Subsynchronous Oscillation Analysis and Phase-Shift Damping Control of Grid-Following Direct-Drive Wind Farms with Grid-Forming Energy Storage

Subsynchronous oscillation (SSO) is a critical stability issue in grid-following direct-drive wind farms connected to weak grids. To mitigate this issue, this paper proposes a phase-shift subsynchronous damping control strategy based on grid-forming energy storage (GF-ES). First, a small-signal state-space model of a grid-connected wind-storage system incorporating GF-ES is established, and eigenvalue analysis is conducted to examine the effects of GF-ES capacity share, virtual synchronous control parameters, and grid strength on the dominant SSO mode. The results show that, under weak-grid conditions, the coupling among point of common coupling (PCC) voltage disturbances, the wind turbine Phase-Locked Loop (PLL), and grid-side current control reduces system damping, causing the dominant SSO mode around 22.1 Hz to exhibit weak or even negative damping. To enhance damping under low-capacity conditions, a phase-shift subsynchronous damping controller (PS-SDC) is designed, and its additional damping voltage signal is superimposed onto the q-axis voltage command of the GF-ES inner current control loop. Eigenvalue analysis shows that, under conventional virtual synchronous generator (VSG)-controlled GF-ES, increasing the GF-ES capacity share from 2% to 20% shifts the dominant SSO eigenvalue from 1.0128 ± j138.8370 to −1.7111 ± j138.8097, and increases the damping ratio from −0.0073 to 0.0123. At the baseline 10% GF-ES capacity share, the proposed PS-SDC further shifts the dominant eigenvalue from −0.4780 ± j138.8223 to −1.5691 ± j138.8224, increasing the damping ratio from 0.0034 to 0.0113. The small-signal stability boundary is also improved from between 6.5% and 10% GF-ES capacity share to between 4% and 6.5%, demonstrating that the proposed PS-SDC provides enhanced damping capability for the 22.1 Hz dominant SSO mode under weak-grid and low-capacity GF-ES conditions.