This paper proposes three generator control strategies for Wells turbine-based floating oscillating water column (OWC) devices comprising electrical or mechanical energy storage systems. The first control strategy is indicated for low inertia turbine OWC devices that include ultracapacitors. This control law optimizes the power take-off efficiency by means of an instantaneous speed controller that allows variation of the turbine rotational speed in a wave-by-wave basis. In addition, the profile of the electrical power injected into the grid is smoothed, so that a high penetration of wave energy does not threaten the grid stability. The second and third control laws are developed for OWC systems comprising a flywheel. Quasi-constant and variable speed controllers are proposed. These control laws do not maximize the system efficiency but allow the use of simpler, smaller and cheaper power electronics. Additionally the power quality is also optimized. The development of the proposed control algorithms is accomplished by means of simulations and verified with an experimental test rig.