# Spectral Correction of CPV Modules Equipped with GaInP/GaInAs/Ge Solar Cells and Fresnel Lenses
## 1 Introduction  
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 [1]; and even though their market share is small and relatively young, there is still a great interest in the technology due to the higher efficiencies especially at sites with high annual direct normal irradiation [2]. In addition to these, CPVs can achieve greater energy density, and thus less semiconductor material is required [3]. This technology, however, must overcome the technical and economic challenges to achieve success in the energy market [3, 4]. The state-of-the-art triple-junction (3J) solar cell on the market is the lattice-matched (LM) 3J solar cell made of GaInP/GaInAs/Ge subcells [5], while the record efficiency of 46% was achieved by a four-junction (4J) solar cell [6].  
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 (\(AM\), i.e., the path length of the sun through the atmosphere relative to the zenith), aerosol optical depth (\(AOD\), i.e., the amount of aerosols in the atmosphere) and precipitable water (\(PW\), i.e., the total amount of water in a column in the zenith direction). The influence varies depending on the PV technology and, specifically, its corresponding spectral absorption band. In particular, MJ solar cells exhibit a higher spectral sensitivity compared to single-junction ones due to the series connection of different band-gap solar cells [7]. Moreover, the assembly of concentrator optics modifies the input spectra and introduce a strong angular dependence in the system. Therefore, a spectral correction has to be introduced in order to correct the incident irradiance and, thereby, improve the MJ-based CPV performance evaluation and modelling [8; 9].  
A new procedure that uses a simple set of analytical equations and takes into account the \(AM\), \(AOD\) and \(PW\) has been recently proposed and evaluated by the authors for the case of a typical lattice-matched solar cell [10; 11]. The main advantages of the proposed analytical equations are:  
* 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 [10], the influence of the concentrator optics was not taken into account. Therefore, in this study, we incorporate the Fresnel lens dependency in order to achieve a more realistic procedure. The accuracy of the method is examined for four CPV configurations: (1) a lattice-matched (LM) triple-junction (3J) solar cell; (2) a LM 3J solar cell with a poly(methyl methacrylate) (PMMA) Fresnel lens; (3) a metamorphic (MM) 3J solar cell; and (4) a MM 3J solar cell with a silicon-on-glass (SoG) Fresnel lens. The spectral factor (\(SF\)) is used to quantify the spectral effects on the performance of the four MJ-based CPV devices that are considered. The description of the methodology used to extract the equations and information on the experimental set-up used to evaluate the proposed equations of all systems is also provided.