Abstract : Damping of low frequency power system oscillations have been one of the major concerns in modern power system operation. The low frequency power system oscillations may be local to a single generator (local oscillations), or they may involve a number of generators widely separated geographically (inter-area oscillations). The traditional solution to this problem is the application of power system stabilizer (PSS), which is used to generate supplementary control signals for the excitation system in order to damp the low frequency power system oscillations and to improve the power system dynamics performance. In this thesis, various types of power system stabilizers (PSS) are designed at the same operating conditions based on different control methodologies. These power system stabilizers are namely, the conventional power system stabilizer (CPSS) utilizes the rotor speed (Δω,) which is based on the classical control theory. The optimal power system stabilizer (OPSS) utilizes the full states of the machine model, while the sub-optimal power system stabilizer (SOPSS) utilizes partial states of the machine model which are based on the modern control theory. The fuzzy power system stabilizer (FPSS) uses fuzzy logic theory to provide the required control signal. Detailed analysis has been done to the single machine and multi machine systems for the quadrature and direct currents (Iqand Ia) gains, in addition, the mathematical model according to model 1.1, exciter, and the proposed power system stabilizer are analyzed and the state space representation has been derived in presence of power system stabilizer and without. The effectiveness of these four different power system stabilizers are compared through the simulation of a single machine system, and multi machine systems when they are subjected to small disturbance of 5% in the mechanical torque. Moreover the comparison of the designed power system stabilizers have been done by considering the speed droop in the modeling of the power system while the same comparison have been done again when the speed droop is neglected. The comparison of the proposed power system stabilizers show that optimal power system stabilizer (OPSS) and the fuzzy power system stabilizer (FPSS) can give adequate performance for damping the low frequency power system oscillations.