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In this paper the control of a grid-connected Wind Energy Conversion System (WECS), based on a sensorless vector controlled cage induction machine 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 discussed in this work. The influence of a synchronous rotating filter in the dynamic of the proposed WECS is analysed. The implementation of a Model Reference Adaptive System (MRAS) observer for sensorless control of the proposed WECS is also presented in this work.