according to voltage and current measurements. With the "fsolve" function, we will determine five parameters (R<sub>s</sub>, R<sub>sh</sub>, A, T, and I<sub>sat</sub>) from the system. Finally, a comparison between theoretical and experimental results will be presented.

<figure><img src="image_5.png" /></figure>

<footnote n="1">¹CED STI, FST, PERE Laboratory EST-USMBA, Fez, Morocco</footnote>

<footnote n="2">²IRSEEM, ESIGELEC, Normandie University / UNIRouen, Rouen, France</footnote>
## 2. Modeling

PV cells convert sunlight directly into electricity. When the photons of the sun reach the cell, it releases electrons from the negative layer. This electron moves to the positive layer, which gives an electrical current.

Theoretically, the voltage generated by a PV cell is between 0.5 and 0.8 volts, depending on the semiconductor technology. This voltage is very low; this is why several PV cells are made in series or in parallel. The voltage is increased if cells are connected in series and current if they are connected in parallel.

The parameters of a monocrystalline PV panel have been used [2], with 36 cells connected in series and Table 1 shows the characteristics of this panel. The model used in the simulation is PM0115.

<table><caption>**Table1:** Photovoltaic panel feature</caption><thead><tr><td>Characteristic</td><td>Value</td></tr></thead><tbody><tr><td>Maximum power</td><td>115 Watt</td></tr><tr><td>Voltage at maximum power</td><td>17,7 V</td></tr><tr><td>Current at maximum power</td><td>6,5 A</td></tr><tr><td>Open Circuit Voltage</td><td>21,6 V</td></tr><tr><td>Short circuit current</td><td>6,96 A</td></tr><tr><td>Tolerance</td><td>±5%</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 1.** Equivalent electrical circuit of a PV cell</figcaption></figure>

It is possible to represent a cell PV with an electrical equivalent circuit in Figure 1. It consists of a shunt resistance, a series resistance, a diode and a current source [3], [4] and [5].

To implement this PV cell model in simulation software, the following values should be known:
Series Resistance $R_s$, shunt resistance $R_{sh}$, saturation current $I_0$, ideality factor of junction A and temperature T. The manufacturer's values have been taken for $I_0$ and A. Then experimental measurements were done to determine $R_s$ and $R_{sh}$.

## 3. Experimental measurements

The series resistance of the PV cell is very low [6], and its value can influence the variation on the output of PV cells [7], it causes the deviation of the maximum power point.

The shunt resistance of any PV cell should be large enough for higher output power. In fact, if the shunt resistance is low, it will be a higher power loss.

Experimental measurements have been made to determine the two resistances $R_s$ and $R_{sh}$, the measurements were carried out so rapidly to consider temperature as constant.

To determine the series resistance $R_s$, the Figure 2 scheme has been used, which consists of a DC generator, a variable resistance, an ammeter and a voltmeter. The PV panel was fully covered with paper to have: $I_{ph} = 0$.
## 2. Modeling

PV cells convert sunlight directly into electricity. When the photons of the sun reach the cell, it releases electrons from the negative layer. This electron moves to the positive layer, which gives an electrical current.

Theoretically, the voltage generated by a PV cell is between 0.5 and 0.8 volts, depending on the semiconductor technology. This voltage is very low; this is why several PV cells are made in series or in parallel. The voltage is increased if cells are connected in series and current if they are connected in parallel.

The parameters of a monocrystalline PV panel have been used [2], with 36 cells connected in series and Table 1 shows the characteristics of this panel. The model used in the simulation is PM0115.

<table><caption>**Table1:** Photovoltaic panel feature</caption><thead><tr><td>Characteristic</td><td>Value</td></tr></thead><tbody><tr><td>Maximum power</td><td>115 Watt</td></tr><tr><td>Voltage at maximum power</td><td>17,7 V</td></tr><tr><td>Current at maximum power</td><td>6,5 A</td></tr><tr><td>Open Circuit Voltage</td><td>21,6 V</td></tr><tr><td>Short circuit current</td><td>6,96 A</td></tr><tr><td>Tolerance</td><td>±5%</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Figure 1.** Equivalent electrical circuit of a PV cell</figcaption></figure>

It is possible to represent a cell PV with an electrical equivalent circuit in Figure 1. It consists of a shunt resistance, a series resistance, a diode and a current source [3], [4] and [5].

