The ever increasing penetration of renewable energy systems in the distribution grids will inevitably require profound changes in the grid infrastructure. One emerging direction, the medium voltage dc (MVdc) grids, is the cornerstone of this work. They are foreseen for offshore wind parks and onshore large scale renewables collection grids, future on-board ship power systems, repurposed ac lines with increased transport capacity, etc. The shift to dc offers energy savings and reduced impact on the landscape. This thesis provides insights on the presumed most suitable conversion topology between a MVdc and a LVac grid, which is not expected to disappear in the near future. The conversion is characterized by a large voltage ratio between the two terminals. A modular multilevel converter (MMC) with an integrated magnetic component, the galvanically isolated modular converter (GIMC), is proposed and preferred for efficiency and cost reasons over a solid-state transformer, whose efficiency is heavily penalized by the inverter stage on the low voltage side. The thesis opens on a detailed benchmark of the performances of various control, modulation and branch balancing methods, with a focus on medium voltage applications. Extensive simulations are carried out to support the discussion. In case of an application with fast dynamics, the closed-loop control method, comprising energy balancing controllers, offers by far the best performances. For the modulation and branch balancing methods, it was concluded that, as long as both the number of cells per branch and average cell switching frequency are not very low, PWM methods based on the reference branch voltage, rather than the number of inserted cells per branch, feature lower voltage errors. From there, the two GIMC variants sharing the same three-windings transformer, the interleaved GIMC and stacked GIMC, are analyzed. This solution does not suffer from dc bias in the magnetic device, unlike the open-end windings MMC. Since the obtained model is identical to the one for the conventional dc/3-ac MMC, the same control algorithms can be applied without restriction. The volume and efficiency comparison against the conventional case with discrete air-core inductors, supported by FEM simulations, quantifies the benefits of the proposal. It is concluded that the gains are marginal for the considered modest power ratings (0.5 MVA). However, the magnetic design is considerably simplified. Larger gains are expected for designs with higher branch inductance values, since the stacking of the primary windings gives easy access to high leakage inductances. A generic and versatile losses estimation method for modular converters is introduced. Compared to detailed switched simulations, the simulation times are improved by two orders of magnitude, if the assumptions to neglect the branch current ripple and branch capacitor voltage spread hold. The estimation error is below 2 % in the considered comparison. At last, the design of a 0.5 MVA converter prototype connected to 10 kVdc with 96 cells is presented. The cell, with a dedicated Flyback-based auxiliary cell power supply from its dc-link and protection circuits for a cell bypass in case of over-current or -voltage, along with the electric design of the cabinet hosting one converter phase-leg, are verified experimentally. The cell and phase-leg layout provide a platform for further research activities.