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Series and parallel multicell converters have been introduced because they provide benefits in term of efficiency and power density. However, they also allow reducing the amount of energy stored in the filters, which potentially allows for faster dynamic responses. Interleaving the control patterns of different cells is another distinctive feature of these converters and is also the root of another potential improvement of the dynamic response: with one PWM update at each subcycle of the switching period, a n-cell converter may change its average output voltage over each of these intervals, while standard converters can only control the voltage over half the switching period. In this paper, a general multirate modulation strategy taking advantage of this property, while avoiding overswitching, and compatible with any n-cell converter is proposed and validated by simulation and experimental results.