Stability analysis and mitigation of grid-following converters based on describing function method

The increasing proportion of renewable energy sources has promoted the widespread adoption of power electronic converters, which may elevate instability risks and pose new challenges to modern power systems. Traditional stability analysis methods (such as eigenvalue and impedance-based approaches) typically rely on linearized system models, and rarely account for the influence of nonlinear components, potentially leading to incomplete results. In this paper, we investigate the influence of the controller limiter on the stability of grid-following (GFL) converters. By employing the describing function (DF) method, we model the system’s nonlinear and linear components separately and analyze stability via the DF-based Nyquist criterion. On the basis, we further explore two potential oscillatory phenomena: sustained constant-amplitude oscillations and forced oscillations. We demonstrate that the presence of nonlinear components can lead to sustained oscillations in GFL converters, a phenomenon absent in linear systems. Furthermore, we explore the possibility of forced oscillations triggered by external sinusoidal disturbances during such sustained oscillations. In addition, a loop-shaping method accounting for system nonlinearity is proposed to suppress these sustained oscillations. Finally, the above analysis is validated through time-domain simulations. • Sustained oscillations in grid-following (GFL) converters are shown to be induced by the current limiter using the describing function (DF) method. • Periodic disturbances can cause forced synchronization in limit-cycling GFL converters, completely suppressing the original limit cycle frequency. • A loop-shaping mitigation strategy that accounts for nonlinear effects is proposed to effectively suppress sustained oscillations. • A single-input single-output (SISO) model is derived to analyze system stability and the impact of parameters on oscillations using the DF-based Nyquist criterion.