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An adaptive Static Synchronous Series Compensator (SSSC) in single machine infinite bus system is proposed. The model consists of a voltage source. The magnitude and angle of this voltage source depends on the SSSC control parameters. For the eigenvalue analysis, a linear power system model is developed. The stabilizing signal controls the electromechanical mode which is poorly damped. The singular value decomposition based approach is used to select this superior stabilizing signal. The voltage source model of SSSC incorporated into the generator output power equation simplifies the dynamic analysis of the system and this incorporation into the generator output power equation can be easily done. This model which is proposed can be then used to compare and determine a simple system's dynamic behavior, equipped with an adaptive SSSC.