## 5 Results
### Results Using Principal Component Analysis  
This section uses the proposed methodology of Section 4 for solving the OCR coordination problem by only using the graphic results of the PCA technique. The main objective of PCA is to extract the most important information from the data and then represent it as a set of new orthogonal variables called principal components. The original number of variables is generally reduced when using the principal components; hence, the dataset can be analyzed using fewer variables. After carrying out the simulations in the microgrid, a total of 75 variables were identified. After the applications of the PCA technique, 15 principal components were obtained. The 15 new variables or principal components extract the most important information from the data. An analysis of total variance was used to determine the most significant principal components. The analysis of variance allows knowing the principal components found which gather the most information from the original dataset. In Figure 4, the total variance in percentage of the first seven principal components is presented since the rest are not significant enough to express the behavior of the data. It can be seen that principal component number one describes 76.14% of the total information in the original data, while the principal components two, three, and four describe 12.4%, 4.1%, and 3.5%, respectively. As a conclusion, there is only a need to consider the first four principal components for a detailed analysis of the data, since they describe 96.12% of the information within the original dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Clusters** & **OS** & **OT (s)** & **Viol** \\ \hline
1 & OS4 OS8 OS12 OS16 & 109.15 & 0 \\ \hline
2 & OS1 OS5 OS9 OS13 OS15 & 113.73 & 2 \\ \hline
3 & OS6 OS7 OS10 OS11 OS14 & 214.31 & 0 \\ \hline
4 & OS2 OS3 & 34.28 & 0 \\ \hline Total & & 471.49 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results using K-means clustering as proposed in [20; 23]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Relay** & **ipickup** & **TMS C1** & **TMS C2** & **TMS C3** & **TMS C4** \\ \hline R1 & 200 & 0.3042 & 0.1839 & 0.3587 & 0.1871 \\ R2 & 200 & 0.1000 & 0.3979 & 0.2648 & 0.1000 \\ R3 & 200 & 0.2171 & 0.1146 & 0.2545 & 0.1000 \\ R4 & 200 & 0.2071 & 0.5302 & 0.3971 & 0.2323 \\ R5 & 200 & 0.2052 & 0.1000 & 0.1000 & 0.1515 \\ R6 & 200 & 0.1789 & 0.6626 & 0.5294 & 0.3646 \\ R7 & 1200 & 0.4874 & 0.5344 & 0.4394 & 0.3189 \\ R8 & 200 & 0.2454 & 0.1312 & 0.3336 & 0.2500 \\ R9 & 200 & 0.2329 & 0.3217 & 0.4413 & 0.1000 \\ R10 & 200 & 0.1000 & 0.2601 & 0.3634 & 0.1000 \\ R11 & 260 & 0.2628 & 0.1675 & 0.3364 & 0.2666 \\ R12 & 200 & 0.1000 & 0.4229 & 0.4713 & 0.1000 \\ R13 & 352 & 0.2886 & 0.2514 & 0.4079 & 0.2033 \\ R14 & 260 & 0.2523 & 0.3793 & 0.2436 & 0.1415 \\ R15 & 220 & 0.1757 & 0.3117 & 0.2487 & 0.2007 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Coordination adjustments with K-means clustering. Principal components 1 and 2 are studied in order to perform a graphic analysis, since they describe 88.54% of the information within the original dataset. Figure 5 illustrates the behavior of the original variables with respect to the principal components by means of a biplot diagram, this being the original variables represented through a vector. The direction and length of the vector indicate how each original variable contributes to principal components 1 and 2. In the first quadrant of Figure 5, there are several vectors that feature positive coefficients for components 1 and 2. In the second quadrant, the variables that have a positive coefficient for component 2 and negative coefficients for component 1 are observed. In the third quadrant, the variables that have negative coefficients for components 1 and 2 are observed. In the fourth quadrant, the variables that have a positive coefficient for component 1 and negative coefficients for component 2 are depicted.