This paper proposes a static frequency stability of a power system based on Lyapunov methods

which provides a basis for judging the static frequency stablity of system and effectively preventing the static. Firstly

the active power-frequency static model of equivalent single machine power system is established. And then

the stability criterion on static frequency stability is derived based on lyapounov indirect and direct method when the generator has no speed control system. At last

the condition of static frequency stability of the system with fast speed control system is also analyzed by Lyapunov methods. The results show that when the electric generator does not have a speed regulating system and the system damping coefficient is greater than the critical damping

the system can maintain the static frequency stability. When the electric generator has a speed regulating system with a positive damping ratio

the system can maintain static frequency stability

and sufficient hot spare capacity is beneficial to maintaining the static frequency stability of power system.