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Model predictive fault‐tolerant current control (MPFTCC) of permanent magnet synchronous generator (PMSG) drives can make a valuable contribution to improving the reliability and availability levels of wind turbines, because back‐to‐back (BTB) converters are prone to failure. However, MPFTCC suffers from excessive computational burden, because the BTB converter is treated as one system where all feasible voltage vectors (VVs) are used for prediction and evaluation. Accordingly, a computationally efficient MPFTCC algorithm for a PMSG drive is developed and proposed with the ability to handle insulated‐gate bipolar transistor open‐circuit faults. The candidate VVs of both machine‐ and grid‐side converters are separately predicted and evaluated, which significantly reduces calculation effort. The proposed reconfigurable converter is a five‐leg power converter with a common leg that connects the generator first phase to the grid three‐phase, ensuring proper postfault reconfiguration of the grid‐side inverter. Moreover, a three‐switch rectifier is adopted to achieve fault tolerance of the PMSG‐side rectifier. Performance of the considered MPFTCC strategies is evaluated by experimental means. [ABSTRACT FROM AUTHOR]