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Grid-connected unity-power-factor converters based on one-cycle control (OCC) do not require the service of phase-locked loop or any other synchronization circuits for interfacing with the utility. As a result, these schemes are becoming increasingly popular. However, as the power handled by the converter increases, the power factor deteriorates. To understand quantitatively the cause of poor power factor while negotiating high power loads, large signal models for these schemes are developed. Having understood the cause for poor power factor operation, a modified-OCC-based converter is proposed. This scheme has high power factor while supplying high power loads. Detailed simulation studies are carried out to verify the efficacy of the scheme. In order to confirm the viability of the scheme, detailed experimental studies are carried out on a 3-kW laboratory prototype.