Robust Stability Region Analysis of Weak-Grid-Following Converters With Multiple Uncertain Parameters

Robust stability region analysis of voltage source converter (VSC) under DC-link voltage control (DVC) is essential to integrate inverter-based resources (IBRs). The determination of operability specifications (e.g., control loops tuning boundaries) in weak grids becomes particularly challenging when accounting for simultaneous uncertainties in line impedance, transfer power, AC grid voltage and DC-link capacitor. In this paper, warranting the stability of the converter in uncertain contexts is formulated as a robust stability problem with structured singular value (SSV, also called μ). Grey-box modeling is adopted to account for the impact of variations in power stage on operating point by treating them as parametric uncertainties, while control loops tuning is modeled as parametric or unstructured uncertainties depending on the knowledge of control structure. Robust stability margin is then efficiently identified as the smallest structured uncertainty matrix destabilizing the system and the radical effect of the uncertainty on robust stability region can be analytically quantified. Robust design with respect to μ results is proposed to guarantee a specific level of robustness. Exemplary results show a time saving of at least 90% compared to eigenvalues analysis without sacrificing accuracy. The performed analysis results are validated through the simulation and a lab-scale prototype.