## 2 Methodology  
Vector Treatment of the Solar Position and the Estimation of the Solar Irradiance in the Celestial Sphere  
In accordance with the above, this work presents a study of the influence of design variables on the performance of a PV plant with dual-axis tracking and optimal tracking strategy. This tracking strategy, which is described in the following section, will determine the orientation of the solar collectors at all times, which allows for optimizing radiative capture while avoiding shadows between collectors. In the present work, to determine at each instant of time the orientation of these collectors, as well as the position of the Sun in the celestial sphere, vector notation is used. Figure 1 shows the coordinate system used, with the Ox axis oriented towards the west, the Oy axis towards the south, and the Oz axis towards the zenith. In this equation, \(\overset{\rightarrow}{i},\overset{\rightarrow}{j}\), and \(\overset{\rightarrow}{k}\) are the unit vectors on the axes Ox, Oy, and Oz, respectively; the unit vector that points towards the Sun, called the solar vector, \(\overset{\rightarrow}{s}\), will be expressed by Equation (1), in which \(\varphi\) is the latitude of the place, \(\delta\) the declination, and \(t\) the solar hour. \[\overset{\rightarrow}{s}=s_{x}\overset{\rightarrow}{i}+s_{y}\overset{ \rightarrow}{j}+s_{z}\overset{\rightarrow}{k}=\sin\Omega t\cos\delta \overset{\rightarrow}{i}+(\cos\Omega t\cos\delta\sin\varphi-\sin\delta\cos \varphi)\overset{\rightarrow}{j}+(\cos\Omega t\cos\delta\cos\varphi+\sin\delta \sin\varphi)\overset{\rightarrow}{k} \tag{1}\]  
Equation (2) shows the mathematical expression proposed by [PERSON] (1971) for calculating the declination, \(\delta\), as a function of the daily angle, \(\Gamma\), which in turn depends on the Julian day, \(d_{n}\), according to Equation (3). \[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]  
\[-0.002697\cos(3\Gamma)+0.00148\sin(3\Gamma)\]  
\[\Gamma(rad)=\frac{2\pi(d_{n}-1)}{365} \tag{3}\]  
The orientation of the collector plane at each instant of time can be represented by the unit vector perpendicular to it, \(\overset{\rightarrow}{n}\), or by the pair of unit vectors, \(\overset{\rightarrow}{u}\) and \(\overset{\rightarrow}{v}\), contained  
Figure 1: Astronomical and geometric magnitudes considered. in the collector plane, of which \(\overset{\rightarrow}{u}\) is horizontal and \(\overset{\rightarrow}{v}\) is parallel to the maximum slope direction of the collector plane (Figure 1). Thus, \(\gamma\) and \(\beta\) being the angles representing the azimuth and inclination of the collectors, respectively, the vectors \(\overset{\rightarrow}{n}\), \(\overset{\rightarrow}{u}\), and \(\overset{\rightarrow}{v}\) will be given by Equations (4)-(6), respectively. \[\overset{\rightarrow}{n}=\sin\beta\,\sin\gamma\overset{\rightarrow}{i}+ \sin\beta\cos\gamma\overset{\rightarrow}{j}+\cos\beta\overset{\rightarrow}{k} \tag{4}\]  
\[\overset{\rightarrow}{u}=-\cos\gamma\overset{\rightarrow}{i}+\sin\gamma \overset{\rightarrow}{j} \tag{5}\]  
\[\overset{\rightarrow}{v}=-\cos\beta\,\sin\gamma\overset{\rightarrow}{i}- \cos\beta\cos\gamma\overset{\rightarrow}{j}+\sin\beta\overset{\rightarrow}{k} \tag{6}\]  
For the characterization of the incident solar irradiance on the collector planes, the model of [PERSON] et al. [43] has been used.