## 1 Introduction  
At present, population growth, deficiencies in natural resources and global warming are producing challenges around the world. In recent years, various initiatives have been working on the development or replacement of the current power grid to obtain greater efficiency in the electrical system and a reduction in energy waste by reducing losses during distribution [1]. Such a system would contribute to the promotion of renewable resources and the minimisation of the environmental impact in the future. Therefore, there is a global requirement to preserve the environment and to improve the penetration of alternative energy resources [2]. Within the framework of renewable energies, solar energy is the form of energy that has shown the most remarkable growth in recent years thanks to the reduction of costs and to legal requirements in many countries [3, 4]. Similarly, photovoltaic (PV) technology is one of the current technologies with a better future projection due to its simplicity and scalability and the continuous manufacture, operation and maintenance reduction costs it enables for solar panels [5]. However, the lack of the linearity in the solar energy received by solar panels, mainly caused by Earth-Sun relative displacement, is a disadvantage to consider. It is necessary to redefine solar tracking systems by increasing the solar irradiance capture enabled by PV collectors and therefore improve energy production [6]. Classified according to the type of movement, the following systems can be considered: single-axis tracking systems, in which a mobile element adapts its position by rotating around a fixed axis; and two-axis tracking systems, in which the collector plane rotates around two fixed axes, allowing an orientation towards any direction of the celestial sphere [7,8]. Several studies have analysed the efficiency of energy production using two-axis trackers compared with single-axis tracking and fixed panels [9, 10, 11]. [PERSON] et al. [10] determined that the increase in solar production of a PV plant with two-axis trackers compared to a system with single-axis trackers at the same latitude is 0.42-23.4%. Similarly, the improvement compared to a fixed-panel system is around 17.22-31.23%. Other authors, such as [PERSON] et al. [6], concluded that fluctuations in energy production can be reduced depending on the tracker distribution in the PV plant. With regard to movement strategies, two types can be distinguished: those based on information from pyranometers and those based on mathematical statements, determined by terrestrial and solar movement. For this latter option two approaches can be considered. For the first, the sun's position is predicted by spherical trigonometry [12, 13, 14], and for the second, it is acquired by vectorial calculation [15,16]. This article uses vectorial calculation. The most frequently followed strategy in solar tracking is that based on the astronomical model. This method aims to minimise the angle composed by direct sunrays and the normal vector to the collector plane, thereby increasing the direct portion of solar irradiance. However, this strategy is not optimal for the PV energy case since it does not involve the remaining portions (diffuse and reflected) which also contribute to energy production. This issue was thoroughly studied by [PERSON] and [PERSON] [13], who found that on cloudy days astronomical tracking obtained an irradiance lower than fixed panels because during those days direct radiation fails. PV plant yields can be highly affected when panels are shaded by each other [17, 18, 19]. Two consequences can be derived from the shading effect on the panels. The first consequence is the reduction of captured irradiance since the direct component does not reach the cell surface. The second consequence is the increase in temperature of the shaded cell since it works as a resistive load absorbing heat from the adjacent cells which thus accelerates its deterioration [18,20].