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This work exploits the decoupled double synchronous reference frame PLL (DDSRF-PLL) as an effective method for grid synchronization of WT's power converters in the presence of transient faults in the grid. The DDSRF-PLL uses a dual synchronous reference frame and a decoupling network to effectively separate the positive- and negative-sequence voltage components in a fast and accurate way. Excellent behavior of the DDSRF-PLL is demonstrated experimentally. Once sequence components of the faulty grid voltage are properly identified several algorithms computing current references are developed. Additionally, different power delivery strategies to ride-through grid faults are discussed and simulations results are presented. As a conclusion, it will be demonstrated that certain control strategies ensure a stable operation of the front-end inverter while the grid voltage is supported by means of injection of instantaneous reactive power at the same time.