Gain and phase margins based stability analysis of micro grid systems with time delay by using Rekasius substitution [Zaman gecikmeli mikro-şebeke sistemlerin Rekasius yerine koyma yöntemiyle kazanç ve faz payı tabanlı kararlılık analizi]
This paper investigates the delay-dependent stability of a micro-grid system with constant communication delay considering not only stability but also gain-phase margins (GPMs). A gain-phase margin tester is introduced to the micro-grid system as to take into GPMs in delay margin computation. A frequency domain analytical method, Rekasius substitution, is utilized to compute the GPMs based stability delay margins. The method aims to calculate all possible purely complex roots of the characteristic equation for a finite positive time delay. The approach first transforms the characteristic polynomial of the micro-grid system with transcendental terms into a regular polynomial. Routh-Hurwitz stability criterion is then implemented to compute the purely imaginary roots with the crossing frequency and stability delay margin. For a wide range of proportional-integral controller gains and GPMs, time delay values for which the micro-grid system is both stable and has desired stability margin measured by GPMs are computed. The accuracy of complex roots and delay margins are verified by using an independent algorithm, QPMR (the quasi-polynomial mapping-based root finder) algorithm and time-domain simulations, respectively. Simulation studies indicate that delay margins must be determined by considering GPMs to have a better dynamic performance in term of fast damping of oscillations, less overshoot and shorter settling time. © 2019 Gazi Universitesi Muhendislik-Mimarlik. All rights reserved.