A Study of the Temperature Influence on Different Parameters of Mono-Crystalline Silicon Photovoltaic Module

Said Amar^{1,2}^{*},
Mustapha Bahich^{3},
Youness Bentahar^{1},
Mohamed Afifi^{1},
Elmostapha Barj^{1}

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1. Introduction

Photovoltaic solar energy results from the direct transformation of solar radiation into electrical energy. This energy conversion is done using a photovoltaic cell (PV) based on a physical phenomenon known as the photovoltaic effect which consists in producing a potential difference when the surface of this cell is exposed to light. The voltage generated depends on the material used to make the cell.

The PV cell constitutes an electric generator of very low power compared to the needs of domestic or industrial applications. A photovoltaic cell of a few tens of square centimeters delivers at most a few watts at very low voltage (of the order of 0.6 to 0.8 V), which is precisely a PN junction voltage. To increase the operating voltage and increase the power available at the level of the photovoltaic cell, they are connected in series and/or in parallel to obtain a photovoltaic module.

Mono-crystalline silicon (mc-Si) solar module is mostly used to solar modules because it has a number of advantages like low maintenance cost, high reliability, noiseless and eco-friendly [1] [2]. The overall performance of the mc-Si solar module is highly dependent on environmental parameters, such as light intensity, tracking angle and module temperature [3]. Although photovoltaic parameters such as open circuit voltage, short circuit current, maximum output power, fill factor and efficiency are generally affected by temperature.

A study of the electrical characteristics of diodes of crystalline silicon cells with cell temperature was worked by [4]. They found that the ideality factor decreases with cell temperature in the space charge region and increases in the quasi-neutral region. [5] studied the dependence of cell temperature on characteristics of different solar cells using the linear interpolation method and observed that the physical validity of linear interpolation for cell temperature was based on the current-voltage characteristics of the junction p-n. [6] studied the influence of cell temperature on the series resistance of silicon solar cells and observed that the series resistance varies with cell temperature; therefore, the temperature of the cell is a key parameter to judge the quality and crystalline silicon solar cell performance [7] [8]. The expression of current-voltage of a crystalline silicon solar cell [3] is:

$I={I}_{0}\left[\mathrm{exp}\left(\frac{q\left(V-I{R}_{s}\right)}{nkT}\right)-1\right]+\left(V-\frac{I{R}_{s}}{{R}_{sh}}\right)-{I}_{L}$ (1)

Here, *I*_{0} is the reverse saturation current, *q* is the electron charge, *n* is the ideality factor of the diode, *T* is the temperature, *k* is the Boltzmann constant, *R _{sh}* is the shunt resistance,

Consequently, our study is interested on the influence of the temperature on the photovoltaic parameters of the mc-Si solar module using the Matlab/simulink environment. The manipulations were undertaken for module temperatures 25˚C, 40˚C, 50˚C and 60˚C at the constant light intensities 200, 300, 400 and 500 W/m^{2} for studying the influence of temperature on the different parameters of solar module.

2. Presentation and Modeling of PV Module

2.1. The Equivalent Circuit

The equivalent circuit of the PV cell is represented in Figure 1. The current source *I _{ph}* represents the photocurrent of the cell.

The voltage-current characteristic equation of a solar cell is provided as [10]

${I}_{ph}=\left[{I}_{sc}+{K}_{i}\left(T-298\right)\right]\times {I}_{r}/1000$ (2)

In this last relation, *I _{ph}* represents the photo-current (A);

Reverse saturation current *I _{rs}* of the module is given by the relation:

${I}_{rs}={I}_{sc}/\left[\mathrm{exp}\left(q{V}_{oc}/{N}_{s}KnT\right)-1\right]$ (3)

Figure 1. PV cell equivalent circuit [11].

Figure 2. Equivalent circuit of solar array [10].

