*3.1. Cluster Analysis*

As mentioned above, the data used for the analyses included the electrical capacity and GDP in the new EU Member States. Their short forms are introduced for the analysis: **EC** is the **E**lectrical **C**apacity, which is the sum of the capacity of all types of electricity sources; **ECR** is the **E**lectrical **C**apacity **R**enewable, which is the total capacity of the renewable energy sources by the most commonly used divisions, i.e., hydro, geothermal, wind, and solar; and **ECRN** denotes **E**lectrical **C**apacity **R**enewable **N**ew, which is the total capacity of only new types of renewable energy sources, i.e., wind and solar.

Cluster analysis was conducted for the data from the beginning and end of the analyzed period, i.e., 2004 and 2016. For this purpose, the variable designations introduced above were additionally determined for the relevant year: EC2004, ECR2004, ECRN2004, GDP2004, EC2016, ECR2016, ECRN2016, and GDP2016. These variables were used to create indicators describing the ratio of electrical capacity from renewable sources to total electric capacity and the ratio of electrical capacity from renewable sources and all sources in the ratio of GDP, which is referred to in the literature as energy intensity. The developed indicators were divided into those concerning the analysis of all renewable energy sources (indicators renewable energy; IRE) and those that concern only renewable energy sources of new type (indicators renewable energy new; IREN) for both 2004 and 2016, as presented in Tables 1 and 2.





The above division of indicators allowed us to perform four cluster analyses (two for each of the analyzed years) to check how these groups changed over the period, but also to determine how the type of selected energy influenced the formation of these groups. The coefficients of variation of all indicators presented in Table 3 are 10% above the criterion, which means that they could be used for the cluster analysis.


**Table 3.** Coefficients of variation of the indicators.

Correlation coefficients between indicators are presented in Table 4.

The coefficient of correlation only exceeded 90% for the pairs of ECRN2004/GDP2004—ECRN2004/ EC2004. However, due to the high volatility of ECRN2004/GDP2004 of 227.0%, ECRN2004/EC2004 of 240.0%, and the need to examine this indicator, it was not rejected. The need to maintain the same set of variables to ensure comparability of results was also an argumen<sup>t</sup> for including these indicators. When analyzing the source data for 2004, we confirmed that the resulting correlation is apparent because it resulted from the lack of renewable energy sources of a new type in almost all studied countries, which further affected the almost zero value of the discussed factors. In subsequent years, the electrical capacity from new types of renewable energy sources increased, which confirms the need to retain all indicators to ensure the comparability of groups.


**Table 4.** Coefficients of variation of indicators.

Countries were grouped separately for each year: once for the indicators including all renewable energy sources (IRE), and the second for the indicators where only wind and solar power plants (IRENs) were accepted as renewable energy sources. In total, four analyses were performed, where the division of the optimal number of clusters was determined [40,41]. Statistica 12.5 (TIBCO Software Inc., Palo Alto, CA, USA) was used as a tool to develop clusters.

#### 3.1.1. Groups for IRE Indicators in 2004

In 2004 (and many years before), hydroelectric and geothermal power plants were the most frequently used renewable sources of electricity in the world, and the main source of energy in the Central and Eastern European countries (CEES) was hydroelectric power plants. While grouping such data in 2004, a tree diagram was developed, as shown in Figure 5.

**Figure 5.** Tree Diagram for IRE in 2004.

Cutting off the tree diagram at a distance of 10 resulted in three clusters containing countries (Table 5) with the averages of the groups shown in Table 6. The analysis of variance (ANOVA) for the indicators from Table 6 was completed at the 0.05 significance level. The P-value for each of the indicators is smaller than the assumed level of significance, which means statistically significant differences exist between the groups of countries listed in Table 5.





To compare groups, on the basis of Table 6, the values of indicators in each group were determined in relation to the general average, as shown in Figure 6.

**Figure 6.** Comparison of group averages for IRE in 2004.

When using cluster analysis for traditional renewable energy sources, three clusters were created for the IRE data in 2004. In Table 5, groups A and B contain six countries, while group C only contains Bulgaria. When analyzing Figure 6, in this group (and the only country in this group), renewable energy sources (ECR2004/EC2004) mean that it is ranked in the middle of the surveyed countries. However, high energy intensity (EC2004/GDP2004 and ECR2004/GDP2004) was the main reason for the creation of this group, which means high energy costs are responsible for generating the GDP of Bulgaria. Groups A and B are opposites in terms of traditional, renewable energy sources. Group A included countries whose main sources of electricity were non-renewable energy sources, and renewable energy sources accounted for only a small percentage of all electrical capacity or none at all, as shown in Figure 7.

