## 1 Introduction
### Frequency Analysis of Arc Current with Spread Frequency Fluctuationsby Three-Phase Inverter  
Figure 6 represents the current waveform and FFT results of \(I_{arc2}\) when the magnitude of current is 5 A and average switching frequency is 20 kHz. As in the case of Figure 3, the arc commences at the same time that the arc rods are separated. In addition, it is seen that the magnitude of the DC component of the arc current changes a little, as in the case of the arc current with centralized frequency fluctuations by the three-phase inverter.  
Figure 5: Integral results from 5 kHz to 40 kHz for Figure 4.  
The FFT results for the regions(r) and (r)in \(I_{arc2}\) are shown in Figure 6b,c, respectively. From the FFT results of (r), it is seen that the frequency distribution is not concentrated but is spread between 5 and 20 kHz because of the spread frequency fluctuationsin \(I_{arc2}\). From the FFT results of (r), which is the result after arcing, it is confirmed that the components in the 5 to 40 kHz band increase after arcing.  
Figure 7 shows the FFT differences after and before arc generation based on the current magnitude and average switching frequency in \(I_{arc2}\). As in the case of Figure 4, Figure 7 is obtained from the differences between the averages of 100 consecutive FFT results after and before arcing. In addition, when the frequency fluctuation was spread, arcing did not occur at the low current of 3 A, so only the results of 5 and 8 A are shown in Figure 7.  
Figure 6: Current waveform and FFT results of \(I_{arc2}\) when the magnitude of current is 5 A and average switching frequency is 20 kHz: (**a**) current waveform, (**b**) FFT result before arcing, and (**c**) FFT result after arcing.  
From Figure 7, it is seen that the frequency components that increase after arcing are between 5 and 40 kHz. Particularly, the components in the 5 to 20 kHz band increased significantly. Unlike the case of the arc current with centralized frequency fluctuations by three-phase inverter, there was no clear trend inthe average switching frequency. However, smaller currents caused larger increases in the frequency magnitudes in the 5 to 40 kHz band after arcing. Moreover, in the case of \(I_{arc2}\), since the frequency fluctuation was spread, unlike the case of \(I_{arc1}\) in Figure 4, there was no distinct reduction in the average switching frequency component and its multiples.  
Figure 8 shows the integral results from 5 to 40 kHz for Figure 7. Compared to Figure 5, which is the case of the centralized frequency fluctuations by three-phase inverter, no distinct increase is observed in the 5 to 40 kHz band for the average switching frequency. However, smaller currents cause larger integral results in the range of 5 to 40 kHz. The difference between the 5 to 40 kHz integral result for 5 and 8 A is greatest when the average switching frequency is 5 kHz, and the difference between the 5 to 40 kHz integral result for 5 and 8 A decreases as the average switching frequency increases.  
Figure 7: FFT differences after and before arc generation based on the current magnitude and average switching frequency in \(I_{arc2}\): (**a**) 5 kHz, (**b**) 10 kHz, (**c**) 15 kHz, and (**d**) 20 kHz.