## 5 Experimental Results
\begin{array}{cccccc}1&1.8&3.06&3.06&4.284&5.1408\\ 1/1.8&1&1.7&1.7&2.38&2.856\\ 1/3.06&1/1.7&1&1&1.4&1.68\\ 1/3.06&1/1.7&1&1&1.4&1.68\\ 1/4.284&1/2.38&1/1.4&1/1.4&1&1.2\\ 1/5.1408&1/2.856&1/1.68&1/1.68&1/1.2&1\end{array} \right].\]  
According to Equation (2), the subjective weights of six indices such as frequency deviation, voltage total harmonic distortion, voltage fluctuation, voltage flicker, voltage deviation and three-phase voltage unbalance are calculated in order:  
\[\alpha_{j}=(0.379205,\,0.210669,\,0.123923,\,0.123923,\,0.088516,\,0.073764).\]  
The EW method is used to calculate the objective weights of the indices. The data can be normalized according to Equations (4) and (5) to obtain the characteristic proportion matrix \(\mathbf{P}_{ij}\). The objective weights of each index can be calculated according to Equations (6)-(8):  
\[\beta_{j}=(0.126304,\,0.212929,\,0.161242,\,0.18105,\,0.153006,\,0.165469).\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \(\mathbf{x_{1}}\) & \(\mathbf{x_{2}}\) & \(\mathbf{x_{3}}\) & \(\mathbf{x_{4}}\) & \(\mathbf{x_{5}}\) & \(\mathbf{x_{6}}\) \\ \hline \multirow{2}{*}{\(\mathbf{x_{1}}\)} & Pcc & 1 & \(-0.526\) & 0.477 & 0.280 & \(-0.283\) & \(-0.526\) \\  & significance level & — & 0.362 & 0.416 & 0.648 & 0.645 & 0.362 \\ \hline \multirow{2}{*}{\(\mathbf{x_{2}}\)} & Pcc & \(-0.526\) & 1 & 0.478 & 0.328 & 0.950 1 & 1.000 2 \\  & significance level & 0.362 & — & 0.415 & 0.590 & 0.013 & 0.000 \\ \hline \multirow{2}{*}{\(\mathbf{x_{3}}\)} & Pcc & 0.477 & 0.478 & 1 & 0.706 & 0.676 & 0.478 \\  & significance level & 0.416 & 0.415 & — & 0.182 & 0.211 & 0.415 \\ \hline \multirow{2}{*}{\(\mathbf{x_{4}}\)} & Pcc & 0.280 & 0.328 & 0.706 & 1 & 0.344 & 0.328 \\  & significance level & 0.648 & 0.590 & 0.182 & — & 0.571 & 0.590 \\ \hline \multirow{2}{*}{\(\mathbf{x_{5}}\)} & Pcc & \(-0.283\) & 0.950 1 & 0.676 & 0.344 & 1 & 0.950 1 \\  & significance level & 0.645 & 0.013 & 0.211 & 0.571 & — & 0.013 \\ \hline \multirow{2}{*}{\(\mathbf{x_{6}}\)} & Pcc & \(-0.526\) & 1.000 2 & 0.478 & 0.328 & 0.950 1 & 1 \\  & significance level & 0.362 & 0.000 & 0.415 & 0.590 & 0.013 & — \\ \hline \hline \end{tabular} 1
[FOOTNOTE:1]Footnote 1: Correlation is significant on the 0.05 layer (two sides), 2  
\end{table} 
Table 4: Pearson correlation analysis of measured data. According to Equation (9), the combined weights of PQ indices can be calculated as follows:  
\[\mathbf{w}_{j}=(0.297634,\,0.278758,\,0.124171,\,0.139425,\,0.084163,\,0.075849).\]  
According to Equation (10), the measured data of Table 3 is weighted to obtain a weighted normalized matrix \(C_{ij}\), as shown in Table 5. In addition, the positive and negative ideal solutions are determined by Table 5, which are:  
\[A^{+}=(0.011905,\,0.228581,\,0.105545,\,0.030674,\,0.139711,\,0.043992),\]  
\[A^{-}=(0.056550,\,0.376323,\,0.175081,\,0.073895,\,0.324028,\,0.093294).\]  
According to Equations (14) and (15), the Mahalanobis distance of each evaluation sample to positive and negative ideal solutions can be obtained by Matlab (version, Manufacturer, City, US State abbrev. if applicable, Country):  
\[M_{i}^{+}=(2.1176,\,2.5083,\,2.9249,\,1.0889,\,3.1036),\]  
\[M_{i}^{-}=(2.6738,\,2.6294,\,1.2683,\,2.9900,\,1.7596).\]  
According to Equation (16), the proximity of each evaluation sample can be obtained, which are: \(c_{1}=0.558041,\,c_{2}=0.511785,\,c_{3}=0.302466,\,c_{4}=0.733041,\,c_{5}=0.361819\). Then, the proximity of each evaluation sample is sorted as: \(c_{4}>c_{1}>c_{2}>c_{5}>c_{3}\). In order to test the superiority and rationality of the proposed algorithm, the calculation results of the traditional TOPSIS method in [15] are compared with the results in this paper, as shown in Table 6. It can be seen that the proximity values calculated by the traditional TOPSIS method in [15] are: \(c_{4}>c_{1}>c_{2}>c_{3}>c_{5}\), that is, sample \(4>\) sample \(1>\) sample \(2>\) sample \(3>\) sample \(5\), where, \"\(>\)\" means \"better than\".