**Figure 7.** Energy sources of the countries in group A in 2004.

In the countries from group B, traditional renewable energy sources accounted for for several dozen percent of all electricity sources, and the cost of electricity converted into GDP was moderate. This means that group B is the most ecological group of countries according to the assumed criterion for 2004.

#### 3.1.2. Groups for IRE Indicators in 2016

After joining the EU, new countries are obliged to implement a pro-ecological policy. For example, the Directive 2009/29/EC obliged Member States to reduce greenhouse gas emissions. With the increasing demand for electricity and restrictions resulting from EU directives, the most reasonable solution was to increase the electrical infrastructure capacity through investments in renewable energy sources. Treating all types of renewable energy sources in the same way and subjecting the countries to a re-analysis of clusters for 2016, a tree diagram was produced, as shown in Figure 8.

**Figure 8.** Tree diagram for IRE in 2016.

By cutting off the tree diagram at a distance of 10 for 2016 and 2004, three clusters re-emerged. Countries belonging to individual groups and average values in these groups are listed in Tables 7 and 8.


**Table 7.** Clusters for IRE in 2016.



The di fferences between groups are statistically significant, as demonstrated in the analysis of variance (*p*-value in Table 8). The values of the indicators in the groups in relation to the average of all groups are presented in Figure 9.

**Figure 9.** Comparison of group averages for IRE in 2016.

When comparing the results of the clustering analysis for 2016 with previously obtained results from 2004, no major changes are visible. The number of created groups is the same and their composition is identical. When comparing Figure 9 with its counterpart for data from 13 years ago (Figure 6), the similarities are noticeable. When analyzing Figure 9 more precisely, the biggest change is visible in group A, where the share of electrical capacity from renewable energy sources increased the most, both in relation to the total electrical capacity and the GDP. This conclusion is also confirmed by the analysis of the distribution of types of energy sources in the countries of group A, which is presented in Figure 10.

The traditional classification of renewable energy sources means that, as in the analyses presented above, the actual investment of countries in switching their economies to greener and more modern energy sources can be overlooked. This is due to the fact that hydroelectric power plants are also renewable energy sources, which in some countries have been a large part of electricity capacity for decades. This situation mean that with relatively young wind and solar energy infrastructure, expenditure on their development may be unnoticeable or misinterpreted if their electrical capacity in the analysis is included with the electric capacity from hydropower. Despite the classification of hydroelectric power plants as renewable energy sources, only small power plants with a capacity of up to several megawatts are considered as such. Larger hydropower plants have a negative impact on the environment, and thus should not be treated as renewable energy sources.

**Figure 10.** Energy sources in the countries of group A in 2016.

#### 3.1.3. Groups for IREN Indicators in 2004

In the last dozen or so years when writing about renewable energy, we were rather thinking of dynamically developing wind and solar energy, not about hydroelectric power plants. This trend resulted from the global energy policy, which assumes that renewable energy is not enough—it needs to be sustainable. For this reason, the analyses for 2004 and 2016 were reconstructed for a comparison with the assumption that only wind and solar power plants are renewable energy sources. These analyses showed the extent to which the new type of renewable energy sources affect the classification of countries and the ratio of electrical capacity only from this type of energy in relation to GDP. These indicators designated for this type of energy were designated as IREN.

Assuming that only wind and solar power plants are renewable sources of energy, in 2004, they constituted only 0.08% of the total electrical capacity. For comparison, the electrical capacity of the hydroelectric plants alone was 18.60%. The introduced change fully altered the tree diagram (Figure 11) resulting from cluster analysis for IREN indicators compared to that presented earlier for IRE indicators in 2004.

**Figure 11.** Tree diagram for IREN in 2004.

Cutting off the tree diagram as in the previous analyses at a distance of 10 resulted in the creation of three groups, but other than the C group, the groups included different countries (Table 9).


