Comprehensive gain and phase margins based stability analysis of micro‐grid frequency control system with constant communication time delays.

This study presents a comprehensive delay‐dependent stability analysis of a micro‐grid system with constant communication delays. First, an exact method that takes into account both gain and phase margins (GPMs) is proposed to determine stability delay margins in terms of system and controller parameters. The method implements an elimination procedure to transform transcendental characteristic equation into a standard polynomial of the crossing frequency. The real roots of this new standard polynomial exactly match with the purely imaginary roots (crossing frequencies) of the original characteristic equation with transcendental terms. Second, an effective and simple graphical method is implemented to compute all stabilising proportional integral (PI) controller gains for a given time delay. The approach is based on extracting stability region and the stability boundary locus in the PI controller parameter space having user defined GPMs, and relative stability. The time‐domain simulation studies indicate that the proposed schemes give better desired dynamic performance as compared with the recently developed schemes for micro‐grid with communication delays. [ABSTRACT FROM AUTHOR]