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The aim of this work is to present a theoretical study of external magnetic field effect on a bifacial silicon solar cell’s electrical parameters (peak power, fill factor and load resistance) using the J-V and P-V characteristics. After the resolution of the magneto transport equation and continuity equation of excess minority carriers in the base of the bifacial silicon solar cell under multispectral illumination, the photo-current density and the photovoltage are determined and the J-V and P-V curves are plotted. Using simultaneously the J-V and P-V curves, we determine, according to magnetic field intensity, the peak photocurrent density, the peak photovoltage, the peak electric power, the fill factor and the load resistance at the peak power point. The numerical data show that the solar cell’s peak power decreases with magnetic field intensity while the fill factor and the load resistance increase.

The efficiency of a solar cell depends on its electrical parameters such as series and shunt resistances, peak power and fill factor. For the determination of the series and shunt resistances many authors [

In this work, we study the influence of magnetic field intensity on a bifacial silicon solar cell’s electrical parameters (peak power, fill factor and load resistance). Using simultaneously the J-V and P-V curves, we determine the peak power, the fill factor and the load resistance at the peak power point according to magnetic field intensity. Then, we relate the resistance at the peak power point (R_{MPP}) to the junction dynamic velocity at the maxi mum power point (Sf_{MPP}) calculated in the previous article [

This study is focused on the base region of a polycrystalline back surface field bifacial silicon solar cell (

When the bifacial silicon solar cell is illuminated simultaneously on both sides, the solution of excess minority carriers’ continuity equation [

with

In Equation (1), _{i} and b_{i} are tabulated values obtained from modelling of the generation rate considered for over all the solar radiation spectrum under Air Mass 1, 5 standard conditions [

Constants A_{1} and A_{2} are determined solving the boundary conditions [

Since the excess minority carriers’ density is known, from Fick’s law applied at the solar cell junction, we can derive the photocurrent density expression as:

Knowing the excess minority carriers’ density, the photovoltage across the solar cell junction is also expressed

using Boltzmann’s relation:

V_{T} is the thermal voltage, n_{i} is the intrinsic carriers’ density at thermodynamic equilibrium and N_{B} is the base doping density.

The photocurrent density and the photo-voltage depend on junction dynamic velocity Sf. While taking the junction dynamic velocity as parameter, we plot in

The shapes of the different curves in

Each curve is characterized by three remarkable points: the short circuit photocurrent density J_{sc}, the open circuit photovoltage V_{oc} and a point named “knee” or peak power point [_{m} (or J_{p}) and V_{m} (or V_{p}) as coordinates [_{p}= J_{p} × V_{p}) is the maximum electric power (P_{m}= J_{m} × V_{m}) that a solar cell can delivered to an external circuit; so the peak power point is the operating point that permits to obtain the maximum electric power from a solar cell [

The expression of electric power delivered by the base of the bifacial solar cell to an external circuit is:

with

The electric power delivered by the bifacial silicon solar cell to an external circuit depends also on the junction dynamic velocity Sf. While taking the junction dynamic velocity as parameter, we plot in

The curves in

For that, we plot in the same axes system (

Using the two characteristics, we determine the values of peak power P_{p}, peak photovoltage V_{p}, peak photocurrent density J_{p}, short circuit photocurrent density J_{sc} and open circuit photovoltage V_{oc} according to magnetic field intensity.

Then we calculated the solar cell fill factor (FF) using the formula below:

Knowing the peak photovoltage V_{p}, and the peak photocurrent density J_{p}, we calculated the load resistance at ² the peak power point (Maximum Power Point) using Ohm’s law [

The characteristic values of the bifacial solar cell under magnetic field are given in

These results show that the peak photocurrent density and the short circuit photocurrent density decrease with magnetic field intensity while the peak photovoltage and the open circuit photovoltage increase with the same magnetic field intensity. These results have been observed on the Jph-Vph characteristics. The peak power decreases with the magnetic field intensity while the fill factor and the load resistance at the maximum power point or peak power point increase. The decrease of peak power with magnetic field increase corresponds to a displacement of the bifacial solar cell’s operating point towards large values of photovoltage, resulting in an increase of charge resistance at the peak power point.

In

We note that the maximum electric power determined in the previous work [

In this work, we have presented a theoretical study of magnetic field influence on the electrical parameters of a bifacial silicon solar cell. Taking as parameter the junction dynamic velocity, we plot the solar cell Jph-Vph and P-Vph characteristics. The peak power, the peak photovoltage, the peak photocurrent density, the short circuit photocurrent density and the open circuit photovoltage are determined by means of the Jph-Vph and P-Vph characteristics according to magnetic field intensity. Then we calculated the solar cell fill factor (FF) and the load resistance at the peak power point using Ohm’s law.

The numerical data are evidence of an increase in the fill factor and the load resistance at the peak power

B (mT) | 0 | 1 | 2.5 | 5 | 7.5 | 10 |
---|---|---|---|---|---|---|

P_{p} (mW/cm^{2}) | 19.759 | 18.757 | 16.526 | 14.776 | 13.810 | 13.104 |

V_{p} (mV) | 571.150 | 578.250 | 592.120 | 604.700 | 612.110 | 619.460 |

J_{p} (mA/cm^{2}) | 34.591 | 32.437 | 27.952 | 24.435 | 22.561 | 21.167 |

V_{oc} (mV) | 653.890 | 662.690 | 676.430 | 690.000 | 698.270 | 704.400 |

J_{sc} (mA/cm^{2}) | 36.272 | 33.909 | 29.183 | 25.507 | 23.512 | 22.095 |

FF | 0.833 | 0.835 | 0.838 | 0.840 | 0.841 | 0.842 |

R_{MPP} (Ω.cm^{2}) | 16.512 | 17.827 | 21.183 | 24.747 | 27.177 | 29.265 |

B (mT) | 0 | 1 | 2.5 | 5 | 7.5 | 10 |
---|---|---|---|---|---|---|

P_{max} (mW/cm^{2}) | 19.759 | 18.757 | 16.526 | 14.775 | 13.810 | 13.104 |

Sf_{MPP} (cm/s) | 2.928 × 10^{4} | 1.942 × 10^{4} | 1.027 × 10^{4} | 5.727 × 10^{3} | 3.862 × 10^{3} | 2.922 × 10^{3} |

R_{MPP} (Ω.cm^{2}) | 16.512 | 17.827 | 21.183 | 24.747 | 27.177 | 29.265 |

point with the increase of the magnetic field intensity but a decrease in the peak power. We interpreted the variation in the load resistance at the peak power point as a variation in the solar cell’s operating point. The load resistance at the peak power point has been related to the junction dynamic velocity at the maximum power point determined in a previous work. We noted that the junction dynamic velocity and the load resistance at the peak power point evolve in reverse senses. This last analysis permits to conclude that the junction dynamic velocity defines effectively the solar cell operating point.

The authors thank International Science Program (ISP) for supporting their research group (energy and environment) and allowing them to conduct this work.

Issa Zerbo,Martial Zoungrana,Idrissa Sourabié,Adama Ouedraogo,Bernard Zouma,Dieudonné Joseph Bathiebo, (2016) External Magnetic Field Effect on Bifacial Silicon Solar Cell’s Electrical Parameters. Energy and Power Engineering,08,146-151. doi: 10.4236/epe.2016.83013