Wave-energy converters (WECs) need a reaction source against which the wave forces can react. As with shore-based WECs, sometimes also floating WECs react against a fixed point on the seabed. Alternatively, for a floating WEC, force reaction may be obtained by utilizing the relative motion between two bodies. A load force for energy conversion is assumed to be applied only to this relative motion. It is assumed that either body oscillates in one mode only (mostly, the heave mode is considered here). The system, if assumed to be linear, is proved to be phenomenologically equivalent to a one-mode, one-body system, for which the wave excitation force equals the force which is necessary to apply between the two bodies in order to ensure that they are oscillating with zero relative motion. It is discussed how this equivalent excitation force and also the intrinsic mechanical impedance of the equivalent system depend on the mechanical impedances for the two separate bodies, including the radiation impedance matrix (which combines radiation resistances and added masses). The equivalent system is applied for discussing optimum performance for maximizing the absorbed wave energy. It is shown that, for an axisymmetric system utilizing heave modes, it is possible to absorb an energy amounting to the incident wave power on a crest length which equals the wavelength divided by 2π, even though the power take-off is applied to the relative motion only. Moreover, it is shown that it is possible to obtain an equivalent excitation force which exceeds the wave excitation force on either body.
A generic linear non-causal optimal control framework integrated with wave excitation force prediction for multi-mode wave energy converters with application to M4