The Solar Cell Parameters as a Function of Its Temperature in Relation to Its Diurnal Efficiency

The variation of the temperature of the solar cell subjected to the incident global solar radiation along the local daytime in relation to its efficiency is studied. The heat balance equation is solved. The solution revealed that the cell temperature is a function of the maximum value of the daily incident global solar radiation q max , the convection heat transfer coefficient (h), the optical, physical and the geometrical parameters of the cell. The temperature dependence of the short circuit current I sc , the dark saturation current I o , the open circuit voltage V oc , and the energy band gap E g characterizing a Silicon solar cell is considered in evaluating the cell efficiency. Computations of the efficiency concerning operating conditions and astronomical locations (Egypt) as illustrative examples are given.


Introduction
Heating a solar cell subjected to the incident global solar radiation affects its photovoltaic performance [1]- [7]. The solar p-n cell is a semiconductor photovoltaic device.
Solar energy can be converted into electricity are termed as the photovoltaic devices or solar cells. At present this solar cell is the most important long-duration power supply for satellites and space vehicles. Solar cells have also been successfully employed in small-scale terrestrial applications. Due to this the study of the efficiency of the solar cell with the aim to increase its value has aroused the in-How to cite this paper: Shaban, S.S.M. (2020) The Solar Cell Parameters as a Function of Its Temperature in Relation to Its Diurnal Efficiency. Optics and Photonics Journal, 10, 1-12. terest of many investigators [8]- [22].
The efficiency (η ) is a measure of the cell performance which depends on many parameters. Many of such parameters are temperature dependent.
The performance of a solar cell is determined by parameters as a short circuit current I sc (T) and open circuit voltage V oc (T). It has been shown earlier that I sc increases with increasing the temperature whereas open circuit voltage V oc decreases with increasing the temperature.
The aim of the present work is to find theoretically the temperature field within the solar cell considering different optical, physical, geometrical conditions. The temperature functional dependences of the cell parameters V oc , I sc and the efficiency are also taken into consideration.

The Mathematical Formulation of the Problem
In sitting up the problem it is assumed that solar radiation of irradiance q(t) W/m 2 is incident on the front surface of the solar cell, where it is partly absorbed and partly reflected.
The absorbed quantity is Aq(t), where "A" is the absorption coefficient at the front surface of the considered cell. The heat diffusion equation is given in the form: where: Equation (1) can be written as: where, where:  [25] where: φ , is the latitude and δ is the solar declination angle given as: 23.45sin 284 365 n δ + = t r , is the sunrise time in hours; t s , is the sunset time in hours; And "n" is the day of the year (1 ≤ n ≤ 365) starting from 1 January.
The solution is obtained as the form [ Equation (5) represents the temperature of the considering cell after an exposure time "t" along the solar day time.

The Efficiency Temperature Dependence for the Solar Cell
The efficiency ( ) η of the solar cell is defined as the ratio between the maxi- where: is the reverse saturation current and its dependence on temperature is revealed through the following equ- where: 3 2 179 amp K m = ⋅  for silicon solar cell [18], n is non-ideality factor of the cell and is taken as unity, the value of 3 γ = [2]; E g is the energy band gap. The dependence of energy band gap of a semicon-Optics and Photonics Journal ductor on temperature can be described as [27] [28]: E g (0) is the energy band gap of the semiconductor at 0 K T ≈ ; For silicon E g (0) =1.16 eV [29], α = 7 × 10 −14 eV•K −1 and β = 1100 K. Which are constants for each semiconductor material [28], I sc is short circuit current given as [8], where: Q is the collection factor, R(T) is the reflection coefficient at the front face of the cell and its value is given as [30]: ( ) 5 0.322 3.12 10 R T T − = + × (11) µ is the attenuation coefficient and is value given as [30]: where:

Computations
The silicon solar cell is considered with dimensions (5.5 cm × 11 cm × 0.35 cm) is considered [31]. The silicon solar cell temperature as a function of the local day time "t" is calculated using Equation (5) The hourly incident global solar radiation q(t) (Equation (4)) is considered for Egypt [32] as an illustrative example. The values of I sc , I o , and V oc corresponding to each value of T at a certain time "t" are determined.
Hence the efficiency "η" of the cell as a function of the solar local day time "t" is estimated for considered location.
The obtained results are given in Table 1 and illustrated graphically in Figure 1 showing that the temperature of the solar cell increases as the thickness decreases.
Different cooling conditions h = 3, 5, 10 W/m 2 •K are considered at thickness l = 10 −3 m, A = 0.7 the obtained results are given in Table 2    in Figure 2 which show that the temperature of the solar cell increases as the cooling conditions at the front surface decreases.
Different absorption coefficients A = 0.6, 0.7, 0.8 are considered at l = 10 −3 m, h = 3 W/m 2 •K. The obtained results are given in Table 3 and illustrated graphically in Figure 3 which show that the temperature of the solar cell increases as the absorption coefficients at the front surface increases.
The variation of I sc , V oc for the case: l = 5 × 10 −3 m, A = 0.7, h = 1 W/m 2 •K are computed and are illustrated in Figure 4 and Figure 5.
The obtained results revealed that I sc increases with increasing the temperature and vic versa.
Moreover, the dependence of the efficiency of the considered solar cell on the thickness l, are clarified.

Results and Discussions
The obtained results reveal that: The cell temperature decreases as the transfer coefficient for cooling increases, also it decreases as the thickness of the cell increases while it increases as the absorption coefficient "A" at its front surface increases. This is because when "A" increases the value of the solar power absorbed by the cell increases.
Moreover, the short circuit current I sc increases with increasing temperature and vice versa. This variation may be attributed to the fact that for most semi-conductors, as the temperature increases, the energy band gab decreases [19].        V oc has weak dependence on "T" than I sc .

Conclusions
The temperature of the solar cell subjected to incident solar insolation increases with local day time and passes through a maximum value then it decreases gradually toward sunset. The cell parameters V oc , I sc , and the efficiency η are functions of the cell temperature with different degrees.
The efficiency η of the cell decreases with the cell temperature in general.
Thus cooling, the solar cell is recommended.
The open circuit voltage V oc , is less dependent on the temperature than the short circuit current I sc .

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.