Spectral control co-design of wave energy converter array layout
Authors: Peña-Sanchez Yerai , García-Violini Demián , Penalba Markel , Zarketa Ander , Nava Vincenzo , Ringwood John 
Published: September 2023

Wave energy systems are designed to maximise energy absorption from the oscillatory motion of waves, which can make a crucial contribution in a new carbon free generation matrix [1]. Thus, the global ocean energy market (including wave and tidal) is expected to grow by more than 700\% by 2028 [2]. However, the harsh conditions faced in the ocean, the strong variability of the resource, and the high force/velocity ratios pose significant challenges to the development of the different ocean energy technologies. Therefore, to date, wave energy converter (WEC) technology is still under development and still needs a significant progress to enhance the energy conversion efficiency and, consequently, to become commercial viable. Crucially, to meet these existing challenges, there are a number of key considerations to progress the effectiveness and efficiency of WEC technologies. In particular, energy maximising control systems, to maximise energy absorption, and the optimisation of WEC array schemes, to take advantage of constructive interaction effects, are currently considered as some of the key drivers for the development of efficient WECs [1].
Recent studies have shown that total design of WECs, analysing the impact of each individual component on the rest of the system, is a key methodology to achieve effective designs. For example, the levelised cost of energy (LCoE) is considered in the objective function in [3], analysing the interplay between the control system based on a spectral controller and the specifications of the power take-off (PTO) system defined as the maximum stroke and force. This methodology has been generally labelled as `co-design', or, when the development is carried out in a control-aware manner, `control co-design'. Similarly, in [4], the interaction between control and optimal WEC geometry is studied. In addition, as discussed before, another key driver in achieving effective wave energy system is the operation of WEC arrays. In particular, in [5] and [6] different array layouts are analysed in terms of computational efficiency and control, respectively.
Considering the results in [5], where methods based on harmonic balance techniques are used to analyse the computational demand related to different array layouts, an assessment of the impact of different array layouts on the LCoE, is performed in this study. Figure 1 illustrates different array layouts (a), and the impact of different separation and number of WECs on the resulting LCoE (b). (Figure in PDF abstract)For the implementation of this study, a spectral control methodology is considered to virtually achieve optimal control solutions, even in constrained scenarios. In tandem, different layout templates, composed of multiple point absorber WECs, are considered. To achieve a clear global indicator based on the LCoE, each layout is analysed, in terms of the separation distance and the number of WECs, as well as capital and operation expenditure (CapEx and OpEx, respectively). Following the methodological guidelines considered in [3], a general co-design scheme is designed, essentially based on an exhaustive search method, indicating the interplay between different array layouts and LCoE.