In this article, a non-linear coordinated control of generator excitation and a static synchronous compensator is proposed to enhance the transient stability of an electrical power system. The coordinated controller proposed is designed via immersion and invariance methodology. In particular, a non-linear model of the power system and immersion and invariance design method are used to achieve not only power angle stability but also frequency and voltage regulations following a large disturbance (a symmetrical three-phase short-circuit fault) on one transmission line or a small perturbation to mechanical power input to synchronous generators in the system. The controller design is validated using a simulation study on a single-machine infinite bus. Simulation results show that the proposed controller can not only keep the system transiently stable but also simultaneously achieve power angle stability and frequency and voltage regulation.