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Static series synchronous compensators (SSSC) have recently found applications in power oscillation damping (POD) improvement. Nonlinear dynamics associated with the SSSC's dc-link capacitor voltage, and effective interactions among its variables validate the use of nonlinear and multi-variable modeling and control techniques. A novel nonlinear input-affine multivariable model for a series connected SSSC with the transmission line is developed and formulated in this paper. Developing an affine model is a critical step in the design and implementation of many nonlinear and robust control approaches. Based on the proposed affine model, a feedback linearization nonlinear controller is introduced and used to improve the POD. Simulation results validate the feasibility of the proposed modeling and control approaches in maintaining the dc side capacitor voltage constant while effectively damp out power system oscillations. In addition, the zero dynamics of the system remains stable which means no deviation will occur in uncontrolled state variables.