This dissertation covers three primary topics and relates them in context. High frequency transformer design, microgrid modeling and control, and converter design as it pertains to the other topics are each investigated, establishing a summary of the state-of-the-art at the intersection of the three as a baseline. The culminating work produced by the confluence of these topics is a novel modular solid-state transformer (SST) design, featuring an array of dual active bridge (DAB) converters, each of which contains an optimized high-frequency transformer, and an array of grid-forming inverters (GFI) suitable for centralized control in a microgrid environment. While no hardware was produced for this design, detailed modeling and simulation has been completed, and results are contextualized by rigorous analysis and comparison with results from published literature. The main contributions to each topic are best presented by topic area. For transformers, contributions include collation and presentation of the best-known methods of minimum loss high-frequency transformer design and analysis, descriptions of the implementation of these methods into a unified design script as well as access to an example of such a script, and the derivation and presentation of novel tools for analysis of multi-winding and multi-frequency transformers. For microgrid modeling and control, contributions include the modeling and simulation validation of the GFI and SST designs via state space modeling in a multi-scale simulation framework, as well as demonstration of stable and effective participation of these models in a centralized control scheme under phase imbalance. For converters, the SST design, analysis, and simulation are the primary contributions, though several novel derivations and analysis tools are also presented for the asymmetric half bridge and DAB.