In this paper, the optimal design of supplementary controller parameters of a unified power flow controller (UPFC) for damping low-frequency oscillations in a weakly connected system is investigated. The individual design of the UPFC controller, using hybrid particle swarm optimization and gravitational search algorithm (PSOGSA) technique under 3 loading operating conditions, is discussed. The effectiveness of proposed controller on enhancing dynamic stability is tested through eigenvalue analysis and time domain simulation. Also nonlinear and electrical simulation results show the validity and effectiveness of the proposed control schemes over a wide range of loading conditions. It is also observed that the proposed UPFC-based damping stabilizers greatly enhance the power system transient stability. Also, simulation results of coordinated design of stabilizer based on dE and mB is presented and discussed, the system performance analysis under different operating conditions show that the dE-based controller is superior to the mB-based controller.