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This paper presents a current control scheme with instantaneous reactive power minimization for an indirect matrix converter. The strategy uses the commutation state of the converter in the subsequent sampling time according to an optimization algorithm given by a simple cost function and the discrete system model. Using this strategy, harmonics in the input current generated by the resonance of the input filter are strongly reduced. Simulation and experimental results with a laboratory prototype are provided in order to validate the control scheme, and the effects of a distorted source voltage and filter resonance are analyzed.