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This paper presents an experimental characterization of a flywheel energy storage system. The device is based on steel seamless tube mounted as a vertical axis flywheel storing kinetic energy. The motor/generator is a permanent magnet synchronous machine controlled by an AC-AC matrix converter. The matrix control method uses a discrete-time model of the converter system to predict the future values of the input currents for all the 27 possible output voltage vectors generated by the matrix converter. An optimal controller minimizes current errors using a weighted cost functional. This flywheel and control process is intended for dynamic voltage restorer (DVR) to mitigate voltage sags.