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This paper presents an application of unified power flow controller (UPFC), a kind of FACTS devices, to stability enhancement in the multi-machine power system. A new control scheme of FACTS devices using wide-area information is proposed for transient stability improvement. The proposed scheme is based on two control laws to shift a time derivative value of the energy function in a negative direction and to move rotor speed of the critical machine closer to that of the center of inertia. In order to apply the proposed FACTS control laws to controllable components of UPFC, sensitivities of active power outputs with respect to UPFC control variables are newly defined and used in the control system. Numerical simulations are carried out on a 27-machine meshed test system where two UPFCs are installed. The results show that UPFCs controlled by the proposed method can improve the transient stability in the multi-machine power system.