Power spectral density analysis of randomly switched pulse width modulation for DC/AC converters

This paper presents a detailed spectral analysis of the random switching frequency PWM technique for control of three-phase inverters. A number of novel results are reported including criteria for the existence of discrete harmonics in the output voltage waveforms, exact expressions for the power carried by these harmonics and an approximate but accurate formula for the continuous density. Furthermore, the theory is generalized to any periodic modulation function. As an example, the third harmonic injection technique is analyzed, and based on extensive comparisons of predicted spectra with measured spectra and as opposed to all earlier investigations of random PWM schemes, the theory is found to be very accurate for both single phase and line-to-line spectra.