An OA-optimized multi-stage fuzzy PI–PDF control scheme for robust frequency regulation in islanded microgrid

The high penetration of renewable energy sources (RES) with low inertia and stochastic power output in off-grid microgrids significantly affects the rate of change of frequency (RoCoF), leading to degraded dynamic performance and potential instability. To address this challenge, a novel optimized multi-stage fuzzy proportional integral–proportional derivative filter (Fuzzy PI–PDF) controller is proposed for frequency stabilization of an autonomous microgrid (A-μG). The controller parameters are optimally tuned using the Orchard Algorithm (OA), enabling adaptive and robust control performance. The proposed A-μG comprises a biodiesel generator, solar photovoltaic (PV), and sea-wave energy-based generation system, supported by battery energy storage, flywheel energy storage, and an ultra-capacitor to effectively mitigate transient RoCoF. The inclusion of multiple storage technologies enhances both fast and slow dynamic response capabilities under varying operating conditions. The effectiveness of the proposed control strategy is validated in various operating scenarios, including sudden load disturbances, variability and intermittency of the RES, unavailability of energy storage and random load fluctuations. Stability and robustness of the system are rigorously verified through frequency-domain techniques (Nyquist and Bode plots), and α-cut-based eigenvalue analysis. Comprehensive simulation results demonstrate that the OA-based fuzzy PI–PDF controller significantly improves frequency stability, reducing RoCoF, enhancing damping characteristics, and achieving superior time-domain performance compared to existing control approaches. Furthermore, the proposed controller maintains robust performance under simultaneous disturbances and parametric uncertainties, highlighting its suitability for autonomous microgrid applications.