Stability Regions in the Parameter Space of PI Controller for LFC System with EVs Aggregator and Incommensurate Time Delays

This paper presents a graphical method to compute all stabilizing Proportional Integral (PI) controller gains of a single-area Load Frequency Control (LFC) system with Electric Vehicles (EVs) Aggregator and multiple incommensurate communication time delays. The proposed approach is based on extracting stability region and the stability boundary locus in the PI controller parameter space. For various values of communication time delays, stability regions are obtained and the accuracy of Complex Root Boundary (CRB) and Real Root Boundary (RRB) are verified by means of quasi-polynomial mapping-based root finder (QPmR) algorithm and time-domain simulations.