Here, *q*: the electron charge, =1.602 × 10^{−19} C; *V _{oc}*: the open circuit voltage (V);

The module saturation current *I*_{0} varies with the temperature of the cell, which is given by:

${I}_{0}={I}_{rs}{\left[\frac{T}{{T}_{r}}\right]}^{3}\mathrm{exp}\left[\frac{q\times {E}_{g0}}{nK}\left(\frac{1}{T}-\frac{1}{{T}_{r}}\right)\right]$ (4)

Here, *T _{r}*: the nominal temperature = 298.15 K;

$I={N}_{P}\times {I}_{ph}-{N}_{P}\times {I}_{0}\times \left[\mathrm{exp}\left(\frac{\frac{V}{{N}_{S}}+I\times {R}_{S}/{N}_{P}}{n\times {V}_{t}}\right)-1\right]-{I}_{sh}$ (5)

With

${V}_{t}=\frac{K\times T}{q}$ (6)

where *V _{t}* is called the thermal voltage [12]

And

${I}_{sh}=\frac{V\times \frac{{N}_{P}}{{N}_{S}}+I\times {R}_{S}}{{R}_{sh}}$ (7)

Here: *N _{p}*: number of PV modules connected in parallel;

The open circuit voltage (*V _{oc}*) depends on the temperature and is given by the following relationship [2].

${V}_{oc}=\frac{{E}_{g}}{k}-\frac{nkT}{q}\mathrm{ln}\frac{{I}_{0\mathrm{max}}}{{I}_{sc}}$ (8)

In this equation, *E _{g}* is the energy band gap and

$FF=\frac{{P}_{\mathrm{max}}}{{V}_{oc}\times {I}_{sc}}$ (9)

In this equation *P*_{max} is the maximum Power. The efficiency of solar module is given [14]

${\eta}_{M}=\frac{{P}_{\mathrm{max}}}{E\ast {A}_{a}}\ast 100$ (10)

where *P*_{max} is the measured output Power, *E* is the irradiance and *A _{a}* is the module active area.

The dependence between cell temperature and efficiency is given [7] as follows:

${\eta}_{C}={\eta}_{Tref}\left[1-{\beta}_{0}\left({T}_{c}-{T}_{ref}\right)\right]$ (11)

In this equation *η _{c}* and

2.2. Reference Model

The 100 W solar power module is taken as the reference module for the simulation and the detailed module parameters are given in Table 1. The electrical specifications are under test conditions of irradiance of 1 kW/m^{2}, spectrum of 1.5 air masses and cell temperature of 25˚C.

2.3. Step by Step Procedure for Modeling Photovoltaic Modules with Tags

A mathematical model of the photovoltaic generator including the fundamental components of the diode, current source, series resistor and parallel resistor is modeled with tags in the Simulink environment. The simulation of the solar module is based on the equations given in the section above and performed in the following steps.

· Step 1

The input parameters for modeling are as follows:

*T _{r}* is the reference temperature = 298.15 K;

· Step 2

The photon current of the module is given in Equation (2) and modeled as Figure 3.

Table 1. Electrical characteristics data of DS-100M PV module [15].

Figure 3. Modeled circuit for Equation (2).

${I}_{ph}=\left[{I}_{sc}+{K}_{i}\left(T-298\right)\right]\times {I}_{r}/1000$ (12)

· Step 3

The reverse saturation current of the module is given in Equation (3) and modeled as Figure 4.

· Step 4

The saturation current *I*_{0} of the module is given in Equation (4) and modeled as Figure 5.

· Step 5

Modeled circuit for Equation (6) and modeled as Figure 6.

· Step 6

Modeled circuit for Equation (7) and modeled as Figure 7.

To obtain the output current *I* of the solar system, we model the Equation (5), the result is shown in Figure 8.

3. Results and Discussion

With the developed model, the characteristics of the PV module are estimated as follows. The I-V and P-V characteristics under variable temperature at constant irradiation are given in Figure 9. Here, the temperature changes with values of 25˚C, 40.50˚C and 60˚C while the solar irradiation remains constant at 200, 300, 400 and 500 W/m^{2}.

It is clear from Figures 9(a)-(d) that the current-voltage and power-voltage characteristics depend on the temperature of the module. In the current-voltage characteristics, it is observed that the current is maximum and almost constant in the lower voltage range and varies with the cell temperature in the range 1.222 - 1.236 A, 1.833 - 1.854 A, 2.444 - 2.472 A and 3.055 - 3.090 A at constant irradiations 200 W/m^{2}, 300 W/m^{2}, 400 W/m^{2} and 500 W/m^{2} respectively.

