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In this paper the control of a grid-connected Wind Energy Conversion System (WECS), based on a sensorless vector controlled Doubly-Fed Induction Generator (DFIG) fed by a matrix converter, is presented. The matrix converter is controlled using a space vector modulation algorithm. Stability issues related to the operation of the WECS connected to the grid using a matrix converter are also discussed in this work. The influence of a synchronous rotating filter in the dynamic of the proposed WECS is analysed. A Model Reference Adaptive System (MRAS) observer for sensorless control of the proposed WECS is used in this work. Using the speed estimated by the MRAS observer the electrical torque of the induction generator is regulated in order to drive the WECS to the operating point where the aerodynamic efficiency is maximized. Experimental results, obtained with a 3.5 kW prototype are presented, and fully discussed in this work.