The global transition to green energy generation is accelerating, marked by the increasing integration of renewable energy sources and DC loads into power grids. Given this circumstance, DC grid technologies are gaining prominence to accommodate the increasing penetration of renewable energy sources and DC loads. DC transformers, as essential components in DC grids, are responsible for interconnecting DC systems with different voltage levels and facilitating flexible power-flow control. This research is dedicated to the investigation of the isolated modular multilevel DC-DC (IM2DC) converter for medium-voltage DC applications. The objective of this research is to achieve accurate modeling, versatile modulation, performance optimization, and fault protection design of the IM2DC converter, addressing existing gaps in the technical literature. In this study, a unified trapezoidal wave (UTW) modulation scheme is proposed for the IM2DC converter, unifying various existing modulation strategies into a cohesive framework. Furthermore, the introduced harmonic state-space (HSS) modeling method effectively tackles two primary challenges. Firstly, the frequency-domain modeling approach of the HSS equations seamlessly integrates the implementation of the UTW modulation. Secondly, the HSS model adeptly handles the complex harmonic interactions within the converter, ensuring the desired level of accuracy. Following that, the zero-voltage switching boundaries of the IM2DC converter are delineated, considering various system parameters using the HSS model. Next, a sensorless method is introduced for balancing SM capacitor voltages in the IM2DC converter. A predetermined switching signal rotation pattern enables SMs to restore voltage within a rotation period. Finally, a DC fault detection and protection mechanism is designed to promptly limit and clear fault currents while ensuring uninterrupted DC voltage on the healthy side. Additionally, fault detection and fault tolerant control strategies are developed for the presence of an open-circuit fault in a semiconductor device, effectively avoiding disruptions of the system.