## 3 Methodology
### Choice of Solar Irradiance Estimation Model  
In the literature, there are many models for estimating the incident solar irradiance (\(I_{t}\)) on the \(PV\) field of \(PV\) module mounting systems. All the models consider that this solar irradiance can be decomposed into three components [40]: beam component (\(I_{bt}\)), diffuse component (\(I_{dt}\)), and reflected component (\(I_{rt}\)). All the models use the same equations to determine \(I_{bt}\) and \(I_{rt}\). Equations (1) and (3) are used to calculate these components. In contrast, there is no single equation for calculating the diffuse component. Each model has its own equation. These models can be classified as isotropic or anisotropic. The [PERSON] model [41], the [PERSON] model [42], and the [PERSON] model [43] are isotropic models. And the [PERSON] model [44], the [PERSON] model [45], the Hay-Davies model [46], the \(HDKR\) model [47], etc., are anisotropic models. In this study, we used an anisotropic model. Several studies have shown that anisotropic models obtain better results than isotropic models, but they are more complex to use [48]. The Klucher model is more complex and obtains good results in the anisotropic model segment [49]. Therefore, we will use the Klucher model, defined by Equation (4). The three components of the incident solar irradiance (\(I_{t}\)) on the \(PV\) field are shown below:  
**Beam component**  
The researchers consider that the beam component is the geometric relationship between the horizontal surface and the surface of the photovoltaic field. The beam component can be calculated using the following equation [40]:  
\[I_{bt}(n,T,\beta)=I_{bh}(n,T)\cdot\frac{\cos\theta_{i}(n,T)}{\cos\theta_{z}(n,T)} \tag{1}\]  
\[R_{b}=\frac{\cos\theta_{i}(n,T)}{\cos\theta_{z}(n,T)} \tag{2}\]  
where \(I_{bh}(n,T)\) is the hourly distribution of the beam horizontal solar irradiance (\(\rm{W/m^{2}}\)), \(R_{b}\) is the variable geometric factor, which is a ratio of tilted and horizontal solar beam irradiance, \(n\) is the ordinal of the day (day), \(T\) is the solar time (h), \(\theta_{z}\) is the zenith angle of the sun (\({}^{\circ}\)), and \(\theta_{i}\) is the incident angle (\({}^{\circ}\)). **Reflected component**  
The researchers assume that the reflected component depends on numerous factors, and, therefore, it is practically impossible to determine it precisely. The reflected component can be estimated using the following equation proposed by [PERSON] and [PERSON] [41]:  
\[I_{rt}(n,T,\beta)=(I_{bh}(n,T)+I_{dh}(n,T))\cdot\rho_{g}\cdot\left(\frac{1- \cos\beta(n,T)}{2}\right) \tag{3}\]  
Figure 4: A flowchart outlining the proposed methodology. where \(I_{bh}(n,T)\) is the hourly distribution of the beam horizontal solar irradiance (W/m\({}^{2}\)), \(I_{dh}(n,T)\) is the hourly distribution of the diffuse horizontal solar irradiance (W/m\({}^{2}\)), \(n\) is the ordinal of the day (day), \(T\) is the solar time (h), \(\beta\) is the tilt angle of the \(PV\) field (\({}^{\circ}\)), and \(\rho_{g}\) is the ground reflectance (_dimensionless_). **Diffuse component**  
This component can be estimated using the following equation proposed by [PERSON] [44]:  
\[I_{dt}(n,T,\beta)=I_{dh}(n,T)\cdot\left(\frac{1+\cos\beta(n,T)}{ 2}\right)\cdot\left(1+F_{k}\cdot\sin^{3}\left(\frac{\beta(n,T)}{2}\right)\right) \\ \cdot\left(F_{k}\cdot\cos^{2}(\theta_{i}(n,T))\cdot\cos^{3}( \theta_{2}(n,T))\right) \tag{4}\]  
\[F_{k}=1-\left(\frac{I_{dh}}{I_{gh}}\right)^{2} \tag{5}\]  
where \(I_{gh}(n,T)\) is the hourly distribution of the global horizontal solar irradiance (W/m\({}^{2}\)), \(I_{dh}(n,T)\) is the hourly distribution of the diffuse horizontal solar irradiance (W/m\({}^{2}\)), \(n\) is the ordinal of the day (day), \(T\) is the solar time (h), \(\beta\) is the tilt angle of the \(PV\) field (\({}^{\circ}\)), and \(F_{k}\) is the Klucher coefficient (_dimensionless_). To operate with Equations (1)-(4), it is essential to know \(I_{bh}\), \(I_{dh}\), \(\beta\), \(\theta_{z}\), \(\theta_{i}\), and \(\rho_{g}\).