This work presents the analysis and proposes nonlinear controls of a wind energy conversion system (WECS) to pass through symmetrical and asymmetrical voltage failures. The WECS is equipped with a nonsalient pole permanent magnet synchronous generator (PMSG) and two full converters, synchronous generator side converter (SGSC) and grid side converter (GSC), joined by a direct current (DC) link. As a consequence of the strong disturbances considered, a general strategy based on grid voltage values changes control references at SGSC and GSC. This strategy uses two flags for indicating normal grid voltages, symmetrical faults, or asymmetrical ones. Then, while control laws deal with model uncertainties and fast disturbances due to wind gusts, the strategy changes references to surpass strong, probably unbalanced, grid voltages disturbances. To assure robust properties, controllers are designed via a conjunction of Lyapunov and passivity theories. The proposed controllers and the strategy are tested under realistic wind conditions, uncertain parameters, and strong voltage disturbances.