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This paper presents a comprehensive analysis of sub-synchronous interactions in a wind integrated power system to understand and mitigate them. The proposed procedure has two steps. In the first step, a frequency scan is performed to determine the presence of resonant frequencies in the sub-synchronous range. In the second step, a detailed small signal analysis is performed. Participation factors are used to identify the state variables that are involved in the interaction, and the controllability indices are used to determine the mitigation method. It is shown that the sub-synchronous interaction present in Type 3 wind turbine-generators connected to the grid through series compensated lines is an electrical resonance between the generator and the series compensated line which is highly sensitive to the rotor side converter current controller gains.