## 2 Materials and Methods
### Periods of Operation of a Horizontal Single-Axis Tracking  
Knowing the exact instant where the periods of operation of a horizontal single-axis tracker occur is fundamental in this study. These periods of operation are identified as follows [9]: (i) normal tracking mode, (ii) backtracking mode and (iii) static mode. Each of these operation periods has a corresponding tilt angle for the \(PV\) field. These tilt angles are (i) \(\beta\), (ii) \(\beta_{B}\), and (iii) \(\beta_{\rm max}\), respectively. Obviously, these tilt angles influence the incident solar irradiance on the \(PV\) field. In the following section, these angles will be determined.  
The normal tracking mode is characterised by the use of a solar astronomical algorithm that allows the \(PV\) field to follow the daily movement of the Sun. This period of operation lasts for most of the day. This tracking algorithm is based on maximising the solar irradiance incident on the PV field. To do this, it minimises the angle formed by the solar beam and the normal beam to the \(PV\) module [10].  
Figure 3: A flowchart describing the procedure used.  
Figure 2: Photograph of a horizontal single-axis tracking.  
The backtracking mode is characterised by the use of an algorithm that avoids shadowing between adjacent solar trackers. In shaded \(PV\) modules, hot spots appear that are detrimental to the \(PV\) module itself [22]. The backtracking algorithm [14] is used during sunrise and sunset, when the solar height is low. This algorithm avoids shading but does not maximise the incident solar irradiance on the \(PV\) field.  
The static mode is characterised by the \(PV\) field being stationary at the limit of movement (\(\pm\beta_{\max}\)) of the solar tracker.  
These three modes of operation can follow the following sequence of operation (see Figure 4a):  
1. Sunrise backtracking mode. This mode of operation starts at sunrise (\(T_{R}\)) and ends at the limited range of movement (\(T_{b1}\)). During sunrise, the position of the \(PV\) field is horizontal and at the end of sunrise backtracking mode the tilt angle of the \(PV\) field is \(\beta_{\max}\).
2. Static mode. This mode of operation starts at the end of the sunrise backtracking mode (\(T_{b1}\)) and ends at the beginning of the normal tracking mode (\(T_{\beta 1}\)).
3. Normal tracking mode. This mode of operation starts at the movement limit before noon (\(T_{\beta 1}\)) and ends at the movement limit after noon (\(T_{\beta 2}\)).
4. Static mode. This mode of operation starts at the end of normal tracking mode (\(T_{\beta 2}\)) and ends at the beginning of the sunset backtracking mode (\(T_{b2}\)).
5. Sunset backtracking mode. This mode of operation starts at the limited range of movement (\(T_{b2}\)) and ends at sunset (\(T_{S}\)). During the beginning of the sunset backtracking mode, the tilt angle of the \(PV\) field is \(\beta_{\max}\), and at sunset the position of the \(PV\) field, the tilt angle is horizontal.  
There are five zones of operation. This sequence of operation may not be repeated every day. That is, the backtracking mode ends without reaching the static mode. Therefore, it goes directly to the normal tracking mode (see Figure 4b). In the three-zone operation sequence the \(PV\) field does not reach the movement limit. In this case, there is no static mode.