Grid-Synchronization Stability Analysis and Loop Shaping for PLL-Based Power Converters With Different Reactive Power Control

Power converters may lose synchronization with the remaining network when integrated in a weak power grid. Such an instability phenomenon [known as grid-synchronization instability (GSI)] features the frequency divergence of phase-locked loop (PLL) and oscillations of the converter's power output. In this paper, we focus on the influences of reactive power control (RPC) methods on GSI. We develop a single-input-single-output model to explicitly reveal how the PLL interacts with the other parts of the converter system in terms of grid synchronization. Then, after deriving the open-loop transfer function and sensitivity function of the entire converter system, we compare the stability margins for different RPC methods. Furthermore, we elaborate on the interactions among RPC, PLL, and voltage feedforward (VFF), and then demonstrate that different design methods of RPC and VFF will lead to different stability margins. The subsequent stability analysis provides insightful guidelines for coordinating the design of multiple control loops, i.e., RPC, VFF, and PLL. In particular, we demonstrate how the loop shaping of PLL takes effect in increasing the stability margin and eventually preventing the converter from GSI. The validity of the stability analysis is verified through simulations in MATLAB/Simulink.