The estimation of the characteristics follows the order of the temperature of the module as the successive higher underestimates the lower one. The trend is reversed for the voltage intervals 7.8 - 11.52 V, 8.28 - 12 V, 8.64 - 12.24 V and 8.88 - 12.54 V for the irradiations of 200 W/m^{2}, 300 W/m^{2}, 400 W/m^{2} and 500 W/m^{2} respectively. Subsequently, it is found that the current decreases rapidly and the characteristics corresponding to a successive lower module temperature exist beyond the higher one.

Figure 4. Modeled circuit for Equation (3).

Figure 5. Modeled circuit for Equation (4).

Figure 6. Modeled circuit for Equation (6).

Figure 7. Modeled circuit for Equation (7).

Figure 8. Modeled circuit for Equation (5).

(a) Irradiation at 200 W/m^{2}.(b) Irradiation at 300 W/m^{2}.(c) Irradiation at 400 W/m^{2}.(d) Irradiation at 500 W/m^{2}.

Figure 9. The current-voltage and power-voltage characteristics of mc-Si solar module with module temperature at constant irradiation (a) 200 W/m^{2}, (b) 300 W/m^{2}, (c) 400 W/m^{2} and (d) 500 W/m^{2}.

Likewise, the estimation of the power-voltage characteristics follows the same trend for the current-voltage characteristics. It is observed that it increases and is almost linear with the temperature of the module in the low voltage range, reached at the maximum in the range of 13.01 to 50.82 W for all constant irradiations.

Subsequently, it is found to decrease rapidly at a higher voltage range due to the increasing speed of photon generation with cell temperature which revealed the rapid increase in reverse saturation current as reported by [8].

The power-voltage characteristics clearly indicate a point of maximum power and the voltage at this point is less than the open circuit voltage. Likewise, the current at this point is also less than the short circuit current.

The effect of temperature dependence on photovoltaic parameters such as open circuit voltage, short circuit current, and fill factor with module temperature between 25˚C and 60˚C at constant irradiations 200, 300, 400 and 500 W/m^{2} is shown in Figure 10.

(a) Short circuit current *I _{sc}* (b) Open circuit voltage

Figure 10. The variation of (a) short circuit current (*I _{sc}*), (b) open circuit voltage (

It can be seen from Figure 10 that the open circuit voltage (*V _{oc}*) and the fill factor (

These results are in agreement with the literature [16] [17] and their explanation is given on the basis of Equations (9) and (10) those described in previous works [13] [18].

The evolution of open circuit voltage, short circuit current, fill factor, maximum power, efficiency and their relative change of the mc-Si solar module with module temperature at constant solar irradiations of 200, 300, 400 and 500 W/m^{2} are calculated and are given by the Tables 2-6.

Table 2. The open circuit voltage and its relative change of mc-Si solar module with module temperature at different constant irradiation.

Table 3. The short circuit current and its relative change of mc-Si solar module with module temperature at different constant irradiation.

Table 4. The maximum output power *P*_{max} and its relative change of mc-Si solar module with module temperature at different constant irradiation.

Table 5. The fill factor and its relative change of mc-Si solar module with module temperature at different constant irradiation.

Table 6. The efficiency and its change of mc-Si solar module with module temperature at different constant irradiation.

From Equation (8), the open circuit voltage is reduced when the temperature increases, in fact, *E _{g}* decreases with the temperature [19]. The short-circuit current (

We find that the maximum power *P*_{max} decreases with the temperature of the module at all constant solar irradiations, as illustrated in Table 4 which revealed a decrease in voltage with the temperature of the module. We deduce from Equation (9) that the fill factor decreases with module temperature due to the change in the corresponding open circuit voltage and short circuit current.

It is also seen from Table 6 that the efficiency decreases with module temperature at all constant irradiations due to the decrease in the corresponding open circuit voltage and fill factor. According to Equation (11) and as the quantity (*T _{c}*-

4. Conclusion

In this present article, the effect of module temperature on the photovoltaic parameters of the mc-Si photovoltaic module is reported by using a step-by-step procedure for simulating a PV module with Tag tools, with user-friendly icons and dialogs in Matlab/Simulink block libraries. This modeling procedure was carried out with a module temperature between 25˚C and 60˚C at constant solar irradiations of 200, 300, 400 and 500 W/m^{2}. The results show that the module temperature has a significant impact on the photovoltaic parameters and that it controls the quality and the performance of the mc-Si solar panel.

The open circuit voltage (*V _{oc}*), the maximum power point (

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