Leakage faults are common occurrence in low-voltage power grids, and residual current device (RCD) are the primary protective device against such faults. However, in practical applications, frequent tripping of RCD has become a focal issue, highlighting the conflict between power supply safety and reliability, causing to the deactivation of many RCDs. To address this problem, the paper analyzes both the impedance characteristics of low-voltage distribution network and the operating principles of RCD protection. The study shows that the current low-voltage distribution network exhibits complex RLC impedance characteristics, comprising resistive, inductive, and capacitive components. Under the influence of various disturbances, the residual current in the distribution network may include high-amplitude, wide-frequency, and short-duration impact harmonic current, which affect the correct operation of RCD. To adapt to the current distribution network conditions, this paper proposes adding a second-order Butterworth low-pass filter to the residual current signal processing stage of the RCD to eliminate the influence of harmonic current. Simulation results show that the improved RCD can significantly enhance its resistance to impact harmonic residual current, reducing false trips and thereby improving power supply safety and reliability.