Consideration of Control-Loop Interaction in Transient Stability of Grid-Following Inverters using Bandwidth Separation Method

Grid-following inverters are critical for integrating renewable energy into modern power systems, but their transient stability remains challenging due to complex interactions between the phase-locked loop (PLL) and outer-loop controllers like DC-link voltage control (DVC) and AC terminal voltage control (TVC). Simplifying these dynamics often overlooks nonlinear coupling that can lead to instability. Researchers Yifan Zhang, Yunjie Gu, and colleagues from Imperial College London and Cornell University introduce an asymptotic analysis approach called the bandwidth separation method. This technique reduces the order of differential equations when sufficient bandwidth separation exists, enabling explicit characterization of PLL-DVC interactions. Their analysis reveals that such interactions degrade system stability and shrink the stability region, with voltage instability frequently being the actual root cause—not just PLL loss of synchronism.

The study identifies optimal bandwidth configurations under various grid fault conditions: a larger PLL bandwidth improves resilience to phase-jump faults, while a larger DVC bandwidth enhances tolerance to power fluctuations. Additionally, a high TVC bandwidth can mitigate the destabilizing effects of PLL-DVC interaction, further improving transient stability. All analytical findings were validated through hardware-in-the-loop (HIL) experiments, confirming the method's practical relevance. This work provides actionable design guidelines for inverter control loops, helping engineers build more robust renewable energy interfaces that can withstand grid disturbances without cascading failures.