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A versatile mathematical model of a unified power flow controller (UPFC) in a single machine infinite bus system is proposed. The model consists of a simple voltage source whose magnitude and angle depend on the UPFC control parameters. The voltage-source model of UPFC can easily be incorporated into the generator output power equation and that simplifies the dynamic analysis of the system. With some appropriate assumptions, the proposed UPFC model can also be used to represent other FACTS devices, such as, static synchronous compensators, static synchronous series compensators, etc. The proposed model is then used to determine and compare the dynamic behaviour of a simple system equipped with various FACTS devices.