Investigating the Impact of Base Heating and External Electric Field on PV Cell Performance under Intense Illumination ()
1. Introduction
Currently research in PV cell is oriented towards improving performance of PV cells for which the conversion efficiencies remain relatively weak. Studies show that concentrated PV cells have higher efficiencies (up to 47.1%) than ordinary PV cells [1] . But taking into account the mode of illumination, concentrated PV cells operate under high temperatures. Thus, some authors have shown, through studies, that the elevation of temperature causes a drop in the performances of PV cells [2] [3] . Other authors are interested in the effect of light intensity on the performance of PV cells and observed that increasing the intensity of incident light improves performance of PV cell [2] [4] . In addition, studies on the effect of an external magnetic field [5] [6] and of a protons irradiation on the performance of PV cells [7] have been made and it appears that the Magnetic fields as well as protons degrade performances of PV cells. The multiplicity of sources of electromagnetic fields (development of telecommunication systems) and the operating conditions of PV cells under concentration of light (high temperatures) give us the opportunity to investigate the behavior of the electrical parameters of a PV cell under illumination of 50 suns in function of the heating of the base and the intensity of an external electric field. The aim of this study is to demonstrate the simultaneous effect of base heating and an external electric field on a PV cell.
2. Mathematical Modeling
In our study, we used a polycrystalline silicon PV cell under illumination of 50 suns as shown in Figure 1 below.
is the external variable electric field acting on the PV cell. It is supposed to be uniform in all the space around the PV cell.
is concentration gradient electric field [8] .
(1)
Figure 1. PV cell under concentrated illumination and under external electric field.
The mobilities of electrons and holes as a function of base temperature are given by [9] :
and
(2)
with µon = 1500 cm2·V−1·s−1; µop = 475 cm2·V−1·s−1 et T0 = 300 K.
The diffusion parameter is related to mobility by the following equation:
and
(3)
KB is the Boltzmann’s constant and e is the elementary charge. According to our model, the current density is the sum of three currents. It is given by the following equation.
(4)
is a diffusion current.
is a conduction current induced by
.
is a conduction current induced by
.
The continuity equation of charged carriers for the cell is given by the following Equation (5):
(5)
with:
(6)
(7)
(8)
ai and bi are tabulated coefficient given for AM 1.5, by [10] .
The resolution of Equation (5), lead to the expression of the charged carriers generated in the base δ(x, T, E0).
3. Results and Discussions
3.1. Photocurrent Density
The Equation (9) below lead to the determination of photocurrent density as a function of the temperature T of the base and the electric field E0:
(9)
The expression of the photocurrent density is given by the following Equation (10)
(10)
with:
;
and
.
The variations of photocurrent density as a function of base temperature and external electric field are represented in the following Figure 2.
It appears on the curves of Figure 2 that the photocurrent yields by the PV cell increase with the increase of the intensity of electric field. This result is explained by the action of the electric strength which help electrons located in the vicinity of the junction across it, and participated to photocurrent.
Figure 2. Variations of photocurrent versus electric field and the temperature of the base (Sf = 5 × 105 cm/s; Sb = 103 cm/s; H = 0.03 cm; C = 50 suns).
From Figure 2, it also appears that, for a particular value of the electric field, the photocurrent decrease with the increase of the temperature of the base. This is explained by the fact that heating of the base is due to the movement of high number of charged carriers generated. Increasing of the photogenerated charged carriers is following by the increase of thermalization, collision between carriers and concentration gradient electric field E(x).
Thermalization, collisions and braking produce thermal energy into the material of the PV cell. The electric field through the electric strength increases the possibility of collision between charged carriers. Hence, collision and breaking increase the loss of carriers and decrease of photocurrent.
We notice that decrease in photocurrent with increase of the temperature is more significant for high values of the intensity of the electric field. We explain that by the increase in electric strength for high values of electric field and therefore increase of collisions and loss of charged carriers.
3.2. Photovoltage
The expression of photovoltage delivered by the PV cell is given by the Equation (10) below:
(11)
With:
and
(12)
The expression of photovoltage obtained from (11) is given by the equation (12)
(13)
VT is the thermal voltage, n0 is the electrons density at the thermal equilibrium, NB represent the doping rate of the base (NB = 1016 cm−3) and ni is the intrinsic concentration of electrons (ni = 1010 cm−3). The photovoltage profile as function of electric field for different values of temperature is present on the following Figure 3.
