An autonomous microgrid is often formed by incorporating distributed generators into the distribution system. However, distributed generators have less inertia compared to traditional synchronous generators, and can cause the system frequency to become unstable. Additionally, as more clusters are integrated into the distribution microgrid, frequency instability increases. To resolve frequency instability in the microgrid cluster, this study proposes a supercapacitor control approach. The microgrid consists of several clusters which integrate wind power generators, solar PV, STP, fuel cells, aqua electrolyzers, and diesel generators. Initially, a small signal model is developed to facilitate the control design. A fractional-order supercapacitor controller is augmented with the developed small-signal model to stabilize the frequency of the microgrid. Furthermore, the controller parameters are optimized to guarantee robust controller performance. The proposed fractional-order supercapacitor controller provides more degrees of freedom compared to the conventional controller. Time-domain simulations were carried out considering several real-time scenarios to test the performance of the proposed controller. We observed that the presented approach is capable of stabilizing the system frequency in all cases. Furthermore, the proposed approach outperforms existing approaches in stabilizing the frequency of the microgrid cluster.