Analytical model of three-phase four-wire VSC operating as grid forming power converter under unbalanced load conditions

This paper presents an analytical model of typical three-phase, three-leg, four-wire and two-level PWM controlled voltage-source converters (VSCs) suitable to investigate the harmonic generation at dc- and ac-side of the converter under sinusoidal unbalanced current condition, e.g., positive-sequence third order harmonic voltage in the VSC ac-side. The proposed model, based on instantaneous power theory as well as switching functions concepts, permits to evaluate the oscillating voltage that appears on the VSC dc-side. The effect of the zero- and negative-sequence current components are considered on the dc capacitance calculation which consequently enables to size the dc capacitor accurately in order to keep the dc voltage ripple of each split capacitor under pre-defined limits. The model also shows the exact dc-side voltage ripple due to the VSC ac-side zero- and negative-sequence currents. It shows also how to calculate the non-characteristic harmonics on the VSC ac side.