To implement this PV cell model in simulation software, the following values should be known:
Series Resistance $R_s$, shunt resistance $R_{sh}$, saturation current $I_0$, ideality factor of junction A and temperature T. The manufacturer's values have been taken for $I_0$ and A. Then experimental measurements were done to determine $R_s$ and $R_{sh}$.

## 3. Experimental measurements

The series resistance of the PV cell is very low [6], and its value can influence the variation on the output of PV cells [7], it causes the deviation of the maximum power point.

The shunt resistance of any PV cell should be large enough for higher output power. In fact, if the shunt resistance is low, it will be a higher power loss.

Experimental measurements have been made to determine the two resistances $R_s$ and $R_{sh}$, the measurements were carried out so rapidly to consider temperature as constant.

To determine the series resistance $R_s$, the Figure 2 scheme has been used, which consists of a DC generator, a variable resistance, an ammeter and a voltmeter. The PV panel was fully covered with paper to have: $I_{ph} = 0$.
## 3.1 Measurement of R<sub>s</sub>

<figure><img src="image_6.png" /><figcaption>**Figure 2.** Experimental scheme for determining R<sub>s</sub></figcaption></figure>

By decreasing the variable resistance, the values have been taken of voltage and current and the values are presented in Table 2.

<table><caption>**Table 2:** Experimental measurements</caption><tr><td>V (V)</td><td>13.6</td><td>15.3</td><td>16.1</td><td>17</td><td>18</td><td>19</td><td>19.2</td><td>20</td><td>20.95</td><td>21.4</td><td>22</td><td>22.6</td></tr><tr><td>I (A)</td><td>-0.01</td><td>-0.02</td><td>-0.03</td><td>-0.05</td><td>-0.1</td><td>-0.2</td><td>-0.3</td><td>-0.5</td><td>-1</td><td>-1.5</td><td>-2</td><td>-3</td></tr></table>

According to the electrical wiring in Figure 2:

$$R_s = \frac{V - V_s}{I} \qquad (1)$$

To determine V<sub>s</sub>, the curve I-V characteristic has been plotted using TABLE 2 values and it is presented in Figure 3. This curve is likewise the diode characteristic. The extrapolation of the linear part of the curve gives the V<sub>s</sub> value.

<figure><img src="image_7.png" /><figcaption>**Figure 3.** Curve I-V</figcaption></figure>

For 36 cells, Vs = 20.8V.

R<sub>s_36</sub> for 36 cells is calculated by:

$$R_{s\_36} = \frac{\Delta V}{\Delta I} = \frac{23,15-22,6}{4-3} = 0,55\Omega \qquad (2)$$

And to calculate R<sub>s</sub> for one cell, it is enough to divide by 36:

$$R_s = 0,015\Omega$$

## 3.2 Measurement of R<sub>sh</sub>

The same previous electrical scheme will be used but the terminals of the DC generator were inverted, then this wiring presented in Figure 4 will be used. The diode is blocked in this case.
## 3.1 Measurement of R<sub>s</sub>

<figure><img src="image_7.png" /><figcaption>**Figure 2.** Experimental scheme for determining R<sub>s</sub></figcaption></figure>

By decreasing the variable resistance, the values have been taken of voltage and current and the values are presented in Table 2.

<table><caption>**Table 2:** Experimental measurements</caption><tr><td>V (V)</td><td>13.6</td><td>15.3</td><td>16.1</td><td>17</td><td>18</td><td>19</td><td>19.2</td><td>20</td><td>20.95</td><td>21.4</td><td>22</td><td>22.6</td></tr><tr><td>I (A)</td><td>-0.01</td><td>-0.02</td><td>-0.03</td><td>-0.05</td><td>-0.1</td><td>-0.2</td><td>-0.3</td><td>-0.5</td><td>-1</td><td>-1.5</td><td>-2</td><td>-3</td></tr></table>

According to the electrical wiring in Figure 2:

$$R_s = \frac{V - V_s}{I} \qquad (1)$$

To determine V<sub>s</sub>, the curve I-V characteristic has been plotted using TABLE 2 values and it is presented in Figure 3. This curve is likewise the diode characteristic. The extrapolation of the linear part of the curve gives the V<sub>s</sub> value.

