Offshore renewable energy (ORE) systems have a crucial role in the decarbonization of the future energy sector. Due to the relatively low power of isolated ORE devices (about 1 MW), their future lies on large multi-MW arrays of several devices. However, the behavior of these devices in isolated conditions can vary significantly with respect to those in arrays due to the hydrodynamic interaction. In addition, the hydrodynamic interaction can be enhanced or reduced via control in order to maximize the final energy generation of the whole array. Finally, other aspects, such as mooring configurations or requirements of the different maintenance operations, may also have a significant impact on the design of ORE farms. Therefore, a computationally efficient mathematical model that can consider all these aspects and precisely provide the behavior of the array is crucial.
In the case of WECs, the layout optimization is often based on a frequency-domain analysis where nonlinearities of the hydrodynamic interaction and power take-off (PTO) system are neglected. The literature shows that the impact of the inter-device hydrodynamic interaction in the array tends to saturate as the size increases. However, the WEC model and controller of the vast majority of studies analyzing WEC array hydrodynamics are too simplistic for drawing definitive conclusions. Some have analyzed the layout optimization of small WEC arrays considering advanced control strategies for energy maximization. However, the nonlinear and non-ideal effects in the WEC model are generally ignored. In addition, the wave power attenuation due to the presence of WECs is also neglected in most of the studies in the literature.
Therefore, the present study suggests a novel WEC array model based on the harmonic balance (HB) method first suggested in for isolated devices. This HB model is based on Cummins' equation, but allows the articulation of different nonlinear effects, both in the hydrodynamic and PTO models, while keeping a low computational cost by using a hybrid frequency-time domain approach. In addition, the model structure is adequate for the implementation of optimal control strategies in order to maximize the energy generation.
This study includes a preliminary analysis of the HB model for a generic floating heaving cylinder included in two array layouts that including nonlinear viscous effects: (i) three devices in a row and (ii) four devices in a square configuration. This preliminary study shows that results of the HB model are identical to the traditional model based on the Runge-Kutta solver with state-space approximation, reducing the computational burden for short sea-states (tsim<100 s) and low number of devices. Longer time series and larger arrays require the implementation of a windowing technique that enables the use of shorter simulations that, combined, build up the longer signal more efficiently.
Finally, once the HB method including a windowing technique is verified, this method is employed for the analysis of the power generation capabilities of different arrays, comparing it against the case of an isolated WEC. The results show that hydrodynamic interactions can lead to a rather uncertain variation in the final energy generation of up to 10% (either increase or decrease depending on the metocean conditions and array layout). However, he power smoothing (reduction of the variability in the instantaneous power) is achieved always, reducing the mean-to-peak ratio up to a 30% even with relatively small arrays (4 WECs).