As the grid code specifies, wind turbines have to remain connected to the grid at voltage levels far below the nominal values. The improvement of wind turbine performance under such conditions has become a problem of general concern. However, this performance usually relies on conventional linear controllers that operate at network faults far off the nominal point for which they were designed. As a consequence, wind turbines should operate with increasing converter currents, which may result in converter damage. This paper proposes a nonlinear controller for converter-based wind turbines that ensures that the currents are maintained within the design limits. The controller is based on feedback linearization theory and is applied to the system through a sliding mode approach. This controller is robust against system perturbations and uncertainties, and overcomes the usually complex implementation that is associated with feedback linearization controllers.