This study proposes a new architecture of flywheel energy storage system (FESS) which can be implemented at generating unit (GU) level (e.g. wind turbine) or scaled up for application in grid-side converter (GSC) stations of a multiterminal direct current (MTDC) system. The proposed architecture suppresses DC voltage leaps under grid faults, and performs power levelling duty at grid connection points. When implemented at GU level, the proposed FESS features a doubly-fed induction machine (DFIM) - the flywheel machine - where its six stator winding terminals are connected in series between the grid and the GSC. The flywheel converter is of partial power rating, and is connected to the DFIM rotor. When employed at an MTDC GSC station, several submodules are connected to build an FESS station. The study proposes the control concept and the general topology of the FESS station. The performance parameters of the system are tested under normal and abnormal operating conditions. Results and analyses indicate smooth dynamic operation, the economic advantage and the improved fault ride-through capability because of the proposed system.