The increasing share of renewable energy sources causes a reduction of inertia provided by conventional synchronous generators to the grid. To enable a stable operation in converter dominated grids a replacement of the inertial response of synchronous generators is required. This paper describes a flywheel energy storage system for 270 MV A, which provides synthetic inertia and reactive power for voltage stabilization for large grid areas. The flywheel is operated by an induction generator and a Modular Multilevel Matrix Converter (M3C). The authors show that by using the M3C a significant short circuit power of up to 2.5 times the rated power can be delivered, without oversizing the current rating of the converter. This study is conducted analytically and is validated by a simulation of the high power system as well as with an experiment on a small-scale test bench.