<figure><img src="image_8.png" /><figcaption>**Figure 3.** Curve I-V</figcaption></figure>

For 36 cells, Vs = 20.8V.

R<sub>s_36</sub> for 36 cells is calculated by:

$$R_{s\_36} = \frac{\Delta V}{\Delta I} = \frac{23,15-22,6}{4-3} = 0,55\Omega \qquad (2)$$

And to calculate R<sub>s</sub> for one cell, it is enough to divide by 36:

$$R_s = 0,015\Omega$$

## 3.2 Measurement of R<sub>sh</sub>

The same previous electrical scheme will be used but the terminals of the DC generator were inverted, then this wiring presented in Figure 4 will be used. The diode is blocked in this case.
<figure><img src="image_8.png" /><figcaption>Figure 4. Experimental scheme to determine R<sub>sh</sub></figcaption></figure>

According to the Law of Mail:

$$R_{sh\_36} + R_{s\_36} = \frac{V}{I} \qquad (3)$$

Then an electrical measurement is taken: V = 50 V and I = 250 µA. So:

$$R_{sh\_36} + R_{s\_36} = 200 \text{ k}\Omega$$

For one cell:

$$R_{sh} \approx 5550 \Omega$$

## 4. Simulation

From the equivalent circuit of a PV panel represented in Figure 1, the following equations are deduced [8], [9] and [10]:

$$I = n_p I_{ph} - n_p I_{sat} \left( \exp\left(\left(\frac{q}{AKT}\right)\left(\frac{V}{n_s} + R_s I\right)\right) - 1 \right) \qquad (4)$$

$$I_{ph} = (I_{sso} + k_i(T - T_r)) \frac{S}{1000} \qquad (5)$$

$$I_{sat} = I_{rr} \left(\frac{T}{T_r}\right)^3 \exp\left(\left(\frac{qE_{gap}}{kA}\right) \left(\frac{1}{T_r} - \frac{1}{T}\right)\right) \qquad (6)$$

Where the Table 3 presents the values of measured parameters and Table 4 presents the values of the characters in the equation 4.

Then, these equations are used to do simulation on Simulink with the internal parameters found in the experimental measurements and the manufacturer's values.

<table><caption>Table 3: measured parameters</caption><thead><tr><td>Symbol</td><td>Description</td><td>Value</td></tr></thead><tbody><tr><td>T</td><td>Surface temperature of the panel</td><td>303° K</td></tr><tr><td>R<sub>s</sub></td><td>Series resistance of the PV cell</td><td>0,015 Ω</td></tr><tr><td>R<sub>sh</sub></td><td>Parallel resistance of the PV cell</td><td>5500 Ω</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>Figure 4. Experimental scheme to determine R<sub>sh</sub></figcaption></figure>

According to the Law of Mail:

$$R_{sh\_36} + R_{s\_36} = \frac{V}{I} \qquad (3)$$

Then an electrical measurement is taken: V = 50 V and I = 250 µA. So:

$$R_{sh\_36} + R_{s\_36} = 200 \text{ k}\Omega$$

For one cell:

$$R_{sh} \approx 5550 \Omega$$

## 4. Simulation

From the equivalent circuit of a PV panel represented in Figure 1, the following equations are deduced [8], [9] and [10]:

$$I = n_p I_{ph} - n_p I_{sat} \left( \exp\left(\left(\frac{q}{AKT}\right)\left(\frac{V}{n_s} + R_s I\right)\right) - 1 \right) \qquad (4)$$

$$I_{ph} = (I_{sso} + k_i(T - T_r)) \frac{S}{1000} \qquad (5)$$

$$I_{sat} = I_{rr} \left(\frac{T}{T_r}\right)^3 \exp\left(\left(\frac{qE_{gap}}{kA}\right) \left(\frac{1}{T_r} - \frac{1}{T}\right)\right) \qquad (6)$$

Where the Table 3 presents the values of measured parameters and Table 4 presents the values of the characters in the equation 4.

