The theoretical potential for maximising energy output of wave-energy converters by means of optimum control is quantified for a heaving semi-submerged sphere on deep water. The heave amplitude is constrained to not exceed 0.6 units of the radius. Sinusoidal incident waves of amplitudes up to 3 m and period in the range of 6 s to 12 s are considered, when the sphere radius is 5 m. Optimum reactive control, contrary to sub-optimal latching phase control, requires ability for reversing the energy flow through the power take-off machinery. Computed results show that, for a typical wave of 0.5 m amplitude and 9 s period, the maximum absorbed power is 24, 137, and 172 kW for the cases of no phase control (passive system), sub-optimal latching control, and ideally optimal reactive control, respectively. The ratio between the maximum/minimum instantaneous power and the average absorbed power is 2/0, 4.1/0 and 11.0/-9.0, respectively, for the three different strategies.

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