Stability Analysis of DC Microgrids Under Distributed Control Considering Converter Dynamics

DC microgrids (DCMGs) have attracted increasing attention owing to their high efficiency and compatibility with renewable energy sources. However, maintaining system stability under distributed control remains challenging, as the coupling between controller and converter dynamics leads to a high-order system, particularly when numerous converters are involved. For such high-order systems, singular perturbation theory can decouple the dynamics into fast and slow subsystems, allowing the overall stability to be inferred when the fast subsystem responds sufficiently faster than the slow one. Nevertheless, existing studies have not quantified how much faster the converter dynamics must be relative to the controller dynamics to ensure overall stability, which may lead to the failure of stabilization control. Moreover, when system parameters are uncertain—such as under varying load conditions—traditional stability analysis methods face difficulties in deriving explicit analytical criteria. To address these issues, this paper presents a comprehensive stability analysis of DC microgrids based on singular perturbation theory and the small-gain theorem. First, singular perturbation theory is employed to decompose the high-order DCMG into a boundary-layer subsystem and a reduced-order subsystem, and explicit analytical stability conditions are derived for each. Second, based on the small-gain theorem, it is rigorously proven that when both subsystems are stable, smaller filter capacitances, inductances, and controller gain coefficients enhance the system’s stability—and a quantitative analytical criterion is further derived to quantify this relationship. Third, under uncertain load conditions, the singular value inequality is utilized to derive analytical conditions for robust stability. Simulation results show that the relative error between the stability bound derived by the proposed conditions and the actual stability bound is about 15.4% for constant loads, and approximately 44.4% for uncertain loads—verifying the proposed method’s low-conservatism advantage under constant loads and effective robustness under uncertain loads.