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This study is on variable-speed wind turbines with permanent magnet synchronous generator. Three different drive train mass models and three different topologies for the power-electronic converters are considered. The three different topologies considered are, respectively, a matrix, a two-level and a multilevel converter. A novel control strategy, based on fractional-order controllers, is proposed for the wind turbines. The influence of a converter control malfunction on the harmonic current emissions is studied. The performance of disturbance attenuation and system robustness is ascertained. Simulation results are presented, and conclusions are duly drawn.