Asynchronous interconnection between Yunnan Power Grid with China Southern Power Grid can improve the transient angle stability may exist in precise system. However,this measure also bring problem of the frequency stability of system in recent years. In view of the phenomenon that Yunnan Power Grid oscillated near the boundary of the dead band after the governor taken the dead band, this paper uses the damping torque method to analyze that the governor adding different types of dead zones has different amplitude reduction effects on the mechanical power that provides negative damping, resulting in a change in the positive and negative damping state of the system. Then,the frequency stability problem occurred after the disturbance occurred in the system. Moreover, Results of the time-domain simulations on single-machine validates the conclusion that the different dead band can change the damping sate of system.