Integration of doubly‐fed induction generator (DFIG) based wind turbines (WTs), in series‐compensated power grids, may result in a phenomenon known as sub‐synchronous control interaction (SSCI). Indeed, SSCI, created due to interaction between WTs controllers and series‐compensated power grid, may worsen damping of sub‐synchronous resonance (SSR) oscillations. This paper deals with the analytical assessment and mitigation of SSCI phenomenon in series compensated grids comprising of DFIG‐based WTs. In this way, first, theoretical and mathematical expressions and equivalent circuits regarding the SSCI phenomenon and the impacts of the RSC and GSC controls on the SSR oscillations damping are given and then a comprehensive impedance model for the DFIG‐WT at the sub‐synchronous frequency is extracted. Next, the rotor current control is modified, and an efficient approach based on the feedback linearizing technique (FLT), different from approaches presented in the related literature, is presented to mitigate the negative role of the DFIG in SSR frequencies. By mathematical analyses and developing related formula, it is shown that the proposed approach changes the impedance of the rotor circuit to infinity at the SSR frequency. This in turn results in suppression of the SSR oscillations initiated as a result of induction generator effect and SSCI phenomenon.