Stability analysis of Three-phase Grid-Connected inverter under the weak grids with asymmetrical grid impedance by LTP theory in time domain

The Grid-connected inverter (GCI) often operates in the weak grid with asymmetrical grid impedance due to the unbalanced and single-phase loads. However, the time-periodic dynamic behavior effect of the Phase-Locked Loop (PLL) on the GCI operating in an asymmetrical system is not investigated in the time domain. This paper explores the influence of the asymmetrical grid impedance on the stability of the weak grid with GCI. Firstly, GCI's complete harmonic state-space (HSS) model considering PLL under the asymmetrical network is established. Secondly, in view of the developed HSS model, the predominant parameters are determined through the eigenvalues of the system state matrix, along with the participation factors. Afterward, with eigenvalue locus analysis, the stability boundaries of the system's critical parameters involving the current reference, current controller, and PLL controller are determined under different grid impedance asymmetrical indexes. It is found that the stability region of system parameters is narrowed with increasing impedance asymmetrical index. Lastly, simulations and experiments are carried out to verify the effectiveness of the proposed HSS model and the theoretical analysis results.