Comparative Study of PID and FOPID Controllers Tuned by Metaheuristic Algorithms for Microgrid Systems

A growing penetration of renewable generation and electrified loads is pushing distribution systems toward DC microgrids, where tight DC-bus voltage regulation is critical, especially in islanded operation and in transport-adjacent power systems (e.g., depot or station DC buses). This paper presents a comparative study of classical PID and fractional-order PID (FOPID) controllers for a two-distributed generation (DG) microgrid modeled from a standard reference. Both controllers are implemented in MIMO form and tuned via four metaheuristic algorithms: particle swarm optimization (PSO), genetic algorithm (GA), grey wolf optimization (GWO), and differential evolution (DE), using the integral of time-weighted squared error (ITSE) as the objective. All optimizations use an 80-iteration budget with bounded decision variables. Simulations in MATLAB/Simulink show that, relative to PID, FOPID consistently yields lower overshoot, faster settling, and smaller ITSE, while PSO and GWO converge faster than DE and GA. The results highlight the utility of fractional-order control with metaheuristic tuning for robust direct-current (DC) bus voltage regulation in microgrids.