As the practice of high proportion of wind power access to the power system gradually increases, sub-synchronous oscillation may occur in grid-connected wind power system under weak connection conditions, which affects the safe and stable operation of the system. Therefore, it is urgent to reveal the inherent mechanism. Current researches attempt to clarify the small disturbance stability mechanism of grid-connected wind power system under weak connection condition by using various analysis methods from multiple perspectives. The application of these methods promotes the in-depth study of the mechanism of sub-synchronous oscillation, but also leads to the fragmentation of research results, which needs to be further summarized. Given to the above situation, the research results both from China and foreign countries in recent years are reviewed and sorted out. From four aspects of time domain analysis, mode analysis, impedance analysis and complex torque coefficient analysis, the development of mechanism research under each analysis methodology and the application status of weak connection condition are summarized. The advantages and limitations of different analysis methods in mechanism research are summarized and compared. Finally, based on the results, the research trends and application prospects of each method in the future research on the stability mechanism of wind power integrated into the weakly connected power grid with small disturbances are prospected, in order to provide a beneficial reference for the safe and stable long-distance transmission of large-scale wind power. This work is supported by the National Key Research and Development Program of China (No. 2016YFB0900602).