In this paper, the control of the reactive power supplied by a matrix converter to a grid is presented. A matrix converter is used to feed an induction generator using a space vector modulation algorithm. An input current observer, implemented using an estimation of the modulation matrix, is used in a non-linear controller that regulates the reactive power supplied to the grid by a variable-speed wind energy conversion system (WECS). The results obtained are experimentally validated using a 2 kW experimental prototype implemented using a cage machine, a matrix converter and a wind turbine emulator.