Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

This study comprehensively investigates modeling and controller design for two-area load frequency control (LFC) system with demand response (DR) and time delays. An optimized fractional order proportional-integral (FOPI) controller is designed both to improve the stability of grid frequencies and to deal with the time delays. Using the stability boundary locus (SBL) method, the stability region for the FOPI controller parameter space is obtained. The boundaries of these stability regions are used in the optimization process of the FOPI controller parameters. A new objective function is used to minimize the integral time-weighted absolute error (ITAE) and time domain specifications such as overshoot (OS) and undershoot (US) of the frequency and tie-line power deviations. The parameters of the FOPI controller are optimized by Artificial Hummingbird Algorithm (AHA). The simulation results are compared with gray wolf optimizer (GWO) and particle swarm optimization (PSO) tuned FOPI controllers. The AHA tuned FOPI (AHA-FOPI) controller gives very promising results, especially in terms of improving the transient response of the system by reducing the settling time (ST) and steady-state error (ess). Additionally, the effectiveness of the AHA-FOPI is demonstrated under increased time delay. It is evident from the simulation results that the AHA-FOPI controller has successfully improved the time domain characteristics of the LFC-DR system.