This thesis presents a comprehensive procedure to study sub-synchronous interactions in wind integrated power systems effectively and efficiently. The proposed procedure involves a screening phase and a detailed analysis phase. The screening is performed using a frequency scan and the detailed analysis is performed using small signal stability analysis. To facilitate the small signal analysis, a detailed linearized model of a Type 3 wind power plant is presented in this thesis. The model presented includes the generator, a three-mass drive train model, rotor and grid side converter controller models, converter transformer model and the pitch controller model. To accurately capture the effects of sub-synchronous interactions, the ac network is modelled using dynamic phasors. It is shown that using the proposed procedure, the sub-synchronous interaction between a Type 3 wind power plant and a series compensated line is due to an electrical resonance between the wind power plant generator and the series capacitor. It is also shown that this interaction is highly controllable through the rotor side converter current controllers. This fact will be proven by studying the sub-synchronous interactions in a single machine power system as well as in multi machine power systems. This thesis also presents a sub-synchronous interaction mitigation method using network devices. The performance of an SVC and a STATCOM is evaluated in this thesis. A small signal stability analysis based method will be used to design a sub-synchronous damping controller. A method will be presented to estimate the damping controller parameters systematically to obtain the desired performance using small signal stability analysis results. Furthermore, it will be shown that by strongly controlling the voltage of the point of common coupling, the damping of the oscillations produced by the sub-synchronous interaction between the wind power plant and the series compensated line can be improved. Based on the findings of this research, the thesis proposes a number of recommendations to be adopted when studying the sub-synchronous interactions in wind integrated power systems. These recommendations will facilitate to do such studies effectively and pinpoint the root cause of the sub-synchronous interactions.