Robust Choice of Virtual Impedance for Virtual Synchronous Machines Accounting for Grid Impedance Uncertainty

This paper demonstrates how the internal virtual impedance in virtual synchronous machines (VSM) can be chosen to ensure stability and robustness against grid impedance variations. Three VSM implementations are considered: a current controlled VSM with dynamic electrical model (CC DEM) VSM, a current controlled VSM with quasi stationary electrical model (CC QSEM) VSM, and a voltage controlled (VC) VSM with cascaded voltage and current control loops. Eigenvalues analysis is applied to demonstrate how the virtual impedance requirements for ensuring stability are different for the three studied VSM implementations. Moreover, it is shown how tuning of the virtual impedance can ensure stability for all three VSM implementations under all combinations of grid resistance and inductance in the interval rg ∊ (0, 0.2] p.u. and lg ∊ (0, 1] p.u. The results from the small signal analysis are validated using time domain simulations.