Analysis of Figure 3 shows that, for a particular value of a given temperature of the base, the photovoltage increase with the increase in electric field. This is explain by the fact that electric strength which act on the charged carriers increase with the increase in electric field. Thus the charged carriers photogenerated in rear side of the base are easily send in the zone near the junction. It then appear an accumulation of electrons in the zones near the junction and therefore
Figure 3. Evolution of the photovoltage versus electric field and the temperature of the base (Sf = 5 × 105 cm/s; Sb = 103 cm/s; H = 0.03 cm; C = 50 suns).
an increase in photovoltage. In other hand, we notice that, for any given value of the intensity of the electric field, photovoltage decrease with the increase in the temperature of the base.
We explain this result by the fact that (champ electric du gradient de concentration) E(x) induce an increase of thermalization, collisions between charged carriers, braking of charged carriers and consequently produce the heating of the base.
The presence of the electric strength increases the possibilities of collisions and losses of charged carriers into the bulk of the base of the PV cell. Consequently, photovoltage decrease. It appears on the curves of Figure 3 that, decrease in photovoltage with increase in temperature is most significant for high values of electric field. This is the consequence of the increase in losses of charged carriers with the increase of collisions induces by the increase in electric strength.
3.3. Electric Power
Electric power delivered by a PV cell is given by the following equation:
(14)
Variations in electric power as a function of electric field intensity for different values of the base temperature are illustrated in Figure 4 below.
From the analysis of Figure 4, it appears that, for any given temperature of the base, the electric power increases with increasing in electric field. Furthermore, for any values of electric field, the electric power decreases with the increase in the temperature of the base. These results are in good agreement with those obtained in the cases of photocurrent and photovoltage.
Figure 4. Variations of the electrical Power versus electric field and the temperature of the base (Sf = 5 × 105 cm/s; Sb = 103 cm/s; H = 0.03 cm; C = 50 suns).
3.4. Fill Factor
The expression of fill factor of the PV cell is given by the following equation:
(15)
The variation of the fill factor as a function of the intensity of the electric field for different values of the base temperature is presented in the following Figure 5.
The analysis of Figure 5 shows that, for any given temperature of the base, the fill factor increases as the intensity of the electric field increases. Furthermore, for any given values of electric field, the fill factor decrease with the increasing of base temperature. These results are in good agreement with those obtained in the case of variations of the electric power, because the maximum electric power supplied by the PV cell changes from the same way as the electrical power delivered.
3.5. Conversion Efficiency
The expression of conversion efficiency is given by the following equation:
(16)
The curves of conversion efficiency as a function of electric field for different values of base temperature are present in Figure 6 below.
It emerges from the analysis of Figure 6 that for any given value of the base temperature, the conversion efficiency of the PV cell increases with the increase
Figure 5. Variations of Fill Factor versus electric field and the temperature of the base (Sf = 5 × 105 cm/s; Sb = 103 cm/s; H = 0.03 cm; C = 50 suns).
Figure 6. Variations of the conversion efficiency versus electric field and the temperature of the base (Sf = 5 × 105 cm/s; Sb = 103 cm/s; H = 0.03 cm; C = 50 suns).
in the intensity of the electric field. Furthermore, for any given value of the electric field, the conversion efficiency decreases as the base temperature increases. These results are in good agreement with those obtained in the case of fill factor.
4. Conclusion
This work allowed us to establish the expressions of photocurrent density, electric power, fill factor and conversion as function of the base temperature and intensity of electric field. By numerical simulation, we plotted the curves of those different electrical parameters as function of temperature and electric field. The analysis of these curves shows that, for any given temperature, electrical parameters increase with the increase in electric field. It also appears that, the electrical parameters decrease with the increase in base temperature. The curves of electrical parameters reveal that harmful effect of the temperature is more important at large values of the electric field.
Acknowledgements
The authors wish to thank International Science Program (ISP) for funding our research group and allowing to conduct these works.