Finite-Difference-Impedance Method for Time-Delay Systems

The stability issues assessment by the impedance-based method demands the computation of accurate small-signal models. However, obtaining impedance models can be a time-consuming task if analytical models or the perturbation-based method are used. Especially in large-scale, poorly damped, distributed, and frequency-dependent parameter systems. A third approach, which has been less explored, is based on numerical derivative approximations, rather than analytical equations or time-domain simulations. This approach works with large-scale systems, avoiding tedious mathematical expressions and large recursive time-domain simulations. As a step-forward in this approach, this paper proposes a numerical-oriented method, based on the finite-difference method, to compute impedance models of time-delay power-electronics-based power systems. An outstanding feature of the proposal is the capability to incorporate the exact delays into the numerical models of impedance without resorting to approximations nor increasing the size of the system model. We compare the proposed method with the analytical and perturbation methods using a grid-connected microgrid with two power electronic inverters as a test system. The results confirm the correct performance of the proposal.