Katipoğlu, Deniz2023-10-102023-10-1020231582-7445https:/dx.doi.org10.4316/AECE.2023.02005https://hdl.handle.net/20.500.12451/11124The current study investigates the stability analysis based on gain and phase margin (GPM) using fractional-order proportional-integral (FOPI) controller in a time-delayed single-area load frequency control (LFC) system with demand response (DR). The DR control loop is introduced into the classical LFC system to improve the frequency deviation. Although the DR enhances the system’s reliability, the excessive use of open communication networks in the control of the LFC results in time delays that make the system unstable. A frequency-domain approach is proposed to compute the time delay that destabilizes the system using GPM values and different parameter values of the FOPI controller. This method converts the equation into an ordinary polynomial with no exponential terms by eliminating the exponential terms from the system’s characteristic equation. The maximum timedelay values at which the system is marginally stable are calculated analytically using the new polynomial. Finally, the verification of the time delays calculated is demonstrated by simulation studies in the Matlab/Simulink environment and the root finder (quasi-polynomial mapping-based root finder, QPmR) algorithm to define the roots of polynomials with exponential terms providing information about their locations.eninfo:eu-repo/semantics/openAccessDelay SystemsFrequency ControlPI ControlPower System ControlStability AnalysisArticle232394610.4316/AECE.2023.02005Q3WOS:001009953400005Q4