# Simulation of a Low Concentrator Photovoltaic System Using COMSOL
## 3 Results and Discussion
### Concentration Ratio  
The concentration ratio (CR) can be calculated by taking the ratio of the total amount of \(\mathrm{B_{PV}}\) falling on the panel to the total amount of \(\mathrm{B_{S}}\). By using the optimum inclination angles found above, we were able to simulate the performance of the model throughout the longest day in the year, when the system is located at different geographical locations. These simulations allowed the calculation of the CR of the V-trough model. The CR was calculated for the V-trough model for two geometrical designs and two operating methods. The two designs are, firstly, the large mirrors, which guarantee double coverage of the PV panel and, secondly, the smaller mirrors that reduce the size of the system but render the coverage only partial. The operating methods involve the number of times the inclinations of the mirrors are changed during the daylight period. The first case is when the inclination of the mirrors is changed every hour and set at the optimum angle for that hour. The second case is limited to three inclinations per day; one during the morning interval, the second during the noon period, and lastly a position during the afternoon interval. The limitation of positions in the second operation method is aimed at reducing the energy required for operating the system. For comparison, a third case will also be investigated wherein the mirrors remain fixed throughout the day at an angle of 65\({}^{\circ}\). Figure 8a,b show the performance of a PV system when placed in the city of Jeddah for the longest and shortest days of the year. Both figures illustrate the amount of \(\mathrm{B_{PV}}\) falling on the system in seven different situations compared to the amount of \(\mathrm{B_{S}}\). The first situation is when the PV panel is not attached to any mirrors; therefore, no concentration of radiation took place. The second and third situations are double and partial coverage, while changing the mirrors' inclination every hour of the daylight. The fourth and fifth situations are double and partial coverage when the mirrors' inclinations are changed only three  
Figure 7: The irradiance \(\mathrm{B_{PV}}\) at fixed \(\theta_{1}\) angles and variable \(\theta_{2}\) angles for partial coverage for the solar time from sunrise to 10:00 in Jeddah. times during the day; once in the morning period, the second during the noon interval, and the third during the afternoon. The values of the inclination angles that the mirrors were fixed at during these three periods were chosen to give the greatest amount of \(\mathrm{B_{PV}}\) during those intervals. These angles can be deducted from Figures 4-7. Table 2 lists these angles for both double and partial coverages when the mirrors are fixed at three positions. Lastly, as shown in Figure 8, the sixth and seventh situations are double and partial coverage for a fixed mirror's inclinations. The calculated \(\mathrm{B_{PV}}\) values for a simple PV panel followed the same pattern, as \(\mathrm{B_{S}}\) but did not show agreements in the early and later hours of the day. This is due to the large time intervals used during the calculation, in contrast with the empirical continuous function of \(\mathrm{B_{S}}\). When mirrors were attached to the PV panel to form a V-trough, the amount of \(\mathrm{B_{PV}}\) far exceeded that of \(\mathrm{B_{S}}\), reaching a maximum of more than 2000 \(\mathrm{W/m^{2}}\) for the longest day and 1400 \(\mathrm{W/m^{2}}\) for the shortest day during midday, both with double and partial coverage, when the position of the mirrors changed every hour. When the inclination of the mirrors changed only three times during the day, the maximum irradiance reaching the PV panel was also high compared to \(\mathrm{B_{S}}\). It is worth noting, as can be seen from Figure 8b, that, during the shortest day, there was no significant changes between the performance of the LCPV in the double and partial coverage cases, nor when the mirrors' position changed from 13 to 3 position per day.