Small-Signal Modelling and Sub-Synchronous-Mode Identification of DFIG Wind Farms with Series Compensation

Series-compensated transmission lines are widely used to evacuate wind power from remote bases, yet they may excite sub-synchronous oscillations (SSOs) in doubly fed induction generator (DFIG) wind farms. This paper builds a unified 23-state small-signal model that explicitly retains the aerodynamic turbine, two-mass shaft, DFIG electrical dynamics, back-to-back converter control loops and the LC series capacitor. A fully automated eigen-analysis routine-combining QR decomposition with participation-factor filtering-isolates critical SSO modes within one millisecond on a standard laptop. Applied to a 100 MW wind-farm corridor with 30 % series compensation, the method pinpoints an unstable 24 Hz induction-generator-effect mode, its frequency and growth rate deviate from electromagnetic-transient simulation by less than 2 % and 4 %, respectively. The compact model therefore enables real-time stability scanning and provides a solid basis for controllers gain scheduling or virtual-damping design in practical wind-power grids.