This paper explores optimal damping profiles for a heaving buoy wave energy converter (WEC). The approach is mathematical and the model of Eidsmoen (1995) is used as a basis. In order to permit analytical development, the model is initially simplified and an optimal damping profile is determined using numerical optimization. Having found the optimal damping profile, a semi-analytical solution methodology is developed to determine the optimal damping parameters. Finally, the procedure is validated on the original model and some aspects related to the control problem are addressed.


The novel approach in this paper is to employ a parametric profile for damping (with time) where the parameters, initially assigned to give a linear damping profile, are optimised to maximise energy absorbed per wave cycle.

The approach adopted centres on simplification of the detailed hydrodynamic model of the heaving buoy as developed by Eidsmoen (1995). This is necessary, since the equations of motion for the system rapidly become intractable due to the inclusion of a damping coefficient which is dependent on one of the primary system variables. In spite of this simplification, an analytical solution for the optimal damping profile is not possible and some recourse is made to numerical techniques for the optimisation. The problem is conveniently solved, following the employment of an evolutionary algorithm, which surprisingly returns latching as the optimal damping profile.

Following this discovery, the paper then proceeds to determine the optimal latching time, in terms of the parameters of the excitation force and the system parameters. Unsurprisingly, this problem also does not permit a complete analytical solution. However, an analytical equation is developed which can be very simply and efficiently optimized to give the optimum latching time.

Finally, some consideration is given to the control problem of a point absorber WEC.

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