I. Introduction
In the context of power systems with higher penetrations of power electronics connected generation, virtual synchronous generator (VSG) control of converters has been proposed as a means to improve the system transient stability by emulating inertia in the control loop of the converter. To obtain clearer insight into the VSG settings most previous works have analyzed the VSG neglecting the effects of the line resonance [1], [2] and the voltage source converter (VSC) dynamics [3]. This is valid based on the assumption that the overall VSG response is much slower than either the VSC dynamics or the system synchronous frequency. Under these assumptions the VSG dynamics can be approximated by a second order transfer function thus simplifying the analysis and giving useful insight. Of course, in most cases, this assumption is valid. However, reducing system inertia may demand larger virtual inertial response from converters, thus requiring more rapid power response from the VSG. It is therefore important to understand the range of settings for which the simplified second order analysis remains valid so as to avoid stability problems with the overall VSG response. The original contribution of this work is to provide a simple analysis based on transfer functions which gives insight into the choice of VSG virtual inertia and damping settings to ensure VSG stability taking into consideration VSG, VSC and line dynamics. This has important consequences for the range of virtual inertia and damping response which can be obtained from converter connected generation and storage. The proposed constraints define the necessary and sufficient condition to ensure stability and the validity of the reduced VSG model used in power system level analysis.