In this paper we present a FACTS (Flexible AC Transmission Systems)-based control design for electromechanical oscillation damping in large power systems, facilitated by aggregate models that can be constructed using Synchronized phasor measurements. Our approach consists of three steps, namely-1. Model Reduction, where Synchrophasors are used to identify second-order models of the oscillation clusters of the power system retaining the inter-ties on which FACTS devices such as Thyristor Controlled Series Compensators (TCSC) are installed, 2. Aggregate Control, where feedback controllers are designed to achieve a desired closed-loop transient response between every pair of clusters, and finally 3. Control Inversion, where the aggregate control design is distributed and tuned to actual TCSC controllers in the full-order model until its inter-area responses match the respective inter-machine responses of the reduced-order system. It is shown that the inversion problem can be posed equivalently as decomposing the swing dynamics into fast and slow states, and designing the controllers such that the slow dynamics can optimally track a desired closed-loop signal designed for the aggregate model. Application of the approach to two-area power systems is demonstrated through topological examples inspired by the US west coast grid.