With the continuous growth of power demand and the opening of the power market, large-scale distributed power sources are connected to the distribution network through grid-connected converters, forming an active distribution network. The impedance characteristics of the distribution grid will be somewhat different from those of the larger grid with a larger resistive component. At present, there are two main control modes for grid-connected converters: grid following (GFL) and grid forming (GFM), which show different impedance characteristics due to different control modes. For distribution network with changing strengths, converters with a single control mode can no longer satisfy the need for stable operation, and the control modes of grid-connected converters can be flexibly switched to ensure the stable operation of the system in the active distribution network. This article firstly establishes the sequential impedance models of GFL and GFM respectively and analyzed their impedance characteristics comparatively. Then the impedance characteristics and grid stability analysis of the grid under different grid strengths are carried out under the consideration of the distribution network resistance component to derive the grid strength cut-off point that needs to be switched for the converter control mode. Finally, taking into account the grid resistance component，this article verifies through simulation that the proposed control method of switching the grid converter at the grid strength cut-off point can keep the system in stable operation.