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In this paper, a new control system to regulate the reactive power supplied by a variable-speed wind energy conversion system (WECS), based on an induction generator fed by a matrix converter (MC), is presented. The control system discussed in this paper is based on an input current observer, implemented using an estimation of the modulation matrix, and a nonlinear control loop that regulates the displacement angle at the MC input. The reactive power capability of the proposed system is also investigated. The work presented in this paper demonstrates that, for the proposed WECS, the maximum reactive power supplied to the grid is about 40% of the nominal value. Experimental results obtained from an experimental prototype are presented in this paper. The performance of the system using a wind turbine emulator and typical wind profiles is discussed in this paper.