Small-signal modelling and parametric sensitivity of a Virtual Synchronous Machine

The Virtual Synchronous Machine (VSM) concept is emerging as a flexible approach for controlling power electronic converters in grid-connected as well as stand-alone or microgrid applications. Several VSM implementations have been proposed, with the emulation of inertia and damping of a traditional Synchronous Machine (SM) as their common feature. This paper investigates a VSM implementation based on a Voltage Source Converter (VSC), where a virtual swing equation provides the phase reference for cascaded voltage and current control in a synchronous reference frame. The control system includes also a virtual impedance and an outer loop frequency droop controller which is functionally equivalent to the governor of a traditional SM. A linearized small-signal model of the VSM including the converter and its grid side filter, the control system and a simple grid equivalent, is developed and verified by time-domain simulations of a nonlinear system model. The small-signal model is used to identify the critical modes of the system and to investigate their parametric sensitivity.