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This work presents a control strategy to improve the performance of full-converter wind turbines under distorted conditions, particularly with regards to the harmonic rejection capability under grid frequency variations. Resonant filters are often added to the grid-side converter control to achieve a proper operation against network disturbances. However, in weak power networks where frequency deviations are expected, these schemes can lose some performance since they are susceptible to grid frequency drifts. The proposed control structure allows us to adapt the grid frequency involved in different control blocks via a frequency-updating outer loop; thus, the control algorithm is tailored so that full-converter wind turbines inject a harmonic-free current even under severe harmonic distortions and frequency-varying conditions. This facilitates that wind farms overcome most network disturbances such as imbalances, harmonics, and frequency drifts, as well as to fulfill demanding grid code requirements and power quality standards. We also introduce a thorough output filter modeling and design, guidelines for the current reference calculation, computational time delay compensation, and discrete-time domain control description. A state observer is proposed to reduce the amount of sensors needed in the control stage; consequently, a simpler hardware, higher reliability, and lower cost implementation can be accomplished. Several tests, disturbances, and comparisons with other control approaches are performed to validate and illustrate the advantages of the control strategy.