## 1 Introduction
### Frequency Analysis of Arc Current with Centralized Frequency Fluctuationsby Three-Phase Inverter  
For frequency analysis before and after arcing, arc currents are generated under the conditions noted in Table 3. Figure 3 shows an example of frequency analysis for arc current under the various conditions in Table 3.  
Figure 3 shows the current waveform and FFT results of \(I_{arc1}\) when the magnitude of current is 5 A and switching frequency is 20 kHz. As can be seen from the first waveform in Figure 3, when the arc rods are separated, an arc is generated, and the harmonic components are added in \(I_{arc1}\). Further, it can be seen that the magnitude of the DC component of the arc current changes a little. Owing to this property, conventional circuit breakers meant for detecting large currents cannot detect such series DC arcs. The FFT was applied to determine the frequency changes before and after arcing. The current data before arcing are that of the green part marked as \(\Uparrow\); the current data after arcing are that of the red part marked as \(\Uparrow\); the result of FFT using the data in \(\Uparrow\) is shown in Figure 3b. From Figure 3b, it is seen that the switching frequency and its multiples are identified from the FFT of \(I_{arc1}\) before arcing. In particular, the doubled switching frequency is distinctly observed. In Figure 3c, it is seen that the multiples of the switching frequency are clearly visible, similar to that before arcing. However, their magnitudes are smaller than those before arcing. Further, the frequencies between 5 and 40 kHz increase after arcing. Particularly, the components in the 5 to 20 kHz band  
Figure 3: Current waveform and FFT results of \(I_{arc1}\) when the magnitude of current is 5 A and switching frequency is 20 kHz: (**a**) current waveform, (**b**) FFT result before arcing, and (**c**) FFT result after arcing. increase significantly. To investigate this frequency change tendency based on the current magnitude and switching frequency, the FFT results after and before arcing are subtracted. Figure 4 shows the FFT differences after and before arc generation based on the current magnitude and switching frequency in \(I_{arc1}\). To reduce deviations in the FFT results, the average of 100 consecutive FFT results is used. In other words, Figure 4 shows the differences between the averages of 100 consecutive FFT results after and before arcing. It can be seen from Figure 4 that frequencies between 5 and 40 kHz increase after arcing under all conditions. However, the magnitudes of the frequencies in the 5 to 40 kHz band that increase after arcing are different. From Figure 4, it is seen that for 5 and 20 kHz switching frequencies, the magnitudes of the 5 to 40 kHz components that increase after arcing are almost the same, regardless of the current magnitude. In the case where the magnitude of the switching frequency is 10 and 15 kHz, it is confirmed that for smaller currents, the 5 to 40 kHz components increase to a greater extent after arcing. Furthermore, the higher the switching frequency, the larger the increase in the  
Figure 4: FFT differences after and before arc generation based on the current magnitude and switching frequency in \(I_{arc1}\): (**a**) 5 kHz, (**b**) 10 kHz, (**c**) 15 kHz, and (**d**) 20 kHz. magnitudes of the 5 to 40 kHz components after arcing. The magnitudes of the switching frequency and its multiples are negative values, which indicate that these multiples of the switching frequency decrease after arcing. To understand the increase in frequencies in the 5 to 40 kHz range based on each examined current condition, the results of Figure 4 in the range of 5 to 40 kHz are integrated. The large integral results indicate that the 5 to 40 kHz band increases significantly after arcing. Figure 5 shows the trend of increment in the 5 to 40 kHz band depending on the switching frequency.