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In this paper a novel time simulation approach is introduced to implement transient stability analysis with FACTS devices, in which FACTS devices uses dynamic phasor models and interface properly with conventional electromechanical transient-model-based stability program. The unified power flow controller (UPFC) is used as an example to demo the realization of the approach. In the paper, the UPFC dynamic phasor model and control scheme are presented first and followed by the interface formulation. Sequential solution method is proposed to implement step by step simulation. Computer test results from a SMIB power system show clearly the accuracy of dynamic phasor model as compared with EMT model for UPFC; while computer test results from a two-area power system illustrate solidly the effectiveness of the suggested interface and simulation approach to include dynamic-phasor-based FACTS device models into conventional transient stability program.