The Adequacy of Phase-Averaged Models for Modelling Wave Farms

As the wave energy industry develops there is a need to develop tools for the estimation of the energy yield from wave farms, as well as determination of the environmental impact of wave farms and optimisation of wave farm layout. Tools based on spectral wave models are potentially suitable for these tasks and are already used extensively in coastal engineering to estimate wave climate and how waves affect the coastal environment. Examples of these tools include software packages such as SWAN, TOMAWAC and Mike21SW. However, a fundamental characteristic of spectral wave models is that they are phase-averaged models, which implies that the phase of individual wave components is unknown. Interactions between wave energy converters (WECs) in an array have been previously modelled using linear wave theory. These models have shown that phase can be important in determining the interaction between WECs in an array due to the effects of radiated waves. However, these models have typically assumed that the WECs have ideal control. The array interactions for more realistic control strategies are much weaker. In this paper arrays of realistically controlled WECs are modelled using hydrodynamic coefficients obtained from WAMIT, a linear hydrodynamic panel code, to determine the effects that radiated wave amplitude and WEC separation distance have on array interactions. It is shown that array interactions decrease with decreasing radiated wave amplitude and increasing separation distance. Array interactions are shown to change the power capture by less than 10% for typical WECs with realistic control. Moreover, it is shown that the change in power capture becomes highly sensitive to wave frequency and direction as the separation distance increases, although the magnitude of the interaction factor reduces. Finally, realistic wave spectra are applied to the array interactions of WECs. The average array interaction factor is found to be relatively insensitive to the mean wave period and direction. It is argued that this implies that phase-averaged models are adequate for modelling realistically controlled wave farms operating in realistic wave spectra. Consequently, provided a suitable phase-averaged model of a WEC can be developed, then it can be modelled with reasonable accuracy in spectral wave models.