# Increasing Photovoltaic Systems Efficiency Through the Implementation of Statistical Methods
## 4 Results
### Analysis of the ANOVA Method Results  
Regarding the statistical methods, a presentation of the PVGIS platform [30] with input and output data was provided to predict electricity production for a photovoltaic plant based on geographical and meteorological parameters, as well as the technical data of the used PV panels. Based on the data provided by the PVGIS platform, an analysis is conducted to examine the impact of a panel inclination angle on electricity production. The literature shows that orientation tracking systems can increase efficiency by up to 30% (depending on latitude), as shown in Figure 2, generated by the PVGIS platform. Series 1 (blue) represents the monthly electricity production for the photovoltaic system of 1.19 MWp in the case of fixed panels inclined at an angle of 30\({}^{\circ}\), series 2 (red)  
Figure 1: The STEM method algorithm flowchart. Figure 2: Tracking influence on monthly electricity production for latitude 45\({}^{\circ}\) for fixed (blue) and adjustable tilt angle: vertical (red), horizontal (grey), and two-axle (orange). and 3 (grey) for the case of single-axis tracking system--azimuth and tilt (inclination), respectively--and series 4 (orange) for the case of two-axis tracking systems. It is observed that there is no significant difference between the three tracking systems (with one axis and with two axes, respectively). Although the increase in electricity production is significant in the case of tracking systems, they are more complex, require maintenance, and may not be cost-effective for all applications. This analysis is fundamental to deciding to what extent the investment is economically justified, depending on geographical coordinates. In this respect, the statistical analysis carried out by the ANOVA method, corroborated by the data obtained through the PVGIS platform, shows the following: on the one hand, between three consecutive months, there is no statistically significant difference between the groups in terms of the angle of inclination; on the other hand, the panels can be segmented according to the angle of inclination. Keeping the criterion of three consecutive months, obtained by applying the ANOVA method, as an example for the case of latitude 45\({}^{\circ}\), an optimal arrangement would be the following:  
* For June, July, and August, an optimum tilt angle of 30\({}^{\circ}\) is obtained;
* For September, October, and November, an optimal tilt angle of 50\({}^{\circ}\) is obtained;
* For December, January, and February, an optimal tilt angle of 70\({}^{\circ}\) is obtained;
* For March, April, and May, an optimal tilt angle of 40\({}^{\circ}\) is obtained. The methodology remains valid for other geographical coordinates, provided the data are available from the PVGIS platform. **Case analysis--Fixed tilt angle**  
The statistical analysis begins with the specific case of a photovoltaic power plant with a capacity of 1.19 MWp [34], which generates a declared amount of renewable energy of approximately 1428 MWh/year. The envisaged PV system is 26\({}^{\circ}\)55\({}^{\prime}\) east longitude and 46\({}^{\circ}\)35\({}^{\prime}\) north latitude in Romania. Table 3 summarises these data, obtained through the PVGIS platform (PVGIS--re.jrc.europa.eu--European Union [33]) for each month of the year, with the values provided in MWh. The influence of the panels' inclination on annual electricity production will be analysed statistically, applying the Kruskal-Wallis test to sets of cases with three distributions. We propose analysing two sets of cases, each with three distributions, using July as a reference, as shown in Table 4.