# Determining Signatures for Energy Mix Produced by Photovoltaic Systems and Wind Turbines
## 4 Discussion
In this division, it is already possible to distinguish significantly more states. The research on the number of clusters did not have the character of mathematical optimization. The number of clusters was determined by the expert as a result of validation. This continued until a sufficient number of clusters was obtained due to their usefulness in  
Figure 12: Clustering results with 10 classes on a graph of the dependence of the power generated by the turbine on the power generated by the photovoltaic system. describing the photovoltaic-wind mix. In the case of division into seven clusters, the expert decided that the cluster in light green in Figure 11b should be decomposed. This was too large a group containing data responsible for the operation of the photovoltaic system and wind turbine with capacities greater than 1000 kW. As a result of increasing the number of classes to 10, three subclusters were selected for this cluster, as can be seen in Figure 13.  
The authors conducted a sensitivity analysis of the choice of the centroid initialization method in the k-means algorithm, which has a key impact on clustering quality and convergence speed. The authors tested Random Initialization (each centroid is randomly selected from the available data points) and First k rows (the first centroid is randomly selected, and the next ones are selected so that they are as far from the already selected ones as possible). No differences in clustering quality were observed in the measurement data. The authors then performed expert validation of the obtained clustering results in 10 classes. The results are presented in Table 1.  
Using the cluster color, you can introduce an additional dimension to the two-dimensional graph. Figure 13 shows the clustering results for the course of power generated by the photovoltaic system over time. In this two-dimensional graph, the cluster colors immediately provide information about how the power generated at the same time by the second energy source--the wind turbine--behaved. During the idle time of the photovoltaic system between midnight and sunrise, the wind turbine worked in the entire power range, which is not visible, however, because the clusters overlap. This is more visible \begin{table}
\begin{tabular}{c c c} \hline
**Cluster Number** & **Cluster Color** & **Cluster Physical Meaning** \\ \hline
0 & dark green & high and very high photovoltaic power, very low and low wind power \\
1 & red & very low and low photovoltaic power, medium wind power \\
2 & brown & medium photovoltaic power, very low and low wind power \\
3 & violet & medium photovoltaic power, medium wind power \\
4 & blue & very low and low photovoltaic power, high wind power \\
5 & orange & very low and low photovoltaic power, very high wind power \\
6 & light green & very low and low photovoltaic power, low wind power \\
7 & yellow & very low and low photovoltaic power, very low wind power \\
8 & pink & high and very high photovoltaic power, medium wind power \\
9 & mauve & high and very high photovoltaic power, high and very high wind power \\ \hline \end{tabular}
\end{table} 
Table 1: Expert validation of the obtained clustering results. Figure 13: Clustering results for the time history of the power generated by the photovoltaic system. during the day, when the power generation by the photovoltaic system is characterized by a greater spread. The graph also clearly shows clusters of clusters in the colors orange, brown, dark green, purple, light green, and red. The maximum power generated by the photovoltaic system at noon is accompanied by the generation of power by the wind turbine over the entire power range (clusters from dark green through pink to mauve). More about the clustering result can be seen in the time course of the power generated by the wind turbine. A greater spread of the generated power in the individual half-hour intervals allows you to easily see the cluster color and immediately assign the appropriate level of power generated by the photovoltaic system.