Energy storage systems have become an essential pillar in most of electrical engineering applications due to introduced technical and economical merits, particularly following the pronounced grid-integration of renewable energy sources. Flywheel Energy Storage Systems (FESSs) have emerged as reliable and cost effective short term storage system. FESS may be used for critical load support or fault ride-through purposes, therefore the FESS reliability must be ensured. In this paper, FESSs are investigated for medium voltage applications where the main concern is the FESS's reliability. The main challenge for medium voltage FESS is the driving machine ratings and interfacing power conversion system. Therefore, two-parallel three-phase Modular Multilevel Converters (MMCs) are proposed to drive an asymmetrical six-phase Induction Machine (IM) in order to reduce the DC link voltage of the medium voltage system into a proper level for the IMs, where each converter is connected to feed each three-phase set of the six-phase machine. The employment of MMCs and an asymmetrical six-phase IM enhances system reliability as well. The machine and converter mathematical models are presented in this paper. Moreover, a simulation case study for FESS control under the proposed configuration is investigated.