Developing a machine equivalent inertial response for a Virtual Oscillator Controlled Inverter in a machine-inverter based microgrid

Virtual Oscillator Control (VOC) is a decentralized grid-forming inverter control strategy that emulates the dynamics of a class of nonlinear oscillator. It is currently being considered as a promising alternative to conventional power frequency droop control for microgrids. However, the inertial response associated with VOC has proved challenging to quantify. In this paper the per unit inertia constant of a VOC inverter is derived when coupled with a synchronous generator (SG), for a micro-grid operating in an islanded configuration. A proportional derivative (PD) controller is then added to the VOC regulator to create a similar response to that provided by the inertia of a conventional rotating machine SG. Combined with the swing equation of the SG, the equivalent inertia constant of the VOC inverter is expressed analytically as a simple function of control parameters. The effect of altering the equivalent VOC inertia constant is investigated using small-signal analysis, and then assessed and verified by simulation and experiment. The time-domain results under transient conditions of the SG machine frequency variations and the inverter output current verify the analysis and demonstrate the limits of equivalent inertia that can be developed.