This paper presents an application of UPFC (unified power flow controller), a kind of FACTS (flexible AC transmission systems) devices, to stability enhancement in a multi-machine power system. A novel control scheme using wide-area information from generators in the system is proposed for two parts of UPFC, shunt and series connected components, which mainly affect bus voltage and line active power flow around the installation site respectively. The proposed control scheme is based on a control law for shifting a time derivative value of the kinetic energy function in the negative direction. Numerical simulations are carried out on a 27-machine meshed test system where several UPFCs are installed, and the impacts of the two controlled components of UPFC and number of UPFCs on stability enhancement are investigated. The results show that both of the UPFC components controlled by the proposed method are effective for damping enhancement and the shunt connected component is particularly effective for the first-swing stability improvement. It is also made clear that the proposed control scheme can control multiple UPFCs without mutual interference.