The occurrence of Sub-Synchronous Resonance (SSR) phenomena can be attributed to the interaction that takes place between wind turbine generators and series-compensated transmission lines. The Doubly-Fed Induction Generator (DFIG) is widely recognized as a prevalent generator form employed in wind energy conversion systems. The present paper commences with an extensive exposition on modal analysis techniques employed in a series of compensated wind farms featuring Doubly Fed Induction Generators (DFIGs). The system model encompasses various components, including the aerodynamics of a wind turbine, an induction generator characterized by a sixth-order model, a second- order two-mass shaft system, a series compensated transmission line described by a fourth-order model, controllers for the Rotor-Side Converter (RSC) and the Grid-Side Converter (GSC) represented by an eighth-order model, and a first-order DC-link model. The technique of eigenvalue-based SSR analysis is extensively utilized in various academic and research domains. The eigenvalue technique depends on the initial conditions of state variables to yield an accurate outcome. The non-iterative approach, previously employed for the computation of initial values of the state variables, has exhibited issues with convergence, lack of accuracy, and excessive computational time. The comparative study evaluates the time-domain simulation outcomes under different wind speeds and compensation levels, along side the eigenvalue analysis conducted using both the suggested and non-iterative methods. This comparative analysis is conducted to illustrate the proposed approach efficacy and precision. The results indicate that the eigenvalue analysis conducted using the proposed technique exhibits more accuracy, as it aligns with the findings of the simulations across all of the investigated instances. The process of validation is executed with the MATLAB program. Within the context of the investigation, it has been found that increasing compensation levels while simultaneously decreasing wind speed leads to system instability. Therefore, modifying the compensation level by the current wind speed is advisable.