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To attenuate the peaks of harmonics, three carrier-based randomized pulse position modulation schemes are proposed for an indirect matrix converter (IMC), which, to date, have not been discussed in existing literatures. In the first scheme, to avoid commutation of a rectifier stage at instants of carrier transition, one of four different pulse positions of the rectifier stage is selected randomly based on the Markov chain. The second scheme randomly places the center of the pulse position with a limited degree of freedom, which has a lower harmonic spectrum but higher commutation frequency. The maximum degree of freedom is achieved in the third scheme, which randomly varies the pulse position by delaying its edge along entire carrier cycle, resulting in a continuous and flat harmonic spectrum, but the maximum commutation frequency in three proposed schemes. An alternative carrier of an inverter stage is applied in all the schemes to maintain smooth operation at instants of carrier transition. Effectiveness of the proposed schemes is validated through experimental tests on an IMC prototype.