Photovoltaic (PV) devices are spectrally selective, and their performance is influenced by unavoidable spectral variations. In addition, multijunction-based concentrating photovoltaic (CPV) devices show a strong spectral dependence due to the series connection of various junctions with different absorption bands, and also due to the use of concentrator optics. In this work, the accuracy of a new set of analytical equations that quantify the spectral impact caused by the changes in air mass (

Concentrating photovoltaic (CPV) systems employ optical components that focus the direct sunlight by reflection or refraction onto a smaller area usually made of high efficiency III-V multijunction (MJ) solar cells. Such solar cells overcome the thermodynamic Shockley–Queisser limit of single junction solar cells [

It is well-known that the performance of photovoltaic (PV) devices is influenced by the unavoidable spectral variations that are mainly caused by changes in air mass (

A new procedure that uses a simple set of analytical equations and takes into account the

Bulk spectral simulations are not required and therefore the procedure is easy to handle;

The equations can be applied worldwide using ground-based (e.g., the aerosol robotic network, AERONET) or satellite (e.g., the moderate resolution imaging spectroradiometer, MODIS) observations;

Therefore, relatively expensive measuring equipment that evaluates the solar spectrum is not required, given that a meteorological database is available at the specific site

In our previous study [

The short-circuit current density (_{sc,i}_{i,min}_{i,max}_{i}_{opt}_{b}

Due to the series connection of different junctions, the current density of the whole MJ solar cell is given by the minimum current:

The impact of the spectrum is quantified using the

Bearing the above in mind, the

This index quantifies the spectral impact on the performance of a MJ CPV device as a function of the input spectral distribution. In this sense, a value greater than 1 indicates spectral gains, a value lower than 1 indicates spectral losses and a value equal to 1 indicates spectral conditions equivalent to the reference spectrum. This index has been experimentally demonstrated to be valid for approximating the spectral impact on the power or energy output of MJ CPV systems under real operating conditions [

The detailed procedure used to extract the analytical equations evaluated in this work can be found in [

1 ≤

0.05 ≤

0.25 ≤

Hence, a total of 3264 spectra were generated, covering a wide range of spectral conditions. The _{ref}_{ref}

The experimental validation of the proposed equations was carried out at the CEAEMA of the University of Jaén [

It is important to note that all the sensors are within the calibration period and are cleaned once a week and also after rainy days to ensure quality of measurements.

As mentioned in the introduction, the following CPV configurations are considered in this study:

LM: a device based on a lattice-matched GaInP/GaInAs/Ge solar cell

LM + PMMA: a device based on a LM solar cell and a poly(methyl methacrylate) (PMMA) Fresnel lens

MM: a device based on a metamorphic GaInP/GaInAs/Ge solar cell

MM + SoG: a device based on a MM solar cell and a silicone-on-glass (SoG) Fresnel lens.

Further information about the external quantum efficiency (

In order to evaluate the proposed equations for the four CPV devices under study, four days with different atmospheric characteristics were selected and therefore the following were considered:

21 June 2016—clear atmosphere with low

23 December 2016—clear atmosphere with high

29 June 2016—relatively hazy atmosphere (

18 August 2016—relatively wet atmosphere (

These days exhibit different spectral conditions and, therefore, can allow the procedure’s evaluation.

The accuracy of a new set of analytical equations was analysed in this work in order to evaluate the spectral impact of air mass (

The equations exhibited a similar behaviour for all the CPV configurations. A

This work is supported by the EUREKA-Eurostars program (EUREKA/EUSTAR/0116/01) and the Research Promotion Foundation of the Republic of Cyprus. The European Regional Development Fund (ERDF) and Spanish Economy Ministry (ENE2013-45242-R and ENE2016-78251-R); Universidad de Jaén and Caja Rural de Jaén (UJA2015/07/01) are also acknowledged for the financial support.

Marios Theristis and Eduardo F. Fernández designed and performed the experiments. Florencia Almonacid performed the data analysis and George E. Georghiou contributed to the analysis of the results. All authors contributed equally to the writing of the paper.

The authors declare no conflict of interest.

Irradiance (

Actual versus simulated

Proposed spectral corrections for each subcell.

top | ax^{4} + bx^{3} + cx^{2} + dx + e * |
aln(x) + b * | aln(x) + b * |

middle | ax^{2} + bx + c * |
Ax + b * | |

bottom | aln(x) + b * | aln(x) + b * |

* where x =

Mean absolute percentage error (

Device | ||
---|---|---|

LM | 0.91 | −0.32 |

LM + PMMA | 0.92 | −0.32 |

MM | 0.64 | −0.19 |

MM + SoG | 0.56 | −0.17 |