# Detection of Arc Faults in Transformer Windings via Transient Signal Analysis
## 4 Findings
### Simulation Results  
The transformer modeled in the Ansys@Maxwell environment was analyzed with a maximum simulation time of t = 0.1 s and a sampling interval of 0.001 ms. Calculated design specifications for the transformer provided by the manufacturer and simulation results obtained are compared and presented in Table 2. The data in the table are in agreement. The core losses of the analyzed transformer are shown in Figure 5. The core losses are compared with those presented by [PERSON] et al. (2020) and [PERSON] et al. (2013) and good agreement is observed [31; 32]. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Specifications** & **Nominal Ratings** &
\begin{tabular}{l} **Design** \\ **Specifications** \\ \end{tabular} & **Simulation Results** \\ \hline Secondary phase & 156 A & 151.5 A & 154.9 A \\ \hline Secondary line & 11,000 V & 10,883 V & 10,963 V \\ \hline Core losses & 12,000 W & 12,357 W & 12,129 W \\ \hline Copper losses & 97,000 W & 96,848 V & 94,342 W \\ \hline Maximum magnetic flux density & 1.87 T & 1.84 T & 1.87 T \\ \hline Percentage short circuit voltage & 10\% & 9.69\% & 9.76\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of simulation results with design specifications of transformer. Figure 4: High-voltage side winding of phase-B for 5 different fault points (I–V interval represents fault conditions respectively). Figure 3: Integrated execution of system programs. For arcing fault analysis, the maximum simulation time was set to t = 0.04 s and the sampling interval in the simulation was 0.001 ms. Arcing was initiated at t = 0.015 s. This eliminates the transient at the moment of initial energization of the transformer and has no effect on the transients at the moment of arcing. The magnetic flux density distribution in the transformer core at t = 0.35 ms is shown in Figure 6. In the electromagnetic transient analysis designed in 3D in the Ansys@Maxwell environment, the instantaneous flux distribution is monitored locally and provides a wide range of information about the flux distribution. The maximum value of the sheet material used is 1.87 T and shows the most intense flux transition in red. Regions with little or no flux transition are shown in blue. The variation of current and voltage over time for the arc signal initiated at t = 0.015 s for phase B of the HV side winding is shown in Figure 7. The voltage at the moment of the arc remains constant, while the current fluctuates sinusoidally and is rapidly damped when the voltage exceeds the arc ignition level. This indicates that the rigid transient state of the arc current is interrupted at that moment. When the voltage returns to the jump level, the transition reverts to the rigid state. This unbalanced change in current and voltage levels generates high-frequency components at the transformer terminals. The variation of arc current in relation to arc voltage is shown in Figure 8.  
Figure 5: Transformer core losses. Figure 6: Magnetic flux density distribution of the core at t = 0.35 ms. It has been observed that arcing faults in the transformer windings cause fluctuations in the harmonic frequencies at the transformer terminals. As the arcing creates a rigid current around it, it leads to distortion and changes in the structure of the main component. The nonlinear characteristics of the arc produce higher frequency harmonics than those of the main component. The effect on the input signals at the transformer is illustrated in Figure 9. In the simulations, the transformer model was initially operated at nominal load. The results indicated that the arc fault did not generate significant harmonics in the frequency spectrum between 2 kHz and 5 kHz, where the arc fault is typically dominant. Based on these findings, it is believed that the transient conditions when the transformer begins operating, with the arc occurring at the 15 th millisecond, do not influence the transient regimes in this frequency range. Figure 8: Change in arc current with respect to the arc voltage.