This thesis focuses on the hierarchical control for a multi-terminal high voltage direct current (MT-HVDC) grid suitable for the integration of large scale renewable energy sources. The proposed control scheme is composed of 4 layers, from the low local control at the power converters in the time scale of units of ms; through distributed droop control (primary control) applied in several terminals in the scale of unit of seconds; and then to communication based Model Predictive Control (MPC) that assures the load flow and the steady state voltage/power plan for the whole system, manage large scale storage and include weather forecast (secondary control); finally reaching the higher level controller that is mostly based on optimization techniques, where economic aspects are considered in the same time as longer timespan weather forecast (tertiary control).Concerning the converters' level, special emphasis is placed on DC/DC bidirectional converters. In this thesis, three different topologies are studied in depth: two phases dual active bridge (DAB), the three phases DAB, and the use of the Modular Multilevel Converter (MMC) technology as DC/DC converter. For each topology a specific non-linear control is presented and discussed. In addition, the DC/DC converter can provide other important services as its use as a direct current circuit breaker (DC-CB). Several operation strategies are studied for these topologies used as DC-CB.With respect to primary control, which is the responsible to maintain the DC voltage control of the grid, we have studied several control philosophies: master/slave, voltage margin control and droop control. Finally we have chosen to use droop control, among other reasons, because the communication between nodes is not required. Relative to the secondary control, its main goal is to schedule power transfer between the network nodes providing voltage and power references to local and primary controllers, providing steady state response to disturbances and managing power reserves. In this part we have proposed a new approach to solve the power flow problem (non-linear equations) based on the contraction mapping theorem, which gives the possibility to use more than one bus for the power balance (slack bus) instead of the classic approach based on the Newton-Raphson method. Secondary control plays a very important role in practical applications, in particular when including time varying power sources, as renewable ones. In such cases, it is interesting to consider storage devices in order to improve the stability and the efficiency of the whole system. Due to the sample time of secondary control is on the order of minutes, it is also possible to consider different kinds of forecast (weather, load,..) and to achieve additional control objectives, based on managing storage reserves. All these characteristics encourage the use of a model predictive control (MPC) approach to design this task. In this context, several possibilities of optimization objective were considered, like to minimize transmission losses or to avoid power network congestions.The main task of tertiary control is to manage the load flow of the whole HVDC grid in order to achieve economical optimization. This control level provides power references to the secondary controller. In this thesis we were able to maximize the economic profit of the system by acting on the spot market, and by optimizing the use of storage devices. In this level it is again used the MPC approach.With the aim of implementing the hierarchical control philosophy explained in this thesis, we have built an experimental test bench. This platform has 4 terminals interconnected via a DC grid, and connected to the main AC grid through VSC power converters. This DC grid can work at a maximum of 400 V, and with a maximum allowed current of 15 A.