Impact of motion limits on sloped wave energy converter optimization

In a previous article [1] (subsequently referred to as the ‘original study’ and whose prior reading is recommended to make the most of what follows), the authors explored the concept of sloped power take-off (PTO) for a free-floating wave energy converter (WEC) using linear potential flow theory. Part of the study focused on the optimization of four parameters: the mass reference m2, its vertical position wG2 r, the PTO angle θ0 and the magnitude of the linear damping α. It was decided for the optimization part of the original study to exclude configurations exhibiting normalized motion amplitude (NMA) maxima in surge, heave and pitch above a certain limit, or threshold. This method to keep results realistic within the context of linear potential flow theory was chosen over adding extra damping coefficients to the hydrodynamic model. The reasoning is that, as the PTO angle varies between configurations, the PTO provides more or less damping in pitch for the same α. Therefore, some configurations require less additional hydrodynamic damping (representing shape drag) than others to keep pitch normalized motion amplitudes within a realistic limit. Adding a fixed additional damping in pitch would dissipate energy, and therefore penalize some configurations more than others. In the original study (§4b(i)), a normalized motion amplitude threshold of 10 was used. Experimental normalized motion amplitudes of this order of magnitude have been reported in the literature [2, p. 44]. Using this value effectively reduced the experimental plan of the initial study from 4000 randomly generated configurations to around 600. No configuration with PTO angle −30◦ (i.e. close to vertical) was selected with this approach. One could argue that point absorbers