Abstract: Studies have shown that SVG (static var generator), a reactive power compensation device that improves voltage stability, may interact with DFIG to form sub-synchronous oscillations, threatening the safety of the power grid. However, the mechanism of this function has not yet been fully clear. This paper studies the subsynchronous oscillation of the doubly-fed system with SVG, which shows that one of the reasons is the switching oscillation caused by the limiting saturation. From the perspective of non-smooth bifurcation thereby, the characteristics of switching oscillation with parameters are analyzed. Firstly, the non-smooth bifurcation theory, the switching oscillation, and the limiting link of the doubly-fed system with SVG are introduced. Secondly, the switching subsynchronous oscillation phenomenon of the doubly-fed system with SVG is analyzed, which reveals that it is the limiting saturation that causes the switching oscillation. Thirdly, the influence of different control parameters of SVG on the switching subsynchronous oscillation is analyzed, confirming the main factors related to system oscillation and showing the non-smooth bifurcation characteristics of switching oscillation on SVG control parameters. Finally, the influence of the external short-circuit capacity and the severity of the fault on the switching oscillation is analyzed, revealing the non-smooth bifurcation characteristics of the external parameters.