This paper presents the design steps and carries a comparative study between three Proportional-Integral-Derivative (PID) controllers. The gains of the first PID are optimized using Genetic Algorithm (GA), named pid. In the second controller, the parameters setting of the Fractional Order PID controller are found using GA, named fopid. The pid and fopid controllers employ cost function that represents the Integral Squared Errors (ISE) to evaluate the controller gains. In the third controller, Multi-Objectives Genetic Algorithm (MOGA) is reformulated to design Fractional Order PID Controller named Mfopid. The proposed controllers have been applied to a Unified Power Flow Controller (UPFC) to control generator terminals voltage and better damping of Low Frequency Oscillation in Single-Machine Infinite-Bus (SMIB) power system. In additional, power system stabilizer (PSS) control parameters are tuned with pid based ISE using GA to increase damping of power system Oscillations. The PSS control parameters remain constant during the design procedure of the two proposed fopid and Mfopid controllers. To show the effectiveness of the designed controllers, the obtained results are compared through sever disturbances with different operating conditions. Results evaluation show that the proposed Mfopid controller achieves good performance and is superior to the other controllers