Abstract: For the non-smooth switching-type ultra-low frequency oscillation (ST-ULFO), in the single-hydro-machine power system (SHM-PS) with enhanced dead zone, the method of sliding/crossing trajectory analysis for Filippov system was used to analyze the sliding and bifurcation characteristics of the ST-ULFO trajectory accompanied by the Hopf-like bifurcation, and a new kind of bifurcation was found. Firstly, the sliding bifurcation theory of Filippov system and the method for determining the sliding or crossing characteristic for trajectories were introduced. Secondly, the simplified model of the SHM-PS with enhanced dead zone was presented. The corresponding simulation shows that the system trajectory may slide on the switching boundary when the Hopf-like bifurcation occurs. Then, the possible sliding area of the switching boundary was obtained by theoretical derivation. Finally, the relationship between the oscillation trajectory and the sliding area, and the trajectory sliding/crossing characteristics were analyzed from the perspective of sudden load disturbance. The results show that the sliding area exists in the Filippov system of SHM-PS with enhanced dead zone, and in the viewpoint of varying load, the Hopf-like bifurcation experienced by the non-smooth ST-ULFOs corresponds to a new sliding bifurcation of Filippov system, which is named critical sliding bifurcation in this paper.