Explicit Impedance Modeling and Shaping of Grid-Connected Converters via an Enhanced PLL for Stabilizing the Weak Grid Connection

The voltage source converters (VSCs) are used to interface and control the renewable energy resources that are integrated into the power grids. However, a weak grid connection raises a stability problem for grid synchronization of the grid-feeding current-controlled VSCs (CCVSCs). This paper handles modeling and controller design for stabilizing the weak grid connection of CCVSCs. The impedance modeling/shaping of the VSC has been recognized as an effective tool to analyze and design the dynamics of the VSC. But an explicit and accurate impedance model of the CCVSC is required. Particularly, modeling the impact of the phase-locked loop (PLL) synchronization unit on the impedance model of the CCVSC is complex. Therefore, at first, an efficient impedance model of the CCVSC is developed while the impact of the PLL is rigorously considered through a complex procedure that results in an explicit/accurate impedance model. The developed impedance model is used to conduct passivity/weak grid connection stability analysis to clarify the underlying causes of instability problems. Then, a novel PLL, with an in-loop low-pass filter (LPF) to account for harmonics/asymmetries, is proposed with enhanced characteristics using the state feedback control. The impedance shaping method (with the aid of the impedance model) is utilized to design the state feedback gains. The state feedback loops provide degrees of freedom for bandwidth design of the PLL considering the current/power control loops and stabilize the system under weak grid connection/distorted conditions. Simulation results prove the accuracy and effectiveness of the models.