To insure a stable and reliable operation of the existing and future grids, it is important to study the stability of the power electronic based converters’ controls which can replace synchronous generation. Most existing studies use a Thévenin equivalent model of the grid to test the grid following controls. The present article demonstrates the limits of these studies. An alternative setup is proposed and is shown to provide more insight into the underlying mechanisms of the grid following control behaviour in weak grids, using a linearized state space model. These insights are exploited to propose further improvements to the control. These improvements are shown to extend the stability of the control while reducing the interactions among converters.