# Assessment of Transformer Fault Severity from Online Dissolved Gas Analysis Using Positive CUSUM
## 6 Case Study
### Transformer in the Steel Industry 2  
The steel factory employs a 96 MVA Arc Furnace transformer manufactured in 1992 with a rated voltage of 22/1.1 kV. This transformer is equipped with an online DGA monitoring device from Morgan Schaffer, Model Calisto 9, installed on 31 May 2012, as shown in Figure 13. The device records gas concentration data every three hours. Sample data from 31 May 2012, to 17 August 2012, are presented in Table 6, accompanied by graphs illustrating gas concentration, as depicted in Figure 14.  
On 18 July 2012, the transformer underwent maintenance and oil filtration. It was subsequently restored on 20 July 2012. On 12 August 2012, there was an abrupt increase in the transformer's gas levels, which comprised hydrogen, methane, ethane, and ethylene, as shown in Figure 15. Consequently, the factory removed the transformer from the system for inspection on 23 August 2012. Figure 11: Positive CUSUM, Actual NEI and Cumulative NEI. Figure 12: NEI\({}_{\text{CO}}\), Cumulative NEI and CO\({}_{2}\)/CO. Figure 14: Data of nine gases and TDCG. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Time** & \begin{tabular}{c} **H\({}_{2}\)** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **CH\({}_{4}\)** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **C\({}_{2}\)H\({}_{6}\)** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **C\({}_{2}\)H\({}_{4}\)** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **C\({}_{2}\)H\({}_{2}\)** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **CO** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **CO\({}_{2}\)** \\ **(ppm)** \\ \end{tabular} & \begin{tabular}{c} **O\({}_{2}\)** \\ **(ppm)** \\ \end{tabular} & \
\begin{tabular}{c} **N\({}_{2}\)** \\ **(ppm)** \\ \end{tabular} &
\begin{tabular}{c} **TDCG** \\ **(ppm)** \\ \end{tabular} \\ \hline
31 May 2012 04:22 & 99 & 91.8 & 50 & 64.2 & 1.6 & 440 & 3240 & 31,200 & 63,000 & 746.6 \\
31 May 2012 07:22 & 104 & 96.6 & 51.4 & 66.6 & 1.6 & 445 & 3350 & 31,400 & 65,000 & 765.2 \\
31 May 2012 10:22 & 107 & 99.6 & 52.6 & 68.2 & 1.6 & 450 & 3400 & 31,500 & 65000 & 779 \\
31 May 2012 13:22 & 108 & 100 & 52.8 & 68.4 & 1.6 & 460 & 3450 & 32,000 & 66,000 & 790.8 \\
31 May 2012 16:22 & 107 & 101 & 53.2 & 69 & 1.6 & 455 & 3450 & 31,300 & 66,000 & 786.8 \\
31 May 2012 19:22 & 108 & 100 & 53.2 & 68.8 & 1.6 & 450 & 3460 & 32,300 & 66,000 & 781.6 \\
31 May 2012 22:22 & 108 & 101 & 53 & 68.8 & 1.6 & 455 & 3470 & 32,300 & 66,000 & 787.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Sample DGA results from the steel factory in Case Study 2. Figure 13: Image of Calisto R9 unit installed at steel industry 2. Use the DGA data collected from the online monitoring device in the following manner:  
1. Using data from May to August 2012, eliminate any incomplete entries from the DGA results for all nine gas types, sampled every three hours. 2. Determine the total dissolved combustible gas (TDCG) and calculate its logarithmic value. 3. Determine the values of NEI\({}_{\text{HC}}\) and NEI\({}_{\text{CO}}\). 4. The information gathered from step 3 will be segmented into monthly data. Evaluate the NEI of hydrocarbon gas  
1. Determine the correlation between the log(TDCG) and the NEI\({}_{\text{HC}}\) using linear regression to calculate the coefficient of determination (R\({}^{2}\)) for each month, as illustrated in Table 7. It is observed that the highest R\({}^{2}\) value before oil purification is 0.9867, and after oil purification, it is 0.9893. The linear equation derived from the linear regression before oil purification, presented in Figure 16, is \[NEI_{Predict}=4.1346\times log(TDCG)-11.03\] (10) The linear regression after oil purification, presented in Figure 17, is \[NEI_{Predict}=0.5813\times log(TDCG)-0.9636\] (11)
2. Determine the difference (Diff) between the NEI data obtained from the DGA results and the NEI data calculated using the baseline equation. 3. Calculate the Positive CUSUM value following the steps outlined in Section 5.