LFO (Low Frequency Oscillation) is a main aspect that affects power system stability. In this paper, the inherent reason that causes LFO is discussed.With Hopf bifurcation theory, it is analyzed that the nonlinear singularity phenomenon happens close to the critical points in a single-infinite power system of four-rank model. The study indicates that because of the Hopf bifurcation, singularity phenomenon in the power system happens close to the critical points, which affects the steady bound.