Then, these equations are used to do simulation on Simulink with the internal parameters found in the experimental measurements and the manufacturer's values.

<table><caption>Table 3: measured parameters</caption><thead><tr><td>Symbol</td><td>Description</td><td>Value</td></tr></thead><tbody><tr><td>T</td><td>Surface temperature of the panel</td><td>303° K</td></tr><tr><td>R<sub>s</sub></td><td>Series resistance of the PV cell</td><td>0,015 Ω</td></tr><tr><td>R<sub>sh</sub></td><td>Parallel resistance of the PV cell</td><td>5500 Ω</td></tr></tbody></table>
<table><caption>**Table 4:** parameters values</caption><thead><tr><th>Symbol</th><th>Description</th><th>Value</th></tr></thead><tbody><tr><td>q</td><td>Electron charge</td><td>1.602×10<sup>-19</sup> C</td></tr><tr><td>A</td><td>Ideality factor</td><td>1.74</td></tr><tr><td>k</td><td>Boltzman constant</td><td>1.38×10<sup>-23</sup> j/K</td></tr><tr><td>I<sub>sso</sub></td><td>Short-circuit current</td><td>6.96 A</td></tr><tr><td>k<sub>i</sub></td><td>SC current temperature coefficient</td><td>1.7×10<sup>-3</sup></td></tr><tr><td>T<sub>r</sub></td><td>Reference temperature</td><td>298.13 °K</td></tr><tr><td>I<sub>rr</sub></td><td>Reverse saturation current at T<sub>r</sub></td><td>2.0793×10<sup>-6</sup> A</td></tr><tr><td>E<sub>gap</sub></td><td>Energy of the band gap for Silicon</td><td>1.1 eV</td></tr><tr><td>n<sub>p</sub></td><td>Number of cells in parallel</td><td>0</td></tr><tr><td>n<sub>s</sub></td><td>Number of cells in series</td><td>36</td></tr><tr><td>S</td><td>Solar radiation level</td><td>0 ~ 1000 W/m<sup>2</sup></td></tr><tr><td>I<sub>ph</sub></td><td>Photocurrent</td><td></td></tr><tr><td>I<sub>sat</sub></td><td>Module reserve saturation current</td><td></td></tr><tr><td>S</td><td>Solar radiation level</td><td>1000 W/m<sup>2</sup></td></tr></tbody></table>

## 5. Programming

To validate in a second way the values found in the experimental part and to give the study more accuracy, a program under Matlab software have been created with "fsolve" function to determine the values of the internal panel: R<sub>s</sub>, R<sub>sh</sub>, T, A and I<sub>sat</sub>.

Matlab's "fsolve" subroutine is very effective in solving the nonlinear equations. Thus, the proposed method is user-friendly, with the use of initial values for to start the simulation.

Equation (4) has been used for a single cell, and also under the same conditions in the experimental measurements by covering the PV panel, so I<sub>ph</sub>= 0 and the equation becomes:

$$ - \mathbf{I}_{\text{sat}} \left( \exp\left(\frac{q(V + \mathbf{R}_s I)}{\mathbf{AKT}}\right) - 1 \right) - \frac{V + \mathbf{R}_s I}{\mathbf{R}_{\text{sh}}} - I = 0 \quad (7) $$

The values of experimental measurements of voltage and current have been used, and five measurements were taken to create a system (8) of five equations:

