## 1 Introduction  
A fundamental aspect of electric power systems is the efficiency of transmission lines from generation centers to consumption ones. This problem has led to important research and technological development in recent years [1; 2; 3]. Currently, most of the transmission grids in the world are based on high-voltage alternating current (HVac). However, HVac grids present serious limitations when it comes to transmitting at large distances [3; 4; 5; 6; 7; 8], then power transmission in HVdc is the preferred alternative and has been largely implemented in different electrical systems around the world [9; 10; 11; 12]. For instance, the \(\pm\)1100 kV Ultra-HVdc line transmission in China [11] or the \(\pm\)650 kV Kimal-Lo-Aguirre HVdc transmission line in Chile [13]. In the future, it is expected there will be an increase in the number of long-distance HVdc transmission systems [14; 15; 16]. On the other hand, an important configuration in HVdc grids is the multi-terminal connection grids (MT-HVdc) [17; 18; 19]. An MT-HVdc grid consists of the interconnection of three or more HVdc sub-stations with different voltage magnitudes (see Figure 1).  
In MT-HVdc grids, there could be bidirectional power flows between the different terminals, therefore dc-dc converters are required to adapt the voltage levels of the individual substations, as shown in Figure 1[20].  
In recent years, research has been carried out on dc-dc converters for HVdc systems [21; 22; 23; 24] and recently for MVdc grids [23]. Several power converter topologies for HVdc systems have been reported in the literature [25]. In particular, modular multilevel converters are very attractive for this type of application [26; 27], since they offer bidirectional power flow capability and low distortion in the input and output currents. Variations of the standard MMC structure have also been proposed, such as the resonant MMC [28; 29; 30; 31], or the novel double-Y and double-Pi topologies [32; 33; 34; 35].  
In this paper, a decoupled control strategy for a dc-dc converter intended for MT-HVdc applications is presented. The topology has been called double-T since it is built with two T-structures (see Figure 2). The proposed MMC operating with the presented control method exhibits the following features: no common-mode voltage at the converter output, the minimum number of cells to build the topology, and null ac components in the input current. The operating principle of the converter is described in detail as well as the proposed control strategy. Simulation results are presented to validate the control method and a sensitivity analysis is carried out to evaluate its performance under variations of the converter parameters.  
The remainder of the paper is organized as follows. In Section 2 the mathematical model of the converter is presented. Section 3 describes the operating principle of the  
Figure 1: Schematic of a multi-terminal HVdc system.  
Figure 2: Double-T topology, with two T-structures called \(T_{1}\) and \(T_{2}\).  
topology. The control strategy proposed is derived in Section 4 whereas the simulation results are presented in Section 5. In Section 6 Brief Sensitive Analysis is presented. Finally, the conclusions are stated in Section 7.