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A fractional order PID (FOPID) controller to damp inter area oscillations of power systems is studied. FOPID is a PID whose derivative and integral orders are fractional rather than integer. The difficulty of design a FOPID controller is how to determine the five key parameters of FOPID. This paper uses genetic algorithm particle swarm optimization (GAPSO) algorithm to design the FOPID controller. A new cost function is defined to facilitate the control strategies over the time domain specifications. Comparisons with a conventional PID controller are made and it is shown that the proposed FOPID controller can highly improve the system robustness with respect to model uncertainties.