Optimal Fractional‐Order PID Control for Multiarea Interconnected Power Systems Using an Adaptive Time‐Varying PSOGSA Algorithm

This study addresses the premature convergence and stagnation of standard metaheuristic algorithms when navigating zero‐gradient hysteresis traps caused by Generation Rate Constraint (GRC) and Governor Dead Band (GDB) in Load Frequency Control (LFC) systems. To overcome these limitations, this study presents a novel Adaptive Time‐Varying Particle Swarm Optimization and Gravitational Search Algorithm (ATV‐PSOGSA). The proposed approach synergizes a nonlinear squared‐cosine inertia weight, asymmetric square‐root sine acceleration coefficients, and a dynamically shrinking active gravitational pool ( K _best floor). The algorithm is utilized to optimally tune decentralized Fractional‐Order PID (FOPID) controllers, which offer superior iso‐damping properties over standard PID frameworks, enabling the control signal to securely bridge mechanical hysteresis zones. Evaluated over 30 independent runs, the ATV‐PSOGSA achieved the most robust worst‐case performance ceiling (37.613), the tightest standard deviation (0.0537), and a suite‐best mean peak frequency overshoot of 0.0723 Hz. Furthermore, sensitivity analysis confirmed the controller’s robust stability under extreme ±25% plant parameter variations. Crucially, the K _best reduction mechanism minimizes redundant gravitational force calculations, keeping ATV‐PSOGSA highly competitive in execution speed within the experimental suite while remaining within the same computational complexity class as the baseline hybrid algorithms. Ultimately, ATV‐PSOGSA is demonstrated, through rigorous statistical analysis, to be a highly reliable and computationally efficient tuning engine for real‐world, edge‐deployed smart grid operations.