# Power Prediction of Bifacial Si PV Module with Different Reflection Conditions on Rooftop
## 2 Modeling and Method
### Prediction of the Total Irradiation  
The amount of total irradiation (_GHI_) can be considered the same as that measured in the solar irradiation system installed at the front of the module. The amount of _DNI_ can be obtained according to the installation location, time, and environment. The amount of direct irradiance can be obtained from Equation (7) [25].  
\[DNI=G\ \times\ cos\theta_{zs} \tag{7}\]  
In Equation (7), \(G\) is the amount of solar irradiation corresponding to the location, time, and environment on d\({}_{n}\) day of experiment and \(\theta_{zs}\) is the angle between the direction perpendicular (Zenith) to the ground and the sun. d\({}_{n}\) day is the number of days that have elapsed since the first day of a year. For example, 31 December has a d\({}_{n}\) day of 365 [26]. The tilted angle was changed from 20\({}^{\circ}\) to 90\({}^{\circ}\) in a step size of 0.1\({}^{\circ}\), and the corresponding value of maximum global irradiance for a specific period is defined as the optimal tilted angle [27].  
Figure 4 supports the process of obtaining the global irradiance value for the formula. Latitude is the angle measured at the center of the earth, between the equator plane and experiment point. It is expressed either north or south and varies from 0\({}^{\circ}\) to 90\({}^{\circ}\). Declination is the angle made between the plane of the equator and the line joining the two center of the earth and the sun. The declination varies between \(-23.45^{\circ}\leq\delta\leq 23.45^{\circ}\). It is positive during summer and negative during winter. The solar time is represented by \(\omega\). It is the sun's angular deviation from south and the range is \(-180^{\circ}\leq\omega\leq 180^{\circ}\), negative before solar noon. \(\theta_{ZS}\) is the Zenith Angle. It is incidence angle of sunbeam on a horizontal surface. During the same day, Zenith angle determines amount of radiation received by surface [25].  
\[G=1367\varepsilon_{0}0.7^{AM^{0.6\prime 8}} \tag{8}\]  
In Equation (8), \(\varepsilon_{0}\) is the eccentricity correction factor that corrects the eccentric observed value and converts it to the value at the original observation point. The Air Mass (_AM_) would be a coefficient that specifies the effect of the atmosphere on a clear day. \(cos\theta_{ZS}\) can be calculated by Equation (9).  
\[cos\theta_{ZS}=sin\delta sin\varnothing+cos\delta cos\varnothing cos\omega \tag{9}\]  
In Equation (9), \(\delta\) is the slope of the sun. \(\omega\) is expressed as \(\omega\) = 0\({}^{\circ}\) at noon and changes by 15\({}^{\circ}\) per hour. \(\varnothing\) represents the latitude of the measurement position.  
Figure 4: Terminologies for the measurement.  
In most engineering applications, the simplest expression for the eccentricity correction factor on \(\mathbf{d}_{n}\) day is given by Equation (10).  
\[\varepsilon=1+0.033 cos(\frac{360d_{n}}{365}) \tag{10}\]  
The slope \(\delta\) of the sun can be obtained from Equation (11).  
\[\delta=23.45^{\circ}sin[\frac{360(d_{n}+284)}{365}] \tag{11}\]  
The \(AM\) can be obtained from Equation (12).  
\[AM=\frac{1}{cos\theta_{ZS}} \tag{12}\]  
Based on the above, the \(DNI\) can be expressed as Equation (13)  
\[DNI\;=\;1367\times 23.45^{\circ}sin[\frac{360(d_{n}+284)}{365}]\times 0.7^{AM0.678}\times cos\theta_{ZS} \tag{13}\]