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Swell is the main disturbance for marine tidal speed. The power harnessed by a marine current turbine (MCT) can be highly fluctuant due to swell effect. Conventional Maximum Power Point Tracking (MPPT) algorithm will require the generator to accelerate/decelerate frequently under swell effect and therefore cause severe fluctuations in the generator power. This paper deals with power smoothing control of grid-connected MCT system. In the first step, a modified MPPT algorithm with filter strategy is proposed in the generator side control to reduce the fluctuation of generator power. In the second step, Supercapacitor (SC) Energy Storage System (ESS) is added to compensate the residual power fluctuations. As the average tidal speed is predictable, it is possible to control the SC ESS to compensate the swell effect and realize a smoothed power injected to the grid. Simulations carried-out on a 1.5 MW direct-driven grid-connected MCT generation system demonstrate that the association of the generator side filter strategy with the SC ESS system achieves a smoothed grid-injected power in case of swell disturbances.