## 2 Materials and Methods
### Incident Solar Irradiance on the Photovoltaic Field
#### 2.2.3 Ground-Reflected Component Modelling  
The ground-reflected component depends on many factors that make it impossible to calculate it accurately. Most authors use the Liu-Jordan model. Equation (3) is used to calculate this component as follows [10]:  
\[I_{rt}(n,T,\beta)=(I_{bh}(n,T)+I_{dh}(n,T))\cdot\rho_{g}\cdot\left(\frac{1- \cos\beta}{2}\right) \tag{3}\]  
where \(I_{rt}(n,T,\beta)\) is the ground-reflected component (\(W/\text{m}^{2}\)), \(I_{bh}(n,T)\) is the horizontal beam solar irradiance (\(W/\text{m}^{2}\)), \(I_{dh}(n,T)\) is the horizontal diffuse solar irradiance (\(W/\text{m}^{2}\)), \(\rho_{g}\) is the ground reflectance (\({}^{\circ}\)), \(n\) is the ordinal of the day (day), \(T\) is the solar time (h), and \(\beta\) is the tilt angle of \(PV\) field (\({}^{\circ}\)). Equations (1)-(3) have been used in many studies across different locations around the world. For example, [PERSON] et al. [23] used these equations in Spain, [PERSON] and [PERSON] [24] in Iran, [PERSON] et al. [25] in China, [PERSON] et al. [26] in Saudi Arabia, etc. Therefore, the incident solar irradiance on the \(PV\) field can be determined by Equation as follows (4):  
\[I_{t}(n,T,\beta,\gamma)=I_{bh}(n,T)\cdot\frac{\cos\theta_{i}}{ \cos\theta_{z}}+I_{dh}(n,T)\cdot\left(\frac{1+\cos\beta}{2}\right)+\\ (I_{bh}(n,T)+I_{dh}(n,T))\cdot\rho_{g}\cdot\left(\frac{1-\cos \beta}{2}\right) \tag{4}\]  
To calculate the three components it is necessary to know the following parameters in each mode of operation: \(\beta\), \(\cos\theta_{i}\), \(I_{bh}\) and \(I_{dh}\). The considerations listed below allow Equation (4) to be used as follows:  
1. \(\beta\) parameter. The equations for determining this parameter in each mode of operation are as follows:Equation (5) defines the position of the \(PV\) field in normal tracking mode as follows [10]:  
\[\beta=\theta_{t}=\arctan(\tan\theta_{z}|\sin\gamma_{s}|) \tag{5}\]  
where \(\theta_{t}\) is the solar transversal angle (\({}^{\circ}\)), \(\theta_{z}\) is the zenith angle of the Sun (\({}^{\circ}\)), and \(\gamma_{s}\) is the azimuth of the Sun (\({}^{\circ}\)). Equation (6) defines the position of the \(PV\) field in backtracking mode as follows [9]:  
\[\beta_{B}=\theta_{t}-\arccos\Bigl{(}\frac{e_{t}}{W}\cos\theta_{t}\Bigr{)} \tag{6}\]  
where \(\theta_{t}\) is the solar transversal angle (\({}^{\circ}\)), \(e_{t}\) is the pich (\(m\)), and \(W\) is the width of a mounting system (\(m\)). Equation (7) defines the position of the \(PV\) field in static mode as follows [9]:  
\[\beta_{s}=\pm\beta_{\rm max} \tag{7}\]  
(ii) \(\cos\theta_{i}\) parameter. The equations for determining this parameter in each mode of operation are as follows:  
Equation (8) defines the \(\cos\theta_{i}\) in normal tracking mode as follows [10]:  
\[\cos\theta_{i}=\sqrt{\cos^{2}\theta_{z}+\cos^{2}\delta\sin^{2}\omega} \tag{8}\]  
where \(\delta\) is the solar declination (\({}^{\circ}\)), and \(\omega\) is the hour angle (\({}^{\circ}\)). Equation (9) defines the \(\cos\theta_{i}\) in backtracking mode as follows [9]:  
\[\cos\theta_{i}=\cos\beta_{B}\cos\theta_{z}+\sin\beta_{B}\sin\theta_{z}\cos( \gamma_{s}-\gamma) \tag{9}\]  
Equation (10) defines the position of the \(PV\) field in static mode as follows [9]:  
\[\cos\theta_{i}=\cos\beta_{\rm max}\cos\theta_{z}+\sin\beta_{\rm max}\sin \theta_{z}\cos(\gamma_{s}-\gamma) \tag{10}\]  
(iii) \(I_{th}\) and \(I_{dh}\) parameters. To calculate the three components of the incident solar irradiance on the \(PV\) field, it is necessary to determine the incident solar irradiance on a horizontal surface, i.e., \(I_{bh}\) and \(I_{dh}\). The incident solar irradiance on a horizontal surface is site-specific, as it is significantly influenced by the local distribution of cloud cover [27]. The ideal situation for calculating \(I_{bh}\) and \(I_{dh}\) is to have a ground-level weather station at each location. The actual situation, however, is that the number of weather stations worldwide is very low.