Ultra-low-frequency oscillations caused by the instability of primary frequency regulation process occurr in actual power systems. Governor deadband introduces nonlinearity to the system and affects frequency oscillation. The influence of non-step deadband

step deadband and hysterisis deadband on frequency oscillation are analyzed with the describing function method in the single-machine equivalent system. The locus of minus reciprocal of the describing function of deadband with oscillation amplitude

and the locus of open-loop transfer function with oscillation frequency are plotted on the complex plane. The relative location of the two loci determines the system stability. When the minus reciprocal locus entirely locates on the left of the open loop frequency characteristic locus

the system is stable. In other cases

the two loci intersect in general and the intersections correspond to limit cycles

and the stability is determined by the specific situation of the intersection. Furthermore

the influence of governor deadband on frequency oscillation in single machine equivalent system is analyzed. Non-step deadband and step deadband do not weaken the stability of the system

but hysterisis deadband may cause continuous oscillation due to stable limit cycle in a system which is initially stable without deadband. Results of time-domain simulations validate the conclusions.