Asymmetric Complex-Vector Models With Application to VSC–Grid Interaction

The properties of complex space-vector models for asymmetric three-phase systems are investigated in this article. Most importantly, three alternative methods for the stability analysis of the asymmetric closed-loop systems are presented. The end results avoid the usage of matrix manipulations. It is shown how the theory can be applied to modeling and stability analysis of a grid-connected voltage-source converter (VSC). The methods are compared using numerical examples.