# Arc Modeling and Kurtosis Detection of Fault with Arc in Power Distribution Networks
## 1 Introduction  
In power distribution networks, it is extremely important to safely supply power under various fault conditions. Specifically, it is difficult to detect faults in a power distribution network because factors such as load and distributed energy resources exist [1, 2, 3]. When the faults persist, it leads to dangerous circumstances for individuals because the faults are typically high voltage or high current. Therefore, it is necessary to develop an effective detection method for determining whether to continuously supply power. Over the past few decades, various approaches have been examined to remedy these problems [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Typically, harmonic patterns are utilized to capture fault characteristics such as magnitude and angles or harmonics [4, 5, 6]. The stator-ground fault location method based on third-harmonic measures was proposed in [4, 5]. Various harmonics in current waveforms were used to design a general purpose model for representing a high impedance fault [6]. In [7], a new approach for fault detection was developed based on the energy variation of the low harmonic orders obtained by the Stockwell transform. In [8], a nonlinear equivalent model and detection algorithm were developed by analyzing odd harmonics amplitudes. In addition, there are many signal processing methodologies, including the Kalman filter-based method, wavelet transform, and short-time Fourier transform [9, 10, 11, 12]. In [9], a Kalman filter-based algorithm was developed for series arc fault detection. In [10, 11, 12], the time domain reflectometry-based fault location method using a wavelet decomposition was proposed. Recently, various methods based on machine learning have been proposed [13, 14, 15]. A hierarchical classification and machine learning method were designed to detect and classify the line-to-ground and line-to-line faults in PV systems in [13]. As a deep learning method, the convolutional autoencoder framework forHIF detection was proposed in [14]. The useful features with advanced machine learning methods were extracted in [15]. Unfortunately, the aforementioned methods were developed without considering arc modeling, which inevitably occurs in actual fault situations. There are many fault situations in which power distribution lines are disconnected or are energized with other conductors. When a distribution line becomes disconnected, an arc can frequently occur along with electrical breakdown because the disconnected distribution line is in contact with other conductors. An arc exhibits an instantaneous low current with respect to high contact pressure. Hence, it can be easily ignited when it comes in contact with other conductors. Therefore, based on the type of conductor it contacts, an arc can cause damage in the form of electric shocks and economic losses from wildfires. Many methods have been examined from different perspectives for arc detection and arc modeling. However, most of the previous methods were performed based on the existing mathematical arc models without considering practical arc fault events. It is challenging to model an arc because the arc fault waveforms vary based on the contacted (energized) conductor. Additionally, given that an arc is instantaneously created, conventional methods, such as unbalanced voltage/current amplitude detection, angle different detection, and n-th harmonic detection, are not effective. This paper contributes to developing an arc model of fault in the power distribution network. Modeling requires experimental data to fulfil its equations and their parameters. Hence, an experimental setup is implemented to establish a single-phase fault with a mathematical arc model in a 3-phase distribution system. To analyze arc phenomenon, phase voltage and phase current are measured via remote terminal units (RTUs) at different locations. The experiment results are used to model the arc. The arc phenomenon is modeled using linear and nonlinear functions after analyzing the arc regions based on the experimental waveforms.