A Theoretical Analysis of the Harmonic Content of PWM Waveforms for Multiple-Frequency Modulators

This paper theoretically identifies the harmonic components of a carrier-based pulsewidth-modulated (PWM) voltage-source converter (VSC) output voltage when the modulating wave includes fundamental and baseband harmonic components. This occurs, for example, when a VSC is used as an active power filter. The general analytical solution provided can be applied with a minimum additional mathematical effort to any harmonic combination in the modulation signal. The analysis undertaken in this paper determines how the fundamental and low-order harmonics (in the modulation signal) interact with the carrier to produce the low (and high) order frequencies in the PWM VSC output voltage. The analysis is based on a double Fourier series expansion in two variables. This approach to harmonic identification is evaluated by a comparison with a fast Fourier transform analysis of simulated PWM waveforms.