The solar array drive assembly (SADA) slip ring is a critical link that provides electrical power and electric signal transmission between solar arrays and satellite power systems, which is prone to arc faults in the space environment. If these arc faults cannot be detected and eliminated quickly enough, they will seriously threaten the safety of the satellite power system and the satellite. In this paper, a fast arc detection method based on fractal dimension is proposed that adapts to different operating modes of power systems. The detection method collects the current differential signal data flowing through the SADA slip ring, and, according to the trend of the fractal dimension change in this signal, the fault identification algorithm is designed for different operating modes of the power system to achieve real-time and rapid identification of arc faults. Finally, the effectiveness of the proposed method is demonstrated using test data under several different fault conditions.