Distributed control is an effective method to coordinate the microgrid with various components, and also in a smart microgrid, communication graph layouts are essential since changing the topology unexpectedly could disrupt the operation of the distributed controllers, and also an imbalance may occur between the production and load. Hence, reducing the exchanged data between units and system operator is essential in order to reduce the transmitted data volume and computational burden. For this purpose, an islanded microgrid with multiple agents which is using cloud-fog computing is proposed here, in order to reduce the computing burden on the central control unit as well as reducing data exchange among units. To balance the production power and loads in a smart island with a stable voltage/frequency, a hybrid backstepping sliding mode controller (BSMC) with disturbance observer (DO) is suggested to control voltage/frequency and current in the MG-based master-slave organization. Therefore, this paper proposes a DO-driven BSMC for controlling voltage/frequency, and power of energy sources within a Master-Slave organization; in addition, the study proposes a clod-fog computing for enhancing performance, reducing transferred data volume, and processing information on time. In the extensive simulations, the suggested controller shows a reduction in steady-state error, a fast response, and a lower total harmonic distortion (THD) for nonlinear and linear loads less than 0.33 %. The fog layer serves as a local processing level, so it reduces the exchanged data between cloud and fog nodes.
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