# Power Transformer Fault Diagnosis Based on Dissolved Gas Analysis by Correlation Coefficient-DBSCAN
## 3 Improved CCDBSCAN Algorithm
### Introduction of Correlation Coefficient
It can be seen that the phenomenon of high correlation of DGA data of the same fault exists, and the correlation coefficient is generally greater than 0.95, but there is also a phenomenon, that is, the correlation of the last six types of faults in the matrix is relatively high. For example, the correlation between the seventh and the eighth data of the same fault type is 0.99, but the correlation coefficient between the seventh data and the ninth to twelfth fault data is also as high as 0.92. Due to the low differentiation, it will bring some difficulties to clustering. The reason is analyzed, because the seventh and eighth data belong to PD, the characteristic gas is hydrogen, while the ninth, tenth and eleventh,  
Figure 1: Line chart of DGA gas content of 12 fault transformers. twelfth data belong to D1 and D2, and acetylene is the characteristic gas. However, due to the lower content of acetylene gas, the correlation coefficient of direct calculation data does not highlight the impact of acetylene gas content in the larger hydrogen content change, that is, the direct correlation analysis of the original data will cause the annihilation of sample attribute information. Therefore, the following research has been carried out in this paper: multiply the percentage of ethylene and acetylene content in seventh to tenth data by the amplification factor \(\alpha_{1},\alpha_{2}\), and then carry out the correlation analysis. \[R=\left[ \begin{array}{cccccccccccc}1.00&0.96&0.51&0.89&0.39&0.40&0.66&0.72&0.49 &0.69&0.61&0.61\\ 0.96&1.00&0.67&0.95&0.62&0.63&0.54&0.59&0.41&0.57&0.58&0.53\\ 0.51&0.67&1.00&0.84&0.78&0.81&-0.22&-0.16&-0.26&-0.18&-0.05&-0.19\\ 0.89&0.95&0.84&1.00&0.64&0.67&0.29&0.36&0.17&0.34&0.35&0.28\\ 0.39&0.62&0.78&0.64&1.00&1.00&0.00&0.00&0.04&0.00&0.29&0.12\\ 0.40&0.63&0.78&0.64&1.00&1.00&-0.01&-0.01&0&-0.02&0.25&0.09\\ 0.66&0.54&-0.22&0.29&0.00&-0.01&1.00&0.99&0.81&0.92&0.83&0.92\\ 0.72&0.59&-0.16&0.36&0.00&-0.01&0.99&1.00&0.79&0.91&0.81&0.89\\ 0.49&0.41&-0.26&0.17&0.04&0.00&0.81&0.79&1.00&0.95&0.96&0.97\\ 0.69&0.57&-0.18&0.34&0.00&-0.02&0.92&0.91&0.95&1.00&0.93&0.97\\ 0.61&0.58&-0.05&0.35&0.29&0.25&0.83&0.81&0.96&0.93&1.00&0.98\\ 0.61&0.53&-0.19&0.28&0.12&0.09&0.92&0.89&0.97&0.97&0.98&1.00\\ \end{array} \right]\]  
The line chart of DGA gas content obtained when \(\alpha_{1}=1,\alpha_{2}=1.35\) is shown in Figure 2.  
The correlation coefficient matrix of data 7 to 10 is:  
\[R=\left[ \begin{array}{cccc}1.00&0.99&0.69&0.88\\ 0.99&1.00&0.64&0.86\\ 0.69&0.64&1.00&0.92\\ 0.88&0.86&0.92&1.00\\ \end{array} \right]\]  
It can be seen that when the acetylene content is multiplied by 1.35, the correlation of the same fault category gas remains high, while the correlation of different types of fault gas becomes smaller. For example, the correlation coefficient of the seventh and the tenth data is reduced from 0.92 to 0.88, which makes the differentiation of different fault gas data more obvious. It can be seen that finding the appropriate amplification coefficient is the next step for research, so that the characteristic gas of each kind of fault can be better reflected in the correlation coefficient. Figure 2: Line chart after gas content amplification.