$$ \left\{ \begin{aligned} -I_{\text{sat}} & \left( \exp\left(\frac{q(V_1 + R_s I_1)}{\text{AKT}}\right) - 1 \right) - \frac{V_1 + R_s I_1}{R_{\text{sh}}} - I_1 = 0 \\ -I_{\text{sat}} & \left( \exp\left(\frac{q(V_2 + R_s I_2)}{\text{AKT}}\right) - 1 \right) - \frac{V_2 + R_s I_2}{R_{\text{sh}}} - I_2 = 0 \\ -I_{\text{sat}} & \left( \exp\left(\frac{q(V_3 + R_s I_3)}{\text{AKT}}\right) - 1 \right) - \frac{V_3 + R_s I_3}{R_{\text{sh}}} - I_3 = 0 \\ -I_{\text{sat}} & \left( \exp\left(\frac{q(V_4 + R_s I_4)}{\text{AKT}}\right) - 1 \right) - \frac{V_4 + R_s I_4}{R_{\text{sh}}} - I_4 = 0 \\ -I_{\text{sat}} & \left( \exp\left(\frac{q(V_5 + R_s I_5)}{\text{AKT}}\right) - 1 \right) - \frac{V_5 + R_s I_5}{R_{\text{sh}}} - I_5 = 0 \end{aligned} \right. \quad (8) $$

Table 5 presents the five measurements of voltage and current used in the program:
<table><caption>**Table 4:** parameters values</caption><thead><tr><th>Symbol</th><th>Description</th><th>Value</th></tr></thead><tbody><tr><td>q</td><td>Electron charge</td><td>1.602×10<sup>-19</sup> C</td></tr><tr><td>A</td><td>Ideality factor</td><td>1.74</td></tr><tr><td>k</td><td>Boltzman constant</td><td>1.38×10<sup>-23</sup> j/K</td></tr><tr><td>I<sub>sso</sub></td><td>Short-circuit current</td><td>6.96 A</td></tr><tr><td>k<sub>i</sub></td><td>SC current temperature coefficient</td><td>1.7×10<sup>-3</sup></td></tr><tr><td>T<sub>r</sub></td><td>Reference temperature</td><td>298.13 °K</td></tr><tr><td>I<sub>rr</sub></td><td>Reverse saturation current at T<sub>r</sub></td><td>2.0793×10<sup>-6</sup> A</td></tr><tr><td>E<sub>gap</sub></td><td>Energy of the band gap for Silicon</td><td>1.1 eV</td></tr><tr><td>n<sub>p</sub></td><td>Number of cells in parallel</td><td>0</td></tr><tr><td>n<sub>s</sub></td><td>Number of cells in series</td><td>36</td></tr><tr><td>S</td><td>Solar radiation level</td><td>0 ~ 1000 W/m<sup>2</sup></td></tr><tr><td>I<sub>ph</sub></td><td>Photocurrent</td><td></td></tr><tr><td>I<sub>sat</sub></td><td>Module reserve saturation current</td><td></td></tr><tr><td>S</td><td>Solar radiation level</td><td>1000 W/m<sup>2</sup></td></tr></tbody></table>

**5. Programming**

To validate in a second way the values found in the experimental part and to give the study more accuracy, a program under Matlab software have been created with “fsolve” function to determine the values of the internal panel: R<sub>s</sub>, R<sub>sh</sub>, T, A and I<sub>sat</sub>.

Matlab's "fsolve" subroutine is very effective in solving the nonlinear equations. Thus, the proposed method is user-friendly, with the use of initial values for to start the simulation.

Equation (4) has been used for a single cell, and also under the same conditions in the experimental measurements by covering the PV panel, so I<sub>ph</sub>= 0 and the equation becomes:

$$ - \mathbf{I}_{\text{sat}} \left( \exp\left(\frac{q(V + \mathbf{R}_s I)}{\mathbf{AKT}}\right) - 1 \right) - \frac{V + \mathbf{R}_s I}{\mathbf{R}_{\text{sh}}} - I = 0 \quad (7) $$

