In power electronics, the modular multilevel converter (MMC) is an easily scalable topology with an high output voltage quality. It is suitable for the transmission of large amounts of electrical power over long distances, which supports the realization of the ongoing energy transition. State-of-the-art methods require a comparatively large total cell capacitance in the system for energy pulsations during operation. In the present paper, in order to minimize this total capacitance, first a new method is developed to model the system, and second, by help of this model, optimal current trajectories are calculated. These currents are used for control to reduce the energy pulsation over the complete operating range, and thus, to better utilize the hardware. The new method independent on the Clarke transformations is implemented on a laboratory scale setup, and measurement results are presented which validate the new method. Furthermore, the new method is compared to the state-of-the-art method of the compensation of the 2nd harmonic and outperforms the latter significantly. This applies to the entire operating range for different power factors. ... mehrA total reduction of up to 44% of the energy pulsations is achieved.