**Table 9.** Clusters for IREN in 2004.

Group averages and their values in relation to the overall average are presented in Table 10 and Figure 12. The analysis of variance at the significance level of 0.05 showed statistically significant differences between the values of indicators in these groups, which means the groups have been correctly created and are significantly different from each other.


**Figure 12.** Comparison of group averages for IREN in 2004.

As mentioned above, the groups based on IREN indicators have different compositions, but, as shown in Figure 12, their nature is also different. Group A only contains Latvia, which stands out from the rest of the world in having the largest electrical capacity from wind energy. Group C, as in previous analyses, contains only Bulgaria. Again, the main reason for this situation is the high cost of energy in relation to GDP. The largest group B contains as many as 11 countries where the electrical capacity from wind and solar plants in relation to the total electrical capacity of each of these countries is negligible.

#### 3.1.4. Groups for IREN Indicators in 2016

An increase in demand for electricity and the EU's climate policy has forced the Member States countries to invest in renewable energy sources. Wind and solar power plants belong to the most frequently developed investments in recent years. In most countries, the construction of new power plants for combustible fuels was practically discontinued due to their negative impact on the environment and long construction time and high costs. Similarly, the construction of nuclear power plants requires large financial outlays and building time. The security of these facilities and the use of radioactive waste are also debatable. Hydroelectric plants, although they are classified as renewable energy sources, but as mentioned before, have a negative impact on the natural environment if their power generated is greater than a dozen or so megawatts, and the vast majority of hydroelectric power plants in the studied countries produce much more power. The time required to design and build such plants is also quite long. Wind and solar power plants have become a natural choice as their construction time is shorter compared to power plants. The electrical capacity of wind and solar power plants depends mainly on the space they occupy, meaning smaller investors can also build them and create a dispersed network of small power plants. Considering only this type of power plants in cluster analysis allowed us to eliminate data disturbances caused by hydroelectric plants, and thus to more accurately group countries in terms of their investments in renewable energy sources. The tree diagram created for IREN indicators for 2016 is presented in Figure 13.

**Figure 13.** Tree diagram for IREN in 2016.

By cutting o ff the tree diagram, as in previous analyses, at a distance of 10, three clusters ere formed. Despite the same number of clusters as in the analysis for IRE 2016 indicators (Table 7), the clusters for IREN 2016 contain other countries (Table 11).


**Table 11.** Clusters for IREN in 2016.

Cluster averages were calculated to characterize clusters (Table 12) and the results are presented in relation to the average of all figures in Figure 14. As in all previous clusters, the analysis of variance of indicators in newly created groups was conducted. With the assumed significance level of 0.05, Table 12 shows that the *p*-value is always less than this value, indicating statistically significant di fferences between the clusters.

**Table 12.** Group averages for IREN in 2016.


The average values in the groups of IREN indicators for 2016 (Figure 14) are similar for IRE indicators for 2016 (Figure 9). However, this similarity is only accidental as the countries in particular groups for IREN indicators (Table 11) only slightly overlap the countries in the groups for the IRE indicators (Table 7). Groups A and B contain countries whose cost of obtaining energy is moderate in relation to GDP, whereas Romania is also in group C in addition to Bulgaria. Group C, therefore, contains the poorest countries of the EU, where the energy cost is highest in relation to GDP, but the share of wind and solar power plants in the electrical capacity simultaneously increased the most in these countries (Figure 15).

*Energies* **2019**, *12*, 2271

**Figure 15.** Energy sources in the countries of group C in 2016.

The structure of the electrical capacity divided into wind and solar power plants (renewable energy sources) and sum of non-renewable energy sources and hydro power is presented for groups A and B in Figures 16 and 17, respectively.

**Figure 16.** Energy sources in the countries of group A in 2016.

**Figure 17.** Energy sources in the countries of group B in 2016.

The exclusion of hydroelectric power plants from renewable energy sources led to the level of investments of individual countries in ecological sources of electricity being more visible in the conducted analyses. The countries of groups A and B in 2016 had a similar cost of energy conversion to GDP, but the level of investment in renewable energy sources was significantly di fferent. Four countries from group A during the 13 years only slightly increased the production of electricity from wind and solar power plants, which means that this group can be considered the least ecological. Group B contains 7 of the 13 countries and is characterized by a much higher increase in energy production from wind and solar farms than the B group with a similar cost of energy conversion to GDP.
