Grey wolf optimization-based fuzzy-PID controller for load frequency control in multi-area power systems

Abstract

This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems. The controller’s effectiveness is demonstrated on thermal–thermal and hybrid thermal–hydro–gas power systems. The controller parameters were tuned using the Integral Time Absolute Error (ITAE) objective function, which was also evaluated alongside other objective functions (IAE, ISE, and ITSE) to ensure high precision in frequency stabilization. To validate the effectiveness of the triangular membership function, comparisons were made with fuzzy-PID controllers employing trapezoidal and Gaussian membership functions. Performance metrics, including ITAE, settling time, overshoot, and undershoot of frequency deviation, as well as tie-line power deviation, were evaluated. Robustness was established through a comprehensive sensitivity analysis with $T_G$, $T_T$, and $T_R$ parameter variations ($\pm 50\text{\%}$), a non-linearity analysis incorporating Generation Rate Constraint (GRC) and Governor Deadband (GDB), a random Step Load Perturbation (SLP) over 0–100 s, and also Stability analysis of the proposed scheme is conducted using multiple approaches, including frequency-domain analysis, Lyapunov stability theory, and eigenvalue analysis. Additionally, the system incorporating thermal, hydro, and gas turbines, along with advanced components like CES and HVDC links, was analysed. Comparisons were conducted against controllers optimized using Modified Grasshopper Optimization Algorithm (MGOA), Honey Badger Algorithm (HBA), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Spider Monkey Optimization (SMO) algorithms. Results demonstrate that the GWO-based fuzzy-PID controller outperforms the alternatives, exhibiting superior performance across all evaluated metrics. This highlights the potential of the proposed approach as a robust solution for load frequency control in complex and dynamic power systems.