Islanded microgrids, powered by renewable energy sources, offer a sustainable electricity solution for remote areas. However, maintaining frequency stability in these systems remains a challenge due to the intermittent nature of renewables. This research proposes an approach to enhance microgrid stability by integrating a green hydrogen energy storage system (GHESS) and employing advanced AI-based control strategies. The GHESS plays a pivotal role in storing excess renewable energy as hydrogen and then converting it back to electricity when needed, reducing reliance on traditional backup generators. To optimize microgrid performance, a hybrid single-neuron PID (SNPID) controller, augmented by machine learning techniques, is developed and compared against conventional proportional, integral, and derivative PID and fuzzy self-tuning PID (FSTPID) controllers. The system’s performance was evaluated using four realistic scenarios. In all cases, the SNPID controller significantly outperformed the existing options. It achieved a 58% reduction in frequency fluctuations compared to the fuzzy self-tuning PID (FSTPID) controller and an impressive 87% reduction compared to the traditional PID controller. The Simulation results underscore the SNPID controller’s exceptional performance in frequency stability, emphasizing the transformative potential of AI for microgrid management.