## 1 Introduction  
Distribution networks play a crucial role in national energy strategies. In order to promote the widespread grid connection of clean energy and ensure the distribution system's safe, dependable, and cost-effective functioning, it is essential to realize the panoramic perception of the region of the low-voltage distribution station [1]. The distribution system is responsible for providing power directly to consumers, but its complicated operational environment is prone to malfunctions. Among all power system, 80% of faults are related to the distribution network, and more than half of these faults are single-phase-to-ground faults [2]. A line failure will have a severe impact on the transformer as well as the power supply of its downstream nodes. When a ground fault occurs close to a transformer, it could result in a transformer discharge at the neutral point, which would further cause a series of complex faults such as transformer gap breakdown, transformer tripping, and gap current transformer damage [3]. This would eventually lead to a significant power outage in the power supply area. In order to increase the reliability of the power supply [4] and restore the power supply as soon as possible, it is essential to swiftly locate the fault section and fix the fault [5]. However, distribution network faults do not always have obvious characteristics. Most branch lines in the distribution network are short. Large amounts of distributed resources are being concealed in the grid at the same time [6]. Electric vehicles are one example of a variable load [7]. The location of distribution network faults has proven to be very difficult to determine as a result of these uncertainties and the features of distribution networks. The main methods for determining fault location are the steady-state method, transient method, the traveling wave method, and the artificial intelligence algorithm [8]. Among them, the steady-state method uses the amplitude and phase relationship of the power frequency voltage and current in the steady state to judge a fault after it occurs [9]. Reference [10] established the zero-sequence impedance model of the distribution network to locate the fault interval according to the zero-sequence fault current characteristics at the nodes. Reference [11] assumed that the fault resistance is purely resistive and does not consume reactive power, and established a quadratic equation with the fault distance as the unknown variable for the location of different fault types. The transient method extracts the zero-sequence current, power, and other features of the fundamental wave or harmonics by means of signal processing technology. Reference [12] proposes a ground fault discrimination method in low-current grounding systems by comparing the relationship between the magnitude and phase angle of the zero-sequence current at the fault outlet and the neutral point in the fault zero-sequence equivalent network. Reference [13] judges the fault location according to the appearance of the first peak value of current and voltage, but does not mention the application effect in a three-phase network. The distribution network's high density of branches and short lines makes it challenging for the traveling wave method to be effectively applicable [14]. [PERSON] [15], based on the double-terminal traveling wave principle, proposed the fault branch judgment principle of three-terminal and multi-terminal transmission lines to accurately determine branch line faults, T-node faults, and line faults between T-nodes. [PERSON] [16] analyzed the particularity of the fault traveling wave signal in the distribution network on the basis of [PERSON] [14], who established a fault branch search matrix based on the arrival time of the multi-terminal initial traveling wave, and compares the changes of the matrix elements before and after the fault to locate the fault section. [PERSON] [17] simulated the injection of DC pulse signals for positioning after the line is disconnected from the grid.