Small-Signal Stability Analysis Considering the Interaction Characteristics of Grid-Forming and Grid-Following Converters

Unlike single-converter grid-connected systems and multi-converter grid-forming (GFM) systems operating in islanded mode, grid-connected multi-converter systems comprising parallel grid-following (GFL) and GFM converters exhibit more complex internal interactions. The negative damping of GFL converters and the low-frequency inertia of GFM converters can reinforce each other, increasing the risk of wideband oscillations. Conventional impedance models do not fully account for frequency-coupling effects among converters, which can lead to impedance-model mismatch and invalidate the Nyquist criterion. Moreover, the high order of the transfer functions of multi-converter systems makes frequency sweeps difficult. Conversely, time-domain state-space models neglect the dynamics of individual control loops, resulting in inaccurate modeling and distorted parameter-sensitivity results. This paper develops a heterogeneous small-signal model that captures the full dynamics of GFM and GFL converters and uses an eigenvalue-sensitivity criterion to reveal their behavior under coupled parameters. On this basis, the effects of GFM inertia and damping on GFL variables, as well as the effect of phase-locked loop (PLL) bandwidth on the eigenvalues of the GFM system, are investigated. The proposed model and associated stability analysis provide a basis for assessing the stability of such systems and optimizing system parameters. Finally, simulations verify the conclusions.