The high-frequency magnetic linked solid-state transformer (SST) has the tremendous potential to solve the issues related to interfacing the grid with renewable energy sources and the non-linear loads as well as to provide the additional control functionalities. Several H-bridges are usually connected in series for the medium voltage grid integration of the SST. The number of the dual active bridge modules and the number of high-frequency magnetic links (HFMLs) usually increase with the increase of the number of series connected H-bridges. This increases the possibility of parameter mismatches and system instability. Therefore, the multiple-active bridge (MAB) dc-dc converter concept has been proposed for next generation SST, where multiple H-bridges share the same HFML. This configuration reduces the number of HFML and increases the cross-coupling power transfer capability. However, the design process of the MAB converter involves a multi-physics research in the field of power electronics, magnetics, switching, control, and energy management. In this paper, the detailed analytical modelling and the control technique of the silicon carbide (SiC)-based MAB converter are investigated. The small and large signal average models of the converter are developed and a voltage balance controller is designed for the better understanding of the controller characteristics. The effect of connecting several H-bridges to a single HFML is investigated in detail. Moreover, to reduce the switching loss, the converter topology adopts the SiC-based switching devices instead of the traditional silicon (Si)-based devices and the nanocrystalline magnetic material is used for the HFML design due to its low specific core loss. A scaled down laboratory prototype of the MAB converter is implemented in the laboratory and can be utilized as a basic building block for the next generation SST.