High-frequency modelling of a three-phase pulse width modulation inverter towards the dc bus considering line and controller harmonics

Closed-form analytical formulas are provided to calculate the dc bus harmonics of a three-phase sinusoidal pulse width modulation (SPWM) inverter. The harmonic analysis is performed by using a double Fourier series approach to determine the dc bus current frequency spectrum. For an arbitrary modulation index and load power factor, the full harmonic components of the inverter dc side current are calculated. Based on the developed analytical model, an equivalent circuit is proposed for the inverter harmonic analysis towards the dc bus. Moreover, the impacts of line harmonics and zero sequence injection in controller towards the dc bus are presented. The results show that the 5th and 7th ac line harmonics on the dc side current is appearance of the 6th harmonic in the dc side. The impact of zero sequence injection to the controller on the dc side is negligible. In addition to analytical formulation, different simulations and extensive measurements performed which the results verified the presented analytical framework.