## 1 Introduction  
Direct current (DC) microgrids exhibit many advantages compared to AC (alternating current) grids; the voltage is lower, less electric power is lost, supply reliability is high, and distributed generation is simple. It is more suitable to choose DC microgrids for interconnecting renewable resources. However, DC microgrids have some challenges attached to them, such as that of the fault protection. The DC current increases rapidly after a fault, which is challenging for existing protective systems that fail to locate and isolate faults. DC microgrids contain a variety of electronic devices generally concentrated within small areas, such as ships, islands, grasslands, and data centers; the environmental conditions in these areas may be challenging [1; 2]. Therefore, DC microgrid cable faults occur frequently because of insulation degradation and breakdown. Line insulator damage, overheating of energy storage elements, loose joints, aging wires, and environmental stress can cause two types of faults: pole-to-pole faults (short circuits) and pole-to-ground faults [3]. The impedance caused by pole-to-pole faults is small because the conductors are directly connected at the fault point. In contrast, pole-to-ground faults often show high resistance (HR) because the conductor connects with the ground via the insulation [4]. During such faults, converter operation may continue, triggering a fault cascade involving cables or converters. Therefore, whenever an HR fault (HRF) occurs, an operator must be informed and then act [5; 6]. After a metal or small-resistance fault, the fault current increases quickly to a prominent peak that is easy to detect; the fault can then be rapidly removed. However, after an HRF, the electrical parameters do not obviously change, making it difficult to detect the fault [7; 8; 9]. Due to the small damping of the DC microgrid line, the fault may spread and affect adjacent circuits, such as photovoltaic modules, energy storage systems, lines, control systems, etc., which will be damaged; this results in the fault operation of the DC microgrid, which will pose a serious threat to personal safety and equipment safety and may even cause accidents such as fires [10; 11]. Therefore, accurate detection and effective treatment of high resistance faults are important conditions to ensure the safe and stable operation of DC microgrids [12]. Existing HRF detection methods [13] use mathematical morphology (MM; two elementary transformations) to detect faults in low-voltage DC (LVDC) distribution systems. However, arc faults are not well-detected. An in-depth analysis [14] yielded the optimal parameters for the detection of serious arc faults. The energies with and without arc faults were compared to determine the effects of combinations of three parameters on arc fault detection. However, this is not practical in the field. A transient algorithm [15] has been used for HRF detection; a discrete wavelet transform is employed to monitor the high- and low-frequency voltage components at several points. The utility of the method was verified by simulation. However, it cannot be applied to a DC grid. An impedance measurement algorithm for equivalent load detection in DC microgrids has been developed [16]: the power converter injects small signal oscillations into the DC bus throughout the duty cycle and an LIA (lock in amplifier) isolates the oscillations and measures the equivalent incremental impedances. However, dedicated hardware is required and it is difficult to distinguish overload from faults. HRF can be detected using a data-mining decision tree [17] and implemented in a distribution network. But the interference problem of communication needs to be considered. A protection method based on the time and polarity of initial current traveling waves is proposed for transmission lines in [18]. However, the calculation process is complicated and requires a high communication speed. The proposed algorithm calculates the fault distance based on the characteristics of the voltage resonance in [19].