# Simulation of a Low Concentrator Photovoltaic System Using COMSOL
## 2 Materials and Methods
### COMSOL Set Up  
This work focuses on studying the optical performance of a V-trough under solar radiation using COMSOL. This program relies on the finite element method (FEM). FEM is a method to solve complex partial differential equations (PDEs) that describe a physical problem by subdividing the system into smaller parts and approximating the PDEs with simple analytical equations [20]. In order to simulate the V-trough, we followed essential steps. Firstly, the parameters that affect the system were defined as global parameters, either geographical or geometrical parameters. The length and the width of the PV panel were fixed to 1.0 m and 0.5 m, respectively, which are the typical measurement of a PV panel present in the market. The day number in the year N was taken to be 172, as it represents summer solstice. This day has the longest daylight period and would give the maximum output for the LCPV system. In addition, for comparison, N was also taken to be 356, for the shortest daylight, to show the minimum output of such systems. Furthermore, B\({}_{\text{S}}\) was defined as a global parameter and used to calculate the intensity of the solar radiation that falls on the system for each city. The geometry of the V-trough for both cases (double and partial coverage) was then built. In this study, the simulation was performed for the ideal case of having 100% reflecting mirrors and the material of the PV panel 100% absorbent. Air and the materials of the system are considered homogeneous; hence, the refractive index is constant within each domain.  
The COMSOL physics module that was applied to the system was the geometrical optics interface, as it contains all the required physical laws to study the optical rays' interaction with the system. The process that was applied to the boundaries of the geometry was mainly the reflection of the rays off the mirrors' surface. The reflection type was set as a specular reflection with a reflectivity equal to one. The solar radiation option was chosen to enable the calculation of the amount of solar radiation falling on the geographical location under investigation. The amount of radiation falling on any specific location will depend on the day of the year, the time of day (which is defined as the solar time over the daylight interval), and the turbidity T\({}_{\text{R}}\).  
Two types of mesh generator were used. The first type is free triangular, which was created for the top surface of a PV, with a maximum element size equal to 0.0095 m. This size is more suitable with the number of incident rays that hit the PV surface satisfying the condition of one ray at each mesh element. The second type is free tetrahedral, which was used for the entire geometry with extremely fine element size.  
Figure 2: The two cases of mirrors’ length: (**a**) double coverage (L\({}_{2}\) = 2 L\({}_{1}\)) and (**b**) partial coverage (L\({}_{2}\) = L\({}_{1}\)). Here, L\({}_{1}\) is the width of the PV panel; L\({}_{2}\) is the width of both mirrors (M1 and M2), and 0 the inclination angle for each mirror.  
For the evaluation steps in the study, the ray-tracing technique was used to trace the solar radiation falling on the system under the conditions of each geographical location. By knowing the amount of power each ray holds, the amount of irradiance, \(\mathrm{B_{PV}}\), in \(\mathrm{W/m^{2}}\) falling on the PV panel can be calculated. Figure 3 shows the COMSOL calculation method structure.