A novel Kharitonov theorem and Rekasius substitution based robust delay‐dependent stability analysis of load frequency control system enhanced with inverter air conditioners

Abstract The widespread use of inverter‐based air conditioners (IACs) as a controllable load makes them a promising tool in the frequency regulation of power systems. However, utilization of an open communication network in the aggregation and control of several IACs introduces time delay (TDs), which adversely affects the frequency stability. Moreover, uncertainties in system parameters make the stability issue a challenging problem together with TDs. Therefore, it is important to study the effect of TDs and the controller gains on the stability of the system with the presence of uncertain system parameters. This paper concentrates on analyzing the robust stability delay margin (RSDM) of a single‐area load frequency control system (LFC) with IACs using Kharitonov theorem and Rekasius substitution. A novel implementation of Rekasius substitution and Resultant Theory together with Kharitonov's Theorem is presented to accurately compute RSDMs. The effects of the proportional integral controller (PI) gains, percentage uncertainty, and the quantity of IACs on RSDMs are thoroughly examined. Findings demonstrate that RSDMs diminish as PI gains rise. The influence of proportional gain is considerable in comparison to that of integral gain. In comparison to the nominal scenario excluding uncertainty, it is noted that a 5% uncertainty in system parameters leads to a reduction in RSDMs ranging from 53.44% to 70.14%, and a 10% uncertainty results in a fall between 92.08% and 96.22%. Correspondingly, for all PI controller gains, RSDMs diminish when the quantity of IACs escalates from 50,000 to 60,000. The percentage drop in this case is determined to be between 62.89% and 74.69%. Finally, the accuracy of theoretical results is verified by using MATLAB Simulink and quasi‐polynomial mapping‐based root finder (QPmR) algorithm.