Fast time-domain model for an array of interactive point-absorbers
Authors: Stavropoulou Charitini , Goude Anders , Engström Jens , Göteman Malin 
Published: September 2023

A fast time-domain model is developed for an array of six interacting point-absorber wave energy converters, based on the design originated at Uppsala University. The point-absorbers are placed in a symmetric grid, were each row contains one pair. The devices interact by scattered and radiated waves, while they are restricted to move in one degree of freedom, heave. Under the assumption of linear potential flow theory, the hydrodynamic coefficients for the excitation and radiation forces are obtained using an analytical multiple-scattering method. The equations of motion are solved directly in the time domain following the Cummins’ formulation. Modelling an array of wave energy converters in the time domain comes down to solving a system of integro-differential equations, were convolution terms appear in the computation of the excitation and radiation forces. In the majority of wave farm models, frequency-domain approaches are used to solve the equations of motion, since time-domain models are more computationally demanding and significantly more challenging to develop. This is not only because of the numerical integration involved, but especially due to the computation of the convolution term accounting for the radiated water waves on the free-surface, implying that waves radiated by the body in the past continue to affect the dynamics in the future. Regardless the computational effort associated with time-domain approaches, their use is required for realistic control applications and complex device dynamics, like non-linearities due to the power take-off configuration. In particular the non-linear effects that arise during the wave energy conversion chain are treated as time-varying coefficients within the system of differential equations describing the motion. Input to the numerical scheme are irregular, long-crested waves, obtained from the Bretschneider spectrum, corresponding to four, different sea states. It is of high interest to study whether the linear numerical model simulates accurately the performance of each interactive surface buoy in response to the irregular waves. Therefore, the numerical results for the full array configuration are compared with experimental data. At this point we emphasize that there are not a lot of experimental works considering arrays of point- absorbers, due to the complexity and costs associated with the task. Therefore, finding a set of data to validate the array model is not trivial. The experimental results we use were carried out in the COAST Lab at Plymouth University, UK, corresponding to a 1:10 scaled prototype of an array of point-absorbers. The set-up consists of six ellipsoid floats free to move in six degrees of freedom and connected via ropes and pulleys to individual power take-off systems. Despite the highly non-linear effects in the physical experiment, the free motion of the buoys in all directions, and the power take-off configuration, the numerical scheme is able to accurately capture the heaving motion of the buoys and their power absorption.