Enhancement of stability delay margins by virtual inertia control for microgrids with time delay

Large-scale deployment of renewable energy sources (RESs) contributes to fluctuations in the system frequency due to their inherent reduced inertia feature. Time delays have emerged as a major source of concern in microgrids (MGs) as a result of the broad adoption of open communication networks since significant delays inevitably reduce the controller's performance and even cause instabilities. In this article, a frequency-domain direct method is used to evaluate the impact of the virtual inertia (VI) control on the stability delay margins of MG with communication delays. By avoiding approximation, the approach first removes transcendental terms from characteristic equations and turns the transcendental characteristic equations into regular polynomials. With this method, roots of the original characteristic equation on the imaginary axis correspond to exactly the positive real roots of the new regular polynomial not including any exponential term. This new polynomial can be used to find out whether the system stability is delay -dependent or not and enables us to compute stability delay margin for the delay-dependent stability case. The proposed analytical method is utilized for evaluating stability delay margins with regard to system parameters for various values of proportional-integral (PI) gains where the MG is marginally stable. Moreover, quantitative effect of virtual inertia and damping gains is comprehensively investigated. Based on the results, it is concluded that incorporating VI control enhances stability delay margins and enhances the MG's stability performance. Theoretical delay margin results are verified using time-domain simulations and quasipolynomial mapping-based root finder (QPmR) algorithm.