Limit-Induced Instability Analysis of Grid-Forming Converter under Large Disturbances Based on Bifurcation Theory

The instability of Grid-Forming (GFM) converters induced by the current limiter under large disturbances brings disaster to the power system but the mechanism of limit-induced instability has seldom been investigated. In this paper, instability phenomena in the GFM converter after large disturbances considering the effect of the current limiter are explored comprehensively and the mechanism is investigated in depth based on the bifurcation theory. First, the full-order state equations of the GFM converter are derived to accurately characterize the nonsmooth properties introduced by the current limiter. Second, the transient behaviors of the GFM converter under current limiting after large disturbances are explored by circuit simulations, with a focus on the evolution of post-fault states. Third, the mechanism of state transition and further instability is investigated thoroughly based on bifurcation analysis. Specifically, the classical bifurcation and nonsmooth bifurcation are identified, and the discontinuous Hopf bifurcation and classical fold bifurcation are found to be the main causes of limit-induced instability. Finally, the stability regions are illustrated in multiparameter space based on analysis of bifurcation boundaries to provide guidance for system design and the results of theoretical analysis are verified by circuit simulations in detail.