Hybrid multi-objective optimization of µ-synthesis robust controller for frequency regulation in isolated microgrids

Frequency regulation in isolated microgrids is challenging due to system uncertainties and varying load demands. This study presents an optimal µ-synthesis robust control strategy that regulates microgrid frequency while enhancing system performance and stability-a proposed fixed-structure approach for selecting performance and robustness weights, informed by subsystem frequency analysis. The controller is optimized using multi-objective particle swarm optimization (MOPSO) and multi-objective genetic algorithm (MOGA) under inequality constraints, employing a Pareto front to identify optimal solutions. Comparative analyses demonstrate that the MOPSO-optimized controller achieves superior robustness and performance, tolerating up to 236% uncertainty compared to 171% for conventional µ-synthesis controllers. Additionally, it significantly reduces frequency deviation and enhances transient response. Nyquist stability analysis confirms robustness across renewable energy uncertainties. The results highlight the proposed controller's effectiveness in isolated microgrid frequency regulation, with future work focused on discrete-time implementation for practical digital signal processing (DSP) applications.