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The back-stepping design methodology of the mathematical-analytical nonlinear control theory has been shown to provide an efficient constructive tool for designing controllers in various systems engineering applications. A novel robust non-linear control design application for electrical power systems employing thyristor controlled series compensation (TCSC) is resolved by means of this methodology. For the case of single machine to infinite bus system with TCSC having internal and external disturbances, storage functions of the system are constructed via adaptive back-stepping design, and a novel nonlinear L2 gain disturbance attenuation controller along with parameter update law is obtained. The construction of both feedback control law and associated storage functions is consistently systematic within the design methodology. Simulation results have demonstrated that the controller designed by back-stepping methodology possesses superior performances relative to the alternative designs for the same power system.