# Simulation of a Low Concentrator Photovoltaic System Using COMSOL
## 3 Results and Discussion
### Optimum Inclination Angles of Mirrors  
#### 3.1.1 Double Coverage  
In order to find the optimum inclination angles of the mirrors, the daylight was divided into three periods: morning (sunrise to 10:00), noon (10:00-14:00), and afternoon (14:00-sunset). The angles for the noon period were determined first, since the rays of the sun are almost normal to the PV panel; hence, \(\theta\) for both mirrors will be the same. Figure 4 shows the amount of \(\mathrm{B_{PV}}\) falling on the PV panel vs. inclination angles at each hour for the selected cities. It can be seen from Figure 4 that, for all chosen cities, the most significant amount of \(\mathrm{B_{PV}}\) was at 12:00, where \(\alpha\) is almost \(90^{\circ}\), as expected. Moreover, the optimum angle for all cities at 12:00 was the same. This value was \(70^{\circ}\) for both mirrors. Although the amount of \(\mathrm{B_{PV}}\) is maximum at \(70^{\circ}\) inclination for both mirrors exactly at noon, its value drops at times before and after 12:00 at this angle. In fact, the amount of \(\mathrm{B_{PV}}\) can become a minimum at \(70^{\circ}\) inclination at the beginning or end of the noon period, and other angles show better performance. However, regardless of this fluctuation at the \(70^{\circ}\) inclination, this angle remains the optimum angle for the whole noon period, since the average \(\mathrm{B_{PV}}\) value over the whole length of this period is the highest among all inclination angles. Moreover, the behavior of \(\mathrm{B_{PV}}\) away from sharp noon was found to be different for the different cities. This is attributed to the effect of the location of each city and its longitude angle. For examples, cities that have comparable longitude angles, such as Jeddah and Aljawf (\(\mathrm{l}\approx 39^{\circ}\)), exhibited similar \(\mathrm{B_{PV}}\) behavior throughout the noon period. The other three cities, Dhahran (\(\mathrm{l}\approx 50^{\circ}\)), Sharurah (\(\mathrm{l}\approx 47^{\circ}\)), and Riyadh (\(\mathrm{l}\approx 46.7^{\circ}\)), showed similar behavior since their longitude angles are similar.  
Figure 3: Detailed steps of the COMSOL calculation method structure.  
For the morning and afternoon periods, \(\theta\) has to be different for both mirrors in order to avoid the effect of shading from the opposite mirror. Figure 5 illustrates the performance of the model in the morning period for each city when \(\theta_{1}\) is fixed at specific angles equal to, greater than, or smaller than \(\alpha\), while \(\theta_{2}\) varies from 70\({}^{\circ}\) to 125\({}^{\circ}\) (measured from the horizontal of the opposite mirror). It can be seen from Figure 5 how the amount of \(\mathrm{B_{PV}}\) is greatly influenced by the inclination angles of the two mirrors. At 6:00 a.m., the highest  
Figure 4: The irradiance \(\mathrm{B_{PV}}\) at different inclination angles in the case of double coverage for the solar time from 10:00 to 14:00 (\(\theta_{1}=\theta_{2}\)) for the selected cities.  
amount of \(\mathrm{B_{PV}}\) was when \(\theta_{1}=5^{\circ}\) and \(\theta_{2}=125^{\circ}\) for all cities, while \(\alpha\) varied between \(5^{\circ}\) to \(14^{\circ}\). As the day progresses, the optimum angle \(\theta_{2}\) shifts toward smaller inclination angles, reaching a value of between \(\theta_{2}=95^{\circ}\) and \(105^{\circ}\) at 9:00 a.m. Furthermore, the amount of \(\mathrm{B_{PV}}\) is affected by the relation between \(\theta_{1}\) and \(\alpha\). As \(\theta_{1}\) becomes comparable to \(\alpha\), the amount of \(\mathrm{B_{PV}}\) decreases. This is due to the fact that, in this case more rays were blocked by mirror M1. Hence, the maximum values for \(\mathrm{B_{PV}}\) occurs when \(\theta_{1}\) is much lesser than \(\alpha\). Due to the symmetrical shape of the CPV, the same results were found when fixing the inclination angle of mirror M2 and varying that of M1. The optimum angles for the afternoon period were similar to the morning period, since the altitude angles are the same for the corresponding solar hour.  
Figure 5: _Cont._