The values of experimental measurements of voltage and current have been used, and five measurements were taken to create a system (8) of five equations:

$$ \left\{ \begin{array}{l} - I_{\text{sat}} \left( \exp\left(\frac{q(V_1 + R_s I_1)}{\text{AKT}}\right) - 1 \right) - \frac{V_1 + R_s I_1}{R_{\text{sh}}} - I_1 = 0 \\ - I_{\text{sat}} \left( \exp\left(\frac{q(V_2 + R_s I_2)}{\text{AKT}}\right) - 1 \right) - \frac{V_2 + R_s I_2}{R_{\text{sh}}} - I_2 = 0 \\ - I_{\text{sat}} \left( \exp\left(\frac{q(V_3 + R_s I_3)}{\text{AKT}}\right) - 1 \right) - \frac{V_3 + R_s I_3}{R_{\text{sh}}} - I_3 = 0 \\ - I_{\text{sat}} \left( \exp\left(\frac{q(V_4 + R_s I_4)}{\text{AKT}}\right) - 1 \right) - \frac{V_4 + R_s I_4}{R_{\text{sh}}} - I_4 = 0 \\ - I_{\text{sat}} \left( \exp\left(\frac{q(V_5 + R_s I_5)}{\text{AKT}}\right) - 1 \right) - \frac{V_5 + R_s I_5}{R_{\text{sh}}} - I_5 = 0 \end{array} \right. \quad (8) $$

Table 5 presents the five measurements of voltage and current used in the program:
<table><caption>**Table 5:** measurements used in the programme</caption><thead><tr><th></th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr></thead><tbody><tr><th>V (V)</th><td>13.6</td><td>16.1</td><td>19</td><td>21.4</td><td>23.15</td></tr><tr><th>I (A)</th><td>- 0.01</td><td>- 0.03</td><td>- 0.2</td><td>- 1.5</td><td>- 4</td></tr></tbody></table>

**6. Results and discussions**

To determine the two experimental characteristics of the PV panel I-V and P-V, the Figure 5 scheme have been used, which consists of a variable resistance, an ammeter and a voltmeter. The PV panel was illuminated by a projector then the power produced is very low.

<figure><img src="image_9.png" /><figcaption>**Figure 5.** Experimental scheme to determine experimental I-V and P-V</figcaption></figure>

By decreasing the variable resistance we have plotted two experimental characteristics I-V and P-V presented in a. and b. successively in Figure 6.

<figure><img src="image_10.png" /><figcaption>**Figure 6.** Experimental characteristics a. I-V and b. P-V</figcaption></figure>

The simulation of the PV panel model on Simulink software was done and figure 7 presents two characteristics I-V and P-V of this PV panel. The results found are exactly what we have in the nameplate presented in table 1.
<table><caption>**Table 5:** measurements used in the programme</caption><thead><tr><th></th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr></thead><tbody><tr><th>V (V)</th><td>13.6</td><td>16.1</td><td>19</td><td>21.4</td><td>23.15</td></tr><tr><th>I (A)</th><td>- 0.01</td><td>- 0.03</td><td>- 0.2</td><td>- 1.5</td><td>- 4</td></tr></tbody></table>

## 6. Results and discussions

To determine the two experimental characteristics of the PV panel I-V and P-V, the Figure 5 scheme have been used, which consists of a variable resistance, an ammeter and a voltmeter. The PV panel was illuminated by a projector then the power produced is very low.

<figure><img src="image_10.png" /><figcaption>**Figure 5.** Experimental scheme to determine experimental I-V and P-V</figcaption></figure>

By decreasing the variable resistance we have plotted two experimental characteristics I-V and P-V presented in a. and b. successively in Figure 6.

<figure><img src="image_11.png" /><figcaption>**Figure 6.** Experimental characteristics a. I-V and b. P-V</figcaption></figure>

The simulation of the PV panel model on Simulink software was done and figure 7 presents two characteristics I-V and P-V of this PV panel. The results found are exactly what we have in the nameplate presented in table 1.
<figure><img src="image_11.png" /><figcaption>**Figure 7.** Characteristics of the PV panel</figcaption></figure>

The results of the programming are presented in table 6:

<table><caption>**Table 6: Program simulation results**</caption><thead><tr><th>Theoretic data</th><th>Measurements data</th></tr></thead><tbody><tr><td>R<sub>s</sub> = 0.016 Ω</td><td>R<sub>s</sub> = 0.015 Ω</td></tr><tr><td>A = 1.733</td><td>A= 1.74</td></tr><tr><td>T = 304.143°K = 29,008 °C</td><td>T = 27 °C</td></tr><tr><td>R<sub>sh</sub> = 5548.210 Ω</td><td>R<sub>sh</sub> ≈ 5550 Ω</td></tr><tr><td>I<sub>0</sub> = 2.44953e-06 A</td><td>I<sub>0</sub> = 4.842*10<sup>-6</sup> A</td></tr></tbody></table>

The results of the simulation and measurement are very close, which gives our study more accuracy.

