# Assessment of Transformer Fault Severity from Online Dissolved Gas Analysis Using Positive CUSUM
## 6 Case Study  
### Transformer in the Steel Industry 1  
A steel factory uses a 130 MVA Arc Furnace transformer with a rated voltage of 33/1.25 kV, manufactured in 1997. The transformer uses a Morgan Schaffer brand online DGA monitor Model Calisto R9, as shown in Figure 1. This device measures nine gases (H\({}_{2}\), CH\({}_{4}\), C\({}_{2}\)H\({}_{6}\), C\({}_{2}\)H\({}_{4}\),C\({}_{2}\)H\({}_{2}\), CO, CO\({}_{2}\), O\({}_{2}\), N\({}_{2}\)) and records concentrations every four hours. The sample data is shown in Table 2. The DGA results from January to December 2023 of gases H\({}_{2}\), CH\({}_{4}\), C\({}_{2}\)H\({}_{6}\), C\({}_{2}\)H\({}_{4}\), C\({}_{2}\)H\({}_{2}\), CO, CO\({}_{2}\), O\({}_{2}\), N\({}_{2}\) and TDCG are shown. From Figure 2, it can be observed that there were abnormal data during the period from 13 February 2023 to 10 March 2023 due to an unusual decrease in DGA values. This was caused by the online DGA analyzer reporting lower-than-normal values for some gases. Therefore, the analysis needs to be divided into two periods: January to February and March to December. Utilize the DGA data obtained from the online measuring device to execute the following steps. 1. Take the data from January to February and March to December 2023 for all nine types of gas, at 4 h intervals. Remove the data points that lack complete information. 2. Determine the total dissolved combustible gas (TDCG) and calculate its logarithmic value. 3. Calculate the value of NEI\({}_{\rm HC}\) using the equation provided in (1) and the value of NEI\({}_{\rm CO}\) using the equation provided in (2). The chemical formula of the gas in the equation indicates its concentration under standard temperature and pressure condi \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**Time** & **H\({}_{2}\)** & **CH\({}_{4}\)** & **C\({}_{2}\)H\({}_{6}\)** & **C\({}_{2}\)H\({}_{4}\)** & **C\({}_{2}\)H\({}_{2}\)** & **CO** & **CO\({}_{2}\)** & **O\({}_{2}\)** & **N\({}_{2}\)** & **TDCG** \\  & **(ppm)** & **(ppm)** & **(ppm)** & **(ppm)** & **(ppm)** & **(ppm)** & **(ppm)** & **(ppm)** & **(ppm)** & **(ppm)** & **(ppm)** \\ \hline
1 January 2023 02:10 & 37 & 111 & 46.4 & 195 & 6.4 & 166 & 1290 & 18,500 & 41,000 & 561.8 \\
1 January 2023 06:10 & 37 & 111 & 46.2 & 194 & 6.4 & 164 & 1280 & 18,700 & 41,000 & 558.6 \\
1 January 2023 10:10 & 37 & 111 & 46.4 & 195 & 6.4 & 164 & 1290 & 18,600 & 40,000 & 559.8 \\
1 January 2023 14:10 & 36.5 & 111 & 46.2 & 194 & 6.4 & 164 & 1290 & 18,600 & 41,000 & 558.1 \\
1 January 2023 18:10 & 37 & 111 & 46.2 & 194 & 6.4 & 164 & 1290 & 18,700 & 41,000 & 558.6 \\
1 January 2023 22:10 & 37 & 112 & 46.2 & 196 & 6.4 & 168 & 1310 & 20,100 & 41,000 & 565.6 \\
2 January 2023 02:10 & 37 & 114 & 46.6 & 198 & 6.6 & 170 & 1330 & 20,300 & 41,000 & 572.2 \\
2 January 2023 06:10 & 37.5 & 113 & 46.8 & 198 & 6.6 & 170 & 1330 & 20,500 & 41,000 & 571.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sample DGA results from the steel factory in Case Study 1. Figure 1: Image of the Calisto R9 unit installed at steel industry 1.  
tions (273.15 K and 101.325 kPa). Table 3 presents the values of log(TDCG), NEI\({}_{\rm HC}\), NEI\({}_{\rm CO}\) and CO\({}_{2}\)/CO ratio. 4. The data obtained from step 3 are segmented into monthly data sets. Evaluate the NEI of hydrocarbon gas from January to February  
1. Determine the correlation between the log(TDCG) and the NEI\({}_{\rm HC}\) using linear regression to calculate the coefficient of determination (R\({}^{2}\)) for each month, as illustrated in Table 4. It was discovered that February had the highest R\({}^{2}\) value of 0.9706. The linear equation derived from the linear regression, presented in Figure 3, is  
\[NEI_{Predict}=1.4306\times log(TDCG)-2.4192 \tag{8}\]