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Indirect matrix converter (IMC) using two stages configuration is an interesting alternative for ac/ac conversions. In some cases, the ac/ac converter needs boost function, which can't be achieved by traditional IMC due to its limited input-to-output voltage transfer gain 0.866. Alternatively, reverse power flow operation of IMC can be implemented to meet voltage boost requirement, where the input ac source is connected to the converter's voltage source side and the output utility grid or load is connected to the current source side. This paper proposes control schemes of IMC under reverse power flow operation for both grid-connected and isolated modes with distributed generation suggested as a potential application. In grid-connected mode, the commanded power must be extracted from the input ac source to the grid, in addition to guarantee sinusoidal input/output waveforms, unity input power factor and controllable grid-side power factor. In isolated mode, the matrix converter is controlled to supply a three-phase ac voltage and also guarantee sinusoidal input/output waveforms as well as unity input power factor. Simulation and experimental results are provided to validate the effectiveness of the control schemes for the proposed matrix converter.