As wave energy converters (WECs) continue their development, improved performance using various energy storage options are constantly being examined. This paper describes the applications of an energy storage system based on supercapacitors in a full-scale, grid-connected offshore WEC. The following areas are examined: Minimisation of the output power fluctuations; start sequences for the machine; and Low-Voltage Ride-Through (LVRT) capability. Focus is placed on ensuring a component lifetime greater than the maintenance period of the WEC. The investigation is based on a Backward-Bent-Duct Buoy (BBDB) Oscillating Water Column (OWC) using a Wells turbine connected to a Permanent-Magnet Synchronous Machine (PMSM) as the power take-off. The full system is modelled in Simulink using real sea data, and results are shown.