Abstract: This paper presents a study of the transient and dynamic stability enhancement and control of a synchronous generator connected to an infinite bus (single machine infinite bus system) via two parallel transmission lines when the power system working under different operating conditions and subjected to different disturbances. An effective mean of damping the oscillations resulting from these disturbances is to provide the synchronous generator with power system stabilizer. An adaptive fractional order proportional integral derivative controller is suggested to play the role of power system stabilizer in this paper. The results obtained from simulation study are presented and discussed.