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Determining suitable locations of series-connected controllers is a practical problem when it is necessary to install them in modern power systems. The aim of this paper is to find the best location of series controllers in order to reduce the proximity to instability of a current operating point of a power system, from a transient stability viewpoint. In order to achieve this goal, a general approach has been developed based on an index of proximity to instability and trajectory sensitivity analysis. An efficient way to carry out multi-parameter sensitivities is formulated analytically and solved simultaneously with the set of differential-algebraic equations representing power systems dynamics within a single-frame of reference. Simulations are performed on 9-bus and 39-bus benchmark power systems for illustration purposes. Results show that the proposed approach provides the most effective location of series-connected controllers to improve the power systems transient behavior.