Computation of stability delay margin for a two‐area load frequency control system enhanced with virtual inertia and damping control

Abstract This article explores the effects of communication delays on the delay‐dependent stability analysis of load frequency control (LFC) systems containing virtual inertia and damping (VID) control. Since LFC systems rely on communication networks, they are prone to delays that could impair the system's dynamic performance and lead to undesired frequency variations. Furthermore, the widespread adoption of renewable energy sources (RESs) could worsen these frequency fluctuations because of their low inertia. The VID control offers a remedy for stability issues by mimicking the necessary damping and inertia response. Delay‐dependent stability analysis aims to identify the largest allowable delays for stability, defined as the stability delay margin (SDM). This study proposes an efficient method to compute critical eigenvalues and corresponding SDMs. The technique swiftly identifies critical eigenvalues along the imaginary axis and calculates SDMs by monitoring eigenvalue loci of a transformation matrix. Stability regions, delineating SDMs in delay space, are determined. The validity of these regions and their boundaries is rigorously verified using the quasi‐polynomial mapping‐based root finder (QPmR) algorithm and time‐domain simulations. The findings demonstrate that the suggested technique computes SDMs correctly, and integration of VID control in LFC systems increases SDM values, improving frequency stability. Additionally, when delays are commensurate, SDMs computed using the proposed method closely match those from the direct method. The proposed method offers a comparative advantage by handling both commensurate and incommensurate delays with less computational burden, unlike the direct method, which only works for commensurate delays.