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This paper presents a new control method for indirect matrix converter operating under unbalanced grid voltages. The proposed method aims to achieve balanced output voltages as well as a near unity input power factor operation. First, an opportune reference current accurately generated, and a proportional integral resonant controller are designed in a dq reference frame that is synchronized with the positive sequence of the grid voltages so as to achieve a perfect tracking of input reactive power reference. Then, a real-time estimator of the virtual dc-link voltage is developed with the aim to provide balanced output voltages; therefore, an almost constant active power free of low frequency ripple is supplied from the grid. Experimental results are presented to verify the feasibility and effectiveness of the proposed control method. UNITY POWER FACTOR OPERATION OF INDIRECT MATRIX CONVERTER TIED TO UNBALANCED GRID