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This paper first presents a step‐by‐step tutorial on modal analysis of a doubly‐fed induction generator (DFIG)‐based series compensated wind farm. The model of the system includes a wind turbine aerodynamics, a sixth‐order order induction generator, a second‐order two‐mass shaft system, a fourth‐order order series compensated transmission line, an eighth‐order rotor‐side converter (RSC) and grid‐side converter (GSC) controllers, and a first‐order DC‐link model. Then, using modal analysis and time‐domain simulations, it is shown that a fixed‐series compensated DFIG is highly unstable due to the sub‐synchronous resonance (SSR) mode. In order to damp the SSR mode, the wind farm is interfaced with the gate‐controlled series capacitor (GCSC) ‐ which is a new series flexible AC transmission system (FACTS) device. A SSR damping controller (SSRDC) is designed for the GCSC using residue‐based analysis and root locus diagrams, and an effective input control signal (ICS) to the SSRDC is identified in order to simultaneously increase damping of both the SSR and super‐synchronous (SupSR) modes. The IEEE first benchmark model on SSR is adapted with an integrated DFIG‐based wind farm to perform studies. Matlab/Simulink is used as a tool for designing process, and PSCAD/EMTDC is used for time‐domain simulations. [ABSTRACT FROM AUTHOR]