Modular multilevel converters offer several benefits, such as high scalability and power quality, which are particularly advantageous for high-voltage dc transmission systems. However, the control of such converters is very challenging due to the number of control objectives to be achieved simultaneously. The input and output currents must be controlled at their own references, and these references must be properly generated in order to keep the average capacitor voltage constant. The circulating current can be controlled either to minimize losses or to reduce capacitor voltage ripple. Additionally, the capacitor voltage must be kept balanced among cells during the converter operation. In this paper, a model with four independent dynamical components of the arm currents, which also considers the effect of ac and dc systems, is proposed. The proposed model facilitates the dynamical analysis of currents and simplifies the design and implementation of current controllers. Analysis of the proposed current model and experimental results, which confirm the performance of the designed controllers, is shown.