Identification of Stability Delay Margin for Load Frequency Control System with Electric Vehicles Aggregator using Rekasius Substitution

This paper implements a frequency-domain exact method, Rekasius substitution to determine the stability delay margin of a single-area load frequency control system (LFC) with electric vehicles (EVs) aggregator having constant communication delay. The method aims to compute all possible, purely complex roots of the characteristic equation for a finite positive time delay. The approach first transforms the characteristic polynomial of the LFC 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 (PI) controller gains, time delay values at which the LFC system with EVs aggregator is marginally stable are computed. The accuracy of stability delay margin results is verified by the time-domain simulations and by using an independent algorithm, the quasi-polynomial mapping-based root finder (QPmR).