The design, modeling and control design of a 48-step inverter based static synchronous series compensator (SSSC) is presented in this paper. A magnetic circuit is chosen which contains eighteen single-phase three winding transformers and six single-phase two winding transformers to add the output voltages of eight three-phase inverters. An equivalent circuit model of the SSSC is derived and based on this model a proportional-plus-integral controller is proposed. The controller gains are chosen through eigenvalue analysis of the IEEE first benchmark model for subsynchronous resonance (SSR) analysis. The SSSC model, its control and the results of the eigenvalue analysis are then validated through PSCAD/EMTDC simulation. It is shown that for certain controller gains torque amplification of the shaft modes can occur.