The tethered-undersea-kite (TUSK) represents a new electric power generation concept for harvesting energy from tidal currents, with higher power density compared to traditional static tidal turbines. However, the power and rotating speed of the turbine fluctuate periodically depending on the kite's motion in the sea creating an additional challenge for the speed control of the generator. The mathematical model of the system's power generation is developed. Two alternative maximum-power-point-tracking (MPPT) algorithms suitable for this application are designed. The electrical torque of the generator is controlled directly or a more accurate closed-loop speed controller is used. The turbine inertia creates an error between the optimal-reference power and the actual generated power. This error is evaluated experimentally for both MPPT-algorithms when fluctuating mechanical torque typical for the TUSK-system is applied on the generator. Experimental results on a 35-kVA laboratory emulator are presented, where an accurate representation of the system dynamics and inertia are implemented.