# Increasing Photovoltaic Systems Efficiency Through the Implementation of Statistical Methods
## 4 Results
### Analysis of the ANOVA Method Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Month** & **10\({}^{\circ}\)** & **20\({}^{\circ}\)** & **30\({}^{\circ}\)** & **37\({}^{\circ}\)** & **40\({}^{\circ}\)** & **50\({}^{\circ}\)** & **60\({}^{\circ}\)** & **70\({}^{\circ}\)** \\ \hline January & 39 & 46 & 52 & 55 & 57 & 60 & 61 & 61 \\ February & 54 & 61 & 66 & 68 & 69 & 71 & 70 & 69 \\ March & 97 & 105 & 110 & 112 & 112 & 112 & 110 & 104 \\ April & 128 & 133 & 135 & 135 & 134 & 130 & 123 & 113 \\ May & 150 & 151 & 149 & 146 & 144 & 137 & 126 & 112 \\ June & 157 & 156 & 152 & 148 & 146 & 136 & 123 & 107 \\ July & 166 & 166 & 163 & 159 & 157 & 147 & 134 & 118 \\ August & 155 & 159 & 160 & 159 & 158 & 152 & 142 & 129 \\ September & 119 & 127 & 132 & 134 & 135 & 134 & 130 & 122 \\ October & 79 & 89 & 97 & 101 & 102 & 105 & 105 & 102 \\ November & 44 & 52 & 59 & 62 & 63 & 66 & 68 & 67 \\ December & 33 & 39 & 45 & 48 & 49 & 52 & 54 & 54 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PVGIS predicts the annual energy production (MWh) of PV plants at seven different tilt angles. The selected cases were chosen so that we have two sets of data with different ranges of variation (5 months and 3 months, respectively) to apply the presented statistical method. Table 5 shows the characteristic values that express the amount of electrical energy obtained depending on the inclination angle. These values were selected from Table 3 above. Column 37\({}^{\circ}\) means the optimum value of the tilt angle of the panel for which the maximum annual electric energy is obtained according to the PVGIS platform for the geographical and climatological coordinates considered. Next, Table 6 was built with 24 columns corresponding to the 24 values from Table 5, representing the ranks under Relation (2). The values are placed in ascending order. Where we have identical values, the corresponding rank is the arithmetic mean of the ranks corresponding to similar values. Ranks are relative numbers to 100, which represents the minimum value. Next, the table of ranks was built for the three analysed months: May, July, and September (Table 7). The last two rows in Table 7 represent the sum of the ranks and the square of the sum of the ranks for the analysed cases, respectively. Next, the equation characteristic of the \(H_{STAT}\) (Kruskal-Wallis test) was applied:  
\[H_{STAT}=\text{14.03} \tag{6}\]  
Relationship (6) represents the value of the test applied in the present case, called the H statistic (\(H_{STAT}\)). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Rank** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** \\ \hline Value & 112 & 118 & 119 & 122 & 126 & 127 & 130 & 132 & 134 & 134 & 134 & 135 \\ Avg rank & & & & & & & & & **10** & & \\ \hline
**Rank** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** & **21** & **22** & **23** & **24** \\ \hline Value & 137 & 144 & 146 & 147 & 149 & 150 & 151 & 157 & 159 & 163 & 166 & 166 & **23.5** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Case A: Table of values with explanation of ranks. \begin{table}
\begin{tabular}{c c c} \hline
**Case** & **Months Under Surveillance** \\ \hline A & May 2024 & July 2024 & September 2024 \\ B & June 2024 & July 2024 & August 2024 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Distributions per month for the data analysed. \begin{table}
\begin{tabular}{c c c} \hline
**Orientation** & **May** & **July** & **September** \\ \hline
10\({}^{\circ}\) & 150 & 166 & 119 \\
20\({}^{\circ}\) & 151 & 166 & 127 \\
30\({}^{\circ}\) & 149 & 163 & 132 \\
37\({}^{\circ}\) & 146 & 159 & 134 \\
40\({}^{\circ}\) & 144 & 157 & 135 \\
50\({}^{\circ}\) & 137 & 147 & 134 \\
60\({}^{\circ}\) & 126 & 134 & 130 \\
70\({}^{\circ}\) & 112 & 118 & 122 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Case A: Monthly energy production and ranks related to the panel’s angle (in MWh).