Birds-of-Prey-Optimized FOPID for Stochastic-Resilient LFC in Islanded Microgrids

Growth in power demand has driven a broad shift toward renewable energy sources (RES). Still, this shift poses significant stability challenges for the system due to a power imbalance between supply and demand. This paper addresses secondary load frequency control for an islanded microgrid with stochastic RESs and variable demand. A controller architecture is formulated in which a fractional-order PID (FOPID), parameterized by (Kp, Ki, Kd, λ, μ). It is optimized using Birds-of-Prey-Based Optimization (BPBO) and benchmarked against Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO) under identical scenarios. The plant comprises a diesel generator, photovoltaic and wind sources, a fuel cell, and fast storage (flywheel and battery energy storage system), with converter dynamics and device limits explicitly represented. Performance is assessed using rise time, peak time, overshoot, and integral error indices (ISE, IAE, ITSE, ITAE). Across representative realizations, BPBO-FOPID delivers faster transients and lower cumulative error than PSO-FOPID and GWO-FOPID, with a rise time of (7.96 ×10-5 s) compared to (1.20 ×10-4), (5.34 ×10-4), and ISE, IAE, ITSE, and ITAE of 0.01612, 1.147, 0.9654, and 156.4 compared to 0.04289, 1.907, 1.922, 230.5, and 0.06603, 2.016, 2.650, 276.5. Time series responses demonstrate earlier, better-phased engagement of fast storage, which attenuates both initial excursions and late-time residuals without excessive actuation. The results indicate that the BPBO-based FOPID is robust in terms of reliability and critical-frequency regulation in renewable-rich islanded microgrids.