## 7. Conclusion

In this paper, experimentally internal resistances of a PV panel have been determined: series and shunt resistances.

The PV panel was simulated using Simulink to determine theoretical I-V and P-V characteristics.

Also Experimental characteristics of the PV panel: I-V and P-V were plotted.

In order to determine all internal characteristics, a program on Matlab with “fsolve” function have been created to solve the nonlinear equation. With “fsolve” function, parameters (R<sub>s</sub>, R<sub>sh</sub>, A, T, and I<sub>sat</sub>) from a system of five equations have been determined. The system is obtained from experimental measurements, by using the values of the voltage and current.

Finally, theoretical results are very close to the experimental values.

## Acknowledgment

This research work is within the framework of the project “intelligent management of renewable energy sources” GISER, funded by the CNRST (for the MESRSFC, Morocco).

## References

[1] J. Selvaraj and A. R. Nasrudin, “Multilevel Inverter For Grid-Connected PV System Employing Digital PI Controller”, IEEE Transactions On Industrial Electronics, vol. 56, No. 1 2009, pp. 149-158.

[2] S. Nema, R.K. Nema and G. Agnihotri, “MATLAB/Simulink based study of photovoltaic cells / modules / array and their experimental verification”, International journal of Energy and Environment, vol.1, No.3, pp.487-500, 2010.

[3] H. L. Tsai, C. S. Tu and Y. J. Su, “Development of Generalized Photovoltaic Model Using MATLAB/SIMULINK”, Proceedings of the World Congress on Engineering and Computer Science WCECS, San Francisco, USA, 2008.
<figure><img src="image_12.png" /><figcaption>**Figure 7.** Characteristics of the PV panel</figcaption></figure>

The results of the programming are presented in table 6:

<table><caption>**Table 6:** Program simulation results</caption><thead><tr><th>Theoretic data</th><th>Measurements data</th></tr></thead><tbody><tr><td>R<sub>s</sub> = 0.016 Ω</td><td>R<sub>s</sub> = 0.015 Ω</td></tr><tr><td>A = 1.733</td><td>A= 1.74</td></tr><tr><td>T = 304.143°K = 29,008 °C</td><td>T = 27 °C</td></tr><tr><td>R<sub>sh</sub> = 5548.210 Ω</td><td>R<sub>sh</sub> ≈ 5550 Ω</td></tr><tr><td>I<sub>0</sub> = 2.44953e-06 A</td><td>I<sub>0</sub> = 4.842*10<sup>-6</sup> A</td></tr></tbody></table>

The results of the simulation and measurement are very close, which gives our study more accuracy.

## 7. Conclusion

In this paper, experimentally internal resistances of a PV panel have been determined: series and shunt resistances.

The PV panel was simulated using Simulink to determine theoretical I-V and P-V characteristics.

Also Experimental characteristics of the PV panel: I-V and P-V were plotted.

In order to determine all internal characteristics, a program on Matlab with “fsolve” function have been created to solve the nonlinear equation. With “fsolve” function, parameters (R<sub>s</sub>, R<sub>sh</sub>, A, T, and I<sub>sat</sub>) from a system of five equations have been determined. The system is obtained from experimental measurements, by using the values of the voltage and current.

Finally, theoretical results are very close to the experimental values.

## Acknowledgment

This research work is within the framework of the project “intelligent management of renewable energy sources” GISER, funded by the CNRST (for the MESRSFC, Morocco).

## References

[1] J. Selvaraj and A. R. Nasrudin, “Multilevel Inverter For Grid-Connected PV System Employing Digital PI Controller”, IEEE Transactions On Industrial Electronics, vol. 56, No. 1 2009, pp. 149-158.

