The principle of impedance matching (IM) can be applied to maximize power transfer between two oscillatory systems, being the ocean waves and the power take-off (PTO) of a wave energy converter (WEC) in this paper. The complex conjugate of the intrinsic impedance is approximated by a Proportional (P) and Proportional Integral (PI) IM controller in the peak wave frequency of the design sea state, equivalent to a resistive and reactive controller, respectively. These causal IM controllers are implemented in a MATLAB-Simulink real-time control environment and experimentally tested for an array of two WECfarm heaving point absorber WECs at the Aalborg University (AAU) wave basin for a selection of four sea states, characterized by JONSWAP wave spectra. Literature covers the experimental testing of the IM approach for single, isolated WECs. The research discussed in this paper is unique by applying for the first time the experimental testing of the IM approach on a WEC array, by taking the hydrodynamic interactions between the WECs, occurring through radiation and diffraction of waves, into account. System identification (SID) tests are performed to obtain an accurate dynamic model of the WEC array, in order to design the P and PI controller. The absorbed power and q interaction factor metric are used to quantify interaction effects in the two-WEC array.


Similar to offshore wind turbines, multiple point absorber WECs will be installed in an array configuration, to increase the total capacity, and to benefit from the economies of scale. Whereas wind turbines always interact destructively due to wake effects, WECs can interact constructively, since hydrodynamic interactions between the WECs occur through radiation and diffraction of waves, changing the direction of the incoming wave energy.

A point absorber WEC achieves its highest power absorption if its own oscillation frequency matches the one of the incoming waves, yielding resonance conditions with the velocity of the WEC buoy in phase with the wave excitation force. In reality, the oscillation frequency of the WEC buoy is mostly higher than the typical ocean wave frequencies, and ocean waves are not single-frequency. Therefore, Power Take-Off (PTO) control strategies maximizing power absorption alter the system dynamics in order to achieve resonance. Moreover, the design of WEC array control involves the extra challenge to take the hydrodynamic interactions into account, as these alter the dynamics of each individual WEC.

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