Volterra series modelling of power conversion systems

The nonlinear control-to-output response of pulse-width-modulated (PWM) conversion systems is modeled via the Volterra functional series. The determination of the Volterra kernels in the transform domain is performed on a simplified state space model of the converter. The general system response was determined for the particular case of a two-tone excitation, which allowed the determination of the magnitudes of various harmonic and intermodulation frequency components in the output spectrum. For the frequency components of interest it was sufficient to only consider the first three Volterra operators. It was seen that the frequency components in the output spectrum have contributions from an infinite number of Volterra operators. Generally, the contribution diminishes with the order of the operator, such that the dominant contributions is attributed to the lowest order operator. It was seen that the magnitude (with an appropriate scaling factor and phase) of the Laplace transform of the lowest order Volterra kernel which contributes to the frequency component of interest.<>