Impact of Virtual Inertia on Stability Delay Margins of Micro grids with Communication Time Delay

High penetration of renewable energy sources (RESs) may contribute to power system oscillations due to diminished inertia, while communication networks generate time delays that can compromise system performance and induce frequency fluctuations. This paper uses Rekasius substitution to compute the stability delay margin of an islanded micro grid (MG) with virtual inertia (VI) and constant communication delay. For a finite positive time delay, the approach seeks to find all possible purely complex roots of the characteristic equation. The method starts by converting the transcendental terms in the characteristic polynomial into a regular polynomial. After that, the Routh-Hurwitz Stability Criterion is used to calculate the purely imaginary roots with the crossing frequency and stability delay margin. Time delay values at which the MG is marginally stable are estimated for a wide range of proportional-integral (PI) controller gains. Accuracy of results is verified using quasi-polynomial mapping-based root finder (QPmR) algorithm and time-domain simulations in Matlab/Simulink.