A Wide-Frequency Stability Characteristic Domain Method for Small-Signal Stability Analysis of Grid-Forming Direct-Drive Wind Turbines

To accurately evaluate the small-signal stability of grid-forming (GFM) direct-drive wind turbines over time-varying operating conditions and broad frequency ranges, this paper proposes a wide-frequency stability characteristic domain method. Unlike grid-following turbines, GFM control relies on power-loop-driven self-synchronization rather than a phase-locked loop, which introduces multi-time-scale couplings among the virtual power angle, inner control loops, digital control delay, and weak-grid impedance. A parametric admittance model embedded with continuous operating-point variables is therefore established to characterize the converter wide-frequency dynamics. By combining physical power-transmission constraints with closed-loop pole-based small-signal stability criteria, a wide-frequency stability characteristic domain is constructed to map the stable, unstable, and physically infeasible regions over the continuous operating space. The boundary evolution under varying grid impedances and VSG control parameters is further analyzed. The experimental cases verify the operating-region transition predicted by the proposed domain. In addition, the supplementary high-frequency pole analysis shows that, when digital delay is considered, another high-frequency mode may become weakly damped or unstable under different grid-impedance conditions. These results indicate that the proposed framework captures both the low-frequency boundary-crossing behavior observed in the experiments and the potential high-frequency instability risk introduced by converter digital dynamics.