## 1 Introduction  
Arcing is a phenomenon in which the gas insulation between electrodes is continuously destroyed and discharged by the potential difference generated between the electrodes. The DC arcs generated by DC currents are less likely to be extinguished naturally than ac arcs. This is because there is no zero-crossing point, as in the ac current. Therefore, the risk of accidents, such as fire damage caused by DC arcs, is greater [1, 2]. Among the various DC arcs, series DC arcs tend to change the magnitude of the arc current a little in the event of an arc accident, thereby making it difficult to prevent arc faults with conventional circuit breakers, which detect large currents [3, 4]. Therefore, a fire accident caused by a series DC arc can be aggravated into a very large fire accident. The series DC arc occurs when the connectors between the conductors are loosely connected or when the conductors are damaged. Series DC arc accidents occur frequently, especially in photovoltaic (PV) systems; the reason for this is attributed to the nature of the PV system, where there is a high possibility of damage to the conductor wire because it is installed in an outdoor environment. Moreover, because PV systems are generally installed as modules, there are many points in the system where arc accidents can occur [5]. Various studies have been conducted to analyze the characteristics of series DC arcs [6, 7, 8].Arcs were studied via an experimental method that mathematically modeled the arc voltage, i.e., the voltage between the arcing conductors, and arc current, i.e., the current flowing through the arcing conductors [6]. Moreover, the frequency characteristics were analyzed for arcs occurring in PV systems with single-phase and three-phase inverters as loads [7]. Meanwhile, a new arc model equation was proposed through arc analysis according to the input voltage, arc current, and distance between the arc rods [8]. Moreover, techniques for detecting series DC arcs using various characteristics observed after arcing have been proposed [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. Despite these studies on arcs, a frequency analysis of the arc current based on the type of frequency fluctuation generated by the inverter has not been conducted. Analysis of Frequency Characteristics of Series DC Arcs According to Type of Frequency Fluctuation Caused by Inverters  
This section presents analysis of the frequency characteristics of the arc current according to the type of frequency fluctuation caused by the inverter of the PV system. These arc currents according to the frequency fluctuation of the inverter are defined as shown in Table 1.  
To gather arc current data, the arc generator and experimental setup were configured as shown in Figure 1 by referring to UL1699B, which contains regulations for verifications of an arc fault circuit interrupter (AFCI) which is a device for detecting and blocking serial DC arcs in PV systems [22]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Arc Current** & **Inverter** & **Frequency Fluctuation** \\ \hline \(I_{arc1}\) & Three-phase inverter & Centralized frequency fluctuation \\ \(I_{arc2}\) & Three-phase inverter & Spread frequency fluctuation \\ \(I_{arc3}\) & Single-phase inverter & Centralized frequency fluctuation \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Arc currents according to the frequency fluctuation. high-frequency components rather than DC components [7]. Therefore, in this study, the DC supply was used as the voltage source, not the PV source. The DC supply used in the experiment is KEYSIGHT N8741A (maximum voltage 300 V, maximum current 11 A, maximum power 3.3 Kw, KEYSIGHT TECHNOLOGIES, Santa Rosa, CA, USA). To generate arcs safely and evenly, the step motor shown in Figure 1d is used to separate the rods. Further, the separated distance of the rods is checked with an electric ruler installed parallel to the rod, as in Figure 1d.