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Series FACTS devices like thyristor controlled series capacitors (TCSC) equipped with appropriate supplementary damping controller can improve the small signal stability of power system if they are located properly. In this paper, trajectory sensitivity analysis (TSA) is used to determine the best locations for installing TCSC to damp out the inter-area mode of oscillation. Based on the modal analysis, an equivalent angle is defined by determining critical and non-critical machines, and then using trajectory sensitivities of this angle with respect to the impedances of the transmission lines; appropriate locations for placing TCSC are found. To verify the accuracy of the proposed method, the residue technique for optimal placement of FACTS devices is also implemented in this paper. Both methods are applied to the IEEE 3-machines 9-buses test system, and the obtained results show the validity and efficiency of the proposed method.