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This paper presents a new modulation method for the modular multilevel converter. The proposed method is based on a fixed pulse pattern where harmonic elimination methods can be applied. In the proposed modulation method, the pulse pattern is chosen in such a way that the stored energy in each submodule remains stable. It is shown that this can be done at the fundamental switching frequency without measuring the capacitor voltages or using any other form of feedback control. Such a modulation scheme has not been presented before. The theoretical results are verified by both simulations and experimental results. The simulation results show successful operation at the fundamental switching frequency with a larger number of submodules. When a smaller number of submodules are used, harmonic elimination methods may be applied. This is verified experimentally on a converter with eight submodules per phase leg. The experimental results verify that stable operation can be maintained at the fundamental switching frequency while successfully eliminating the fifth harmonic in the ac-side voltage.