In recent years

most existing researches on power system oscillation stability problems caused by grid-connected voltage source converters（VSC） under weak connections have focused on the link of phase locked loop（PLL）

and the researches on the stability of the VSC outer loop control system that does not consider the dynamic effect of the PLL are rarely available. In order to study the stability characteristics and affecting factors of this link

this paper establishes a VSC outer loop linearization model in which the DC voltage control link and the reactive power control link are taken into consideration. Based on the Rouss-Herwitz criterion

the stability criterion of the outer loop control model of the grid-connected VSC under the weak connection condition is obtained

and the correctness of the stability criterion derived is verified by the simulation in case study. And then

the key factors affecting the stability and changing rules are analyzed. The research results show that when the dynamic effect of PLL is not considered

the main link that affects the stability of the grid-connected VSC under weak connection conditions is the VSC power control outer loop. The DC voltage outer loop control parameters have a significant impact on the stability of the grid-connected VSC

and the reactive power outer loop control parameters have a relatively small impact on the stability of the grid-connected VSC; at the same time

the more weakly the VSC is connected to the grid

the greater the risk of unstable oscillations in the system will be.