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Random pulse width modulation in static power converters results in the partial transfer of power from the discrete spectrum of the output voltage to the continuous spectrum, with advantageous effects on the operation of the supplied electromechanical systems. In this paper, a random PWM technique with randomized pulse position for three-phase voltage-controlled inverters is analyzed. Closed-form equations for the discrete and continuous power spectra of the line-to-line and line-to-neutral voltages of the inverter have been derived and confirmed by experiments. Presented theory opens the way to numerical optimization of the voltage spectra of randomly modulated inverters.< >