Present paper proposes a method to provide necessary series compensation by formulating transient stability problem as a synchronization problem providing an edge control to keep the line flows within permissible limits. With the aim to satisfy relative rotor angle criteria in addition to line flow control having multiple constraints on a set of state variables as well as on control variables makes it necessary to call for an efficient optimization tool. Knowing the strengths and effectiveness of convex optimization we propose application of the same in finding necessary series compensation using TCSC to address this multidimensional problem in remarkably shortest possible time which facilitates on-line synchronization. In doing so, post fault conditions are mapped to pre-fault healthy conditions so as to guarantee stable and secure power flow even after credible line contingency without shedding any load (i.e. maintaining demand supply balance), which if not followed may lead to cascade tripping.