## 3 Methodology
### Choice of Solar Irradiance Estimation Model
These parameters can be determined as follows:  
1. Determination of \(\beta\). The equations for calculating this parameter for the fixed tilt angle system and for the three operating modes of the horizontal single-axis tracker are as follows:  
**Fixed tilt angle system**:  
\[\beta=constant \tag{6}\]
**Backtracking mode** (horizontal single-axis tracker) [23]:  
\[\beta_{B}=\theta_{t}-\arccos\left(\frac{\varepsilon_{t}}{W}\cos\theta_{t}\right) \tag{7}\]  
where \(\theta_{t}\) is the solar transversal angle (\({}^{\circ}\)), \(\varepsilon_{t}\) is the pitch (m), and \(W\) is the width of a mounting system (m). **Static mode** (horizontal single-axis tracker) [23]:  
\[\beta_{s}=\pm\beta_{\text{max}} \tag{8}\]  
At sunrise, \(\beta_{s}=-\beta_{\text{max}}\), and at sunset, \(\beta_{s}=+\beta_{\text{max}}\). **Normal tracking mode** (horizontal single-axis tracker) [23]:  
\[\beta=\theta_{t}=\arctan(\tan\theta_{z}|\sin\gamma_{s}|) \tag{9}\]  
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 (\({}^{\circ}\)). 1. Determination of the \(\cos\theta_{z}\). The equation for calculating this parameter for both \(PV\) module mounting systems is as follows [23]:  
\[R_{b}=\frac{\cos\theta_{i}(n,T)}{\cos\theta_{z}(n,T)} \tag{2}\]0  
where \(\delta\) is the solar declination (\({}^{\circ}\)), \(\lambda\) is the latitude (\({}^{\circ}\)), and \(\omega\) is the hour angle (\({}^{\circ}\)). 2. Determination of the \(\cos\theta_{i}\). The equations for calculating this parameter for the fixed tilt angle system and for the three operating modes of the horizontal single-axis tracker are as follows:  
**Fixed tilt angle system**[50]:  
\[R_{b}=\frac{\cos\theta_{i}(n,T)}{\cos\theta_{z}(n,T)} \tag{2}\]1  
where \(\delta\) is the solar declination (\({}^{\circ}\)), \(\lambda\) is the latitude (\({}^{\circ}\)), \(\beta\) is the tilt angle (\({}^{\circ}\)), \(\gamma\) is the azimuth angle (\({}^{\circ}\)), and \(\omega\) is the hour angle (\({}^{\circ}\)). [PERSON] and [PERSON] propose two restrictions to apply Equation (11) [50]: (1) \(\theta_{i}\) can exceed 90 (\({}^{\circ}\)), which means that the sun is behind the \(PV\) field, and (2) the earth is not blocking the sun. **Backtracking mode** (horizontal single-axis tracker) [23]:  
\[R_{b}=\frac{\cos\theta_{i}(n,T)}{\cos\theta_{z}(n,T)} \tag{2}\]2  
**Static mode** (horizontal single-axis tracker) [23]:  
\[R_{b}=\frac{\cos\theta_{i}(n,T)}{\cos\theta_{z}(n,T)} \tag{2}\]3  
**Normal tracking mode** (horizontal single-axis tracker) [23]:  
\[R_{b}=\frac{\cos\theta_{i}(n,T)}{\cos\theta_{z}(n,T)} \tag{2}\]4  
where \(\delta\) is the solar declination (\({}^{\circ}\)), \(\beta\) is the tilt angle (\({}^{\circ}\)), \(\gamma_{s}\) is the azimuth of the Sun (\({}^{\circ}\)), \(\gamma\) is the azimuth angle (\({}^{\circ}\)), and \(\omega\) is the hour angle (\({}^{\circ}\)). (iv) Determination of \(\rho_{g}\). The quotient between \(I_{th}(n,T)\) and \(I_{gh}(n,T)\) is \(\rho_{g}\), and it is strongly dependent on the type of soil surrounding the \(PV\) field. A detailed study on the calculation of \(\rho_{g}\) was presented by [51]. This study characterised several types of materials used in the building sector. For example: for weathered concrete, \(\rho_{g}=0.22\); for red brick, dark paints, \(\rho_{g}=0.27\); for light brick, light paints, \(\rho_{g}=0.60\); for green vegetation, \(\rho_{g}=0.20\). If the characteristics of the soil are unknown, 0.2 is usually taken. The parameters \(I_{bh}\) and \(I_{dh}\) are determined in the following sections. Equations (15) and (17) can be used to determine the incident solar irradiation on the \(PV\) field, for fixed tilt angle systems and for horizontal single-axis trackers, respectively:  
**Fixed tilt angle system**[50]:  
\[R_{b}=\frac{\cos\theta_{i}(n,T)}{\cos\theta_{z}(n,T)} \tag{2}\]5  
where \(T_{R}\) is the sunrise solar time (h), and where \(T_{S}\) is the sunset solar time (h).