[2] S. Nema, R.K. Nema and G. Agnihotri, “MATLAB/Simulink based study of photovoltaic cells / modules / array and their experimental verification”, International journal of Energy and Environment, vol.1, No.3, pp.487-500, 2010.

[3] H. L. Tsai, C. S. Tu and Y. J. Su, “Development of Generalized Photovoltaic Model Using MATLAB/SIMULINK”, Proceedings of the World Congress on Engineering and Computer Science WCECS, San Francisco, USA, 2008.
[4] M. Francisco and G. Longatt, “Model of Photovoltaic Module in Matlab™”, 2do congresοι beroamerι cano de estudiantes de ingeniería eléctri ca, electrónica y computación pp.1-5, 2005.

[5] M. Salhi, R. El-Bachtiri and E. Matagne, “The development of a new maximum power point tracker for a PV panel”. International Scientific Journal for Alternative Energy and Ecology (ISJAEE), 2001.

[6] S. Nema, R. K. Nema and G. Agnihotri, “MATLAB/Simulink based study of photovoltaic cells / modules / array and their experimental verification”, International journal of Energy and Environment, vol.1, No.3, pp.487-500, 2010.

[7] T. Salmi, M. Bouzguenda, A. Gastli and A. Masmoudi. « Matlab/simulink based modeling of photovoltaic cell». International Journal of Renewable Energy Research (IJRER), 2(2), 213-218. 2012

[8] M. E. Ropp and S. Gonzalez, “Development of a MATLAB/Simulink model of a single-phase grid-connected photovoltaic system,” IEEE Trans. Energy Conv., vol. 24, no. 1, pp. 195–202, Mar. 2009.

[9] K. H. Chao, C. J. Li and S. H. Ho, “Modeling and fault simulation of photovoltaic generation systems using circuit-based model,” in Proc.

[10] M. Salhi, and R. El-Bachtiri, “Determination of equivalent circuit parameters of a photovoltaic panel,” Seventh International Symposium on Environnement Catalysis and Processes Engineering (ECGP'7), ENIM-Rabat (Morocco), April 2008, pp. 149.

[11] M. ARJUN, K. U. RAO and A. B. RAJU, “A novel simplified approach for evaluation of performance characteristics of SEIG”. International Conference In: Advances in Energy Conversion Technologies (ICAECT), IEEE. p. 31-36 2014.
[4] M. Francisco and G. Longatt, “Model of Photovoltaic Module in Matlab™”, 2do congresοι beroamerι cano de estudiantes de ingeniería eléctri ca, electrónica y computación pp.1-5, 2005.

[5] M. Salhi, R. El-Bachtiri and E. Matagne, “The development of a new maximum power point tracker for a PV panel”. International Scientific Journal for Alternative Energy and Ecology (ISJAEE), 2001.

[6] S. Nema, R. K. Nema and G. Agnihotri, “MATLAB/Simulink based study of photovoltaic cells / modules / array and their experimental verification”, International journal of Energy and Environment, vol.1, No.3, pp.487-500, 2010.

[7] T. Salmi, M. Bouzguenda, A. Gastli and A. Masmoudi. « Matlab/simulink based modeling of photovoltaic cell». International Journal of Renewable Energy Research (IJRER), 2(2), 213-218. 2012

[8] M. E. Ropp and S. Gonzalez, “Development of a MATLAB/Simulink model of a single-phase grid-connected photovoltaic system,” IEEE Trans. Energy Conv., vol. 24, no. 1, pp. 195–202, Mar. 2009.

[9] K. H. Chao, C. J. Li and S. H. Ho, “Modeling and fault simulation of photovoltaic generation systems using circuit-based model,” in Proc.

[10] M. Salhi, and R. El-Bachtiri, “Determination of equivalent circuit parameters of a photovoltaic panel,” Seventh International Symposium on Environnement Catalysis and Processes Engineering (ECGP’7), ENIM-Rabat (Morocco), April 2008, pp. 149.

[11] M. ARJUN, K. U. RAO and A. B. RAJU, “A novel simplified approach for evaluation of performance characteristics of SEIG”. International Conference In: Advances in Energy Conversion Technologies (ICAECT), IEEE. p. 31-36 2014.