Random pulsewidth modulation (RPWM) with variable carrier frequency generally disperses the dominant PWM harmonics more effectively than the RPWM with constant carrier frequency. But variable carrier frequency results in variable sampling frequency, which changes controller parameters and makes RPWM difficult to use in closed-loop applications. To significantly disperse dominant harmonic clusters located nearby the PWM frequency and its multiples, while maintaining constant sampling frequency, in this article, N-state random pulse position space vector pulsewidth modulation is proposed. This method randomly selects one of the N selected carrier patterns with equal probability in each carrier period, resulting in N different pulse position states. By applying two-dimensional Fourier analysis, the additional multiplication factor in the derivation results, named harmonic dispersion coefficient in this article, can intuitively explain the principle from the perspective of mutual cancellation of complex vectors in different directions. All dominant PWM harmonics are significantly dispersed except those located nearby the Nth PWM frequency and its multiples when using the proposed method. Besides, power losses and switching counts are detailed discussed. Both simulation and experimental results verify the effectiveness of the method at last. [ABSTRACT FROM AUTHOR]