Data-base Hydrodynamic Coefficients Interpolator for Control Co-Design of Wave Energy Converters
Authors: Garcia-Violini Demian , Peña Sanchez Yerai , Zarketa Ander , Penalba Markel 
Published: September 2023

Ocean waves store an enormous amount of energy that is still untapped. Several wave energy converter (WEC) prototypes have already been suggested by different developers, but none of these prototypes has demonstrated economical viability, meaning that none of them is ready to compete in the energy market against other energy sources.
In order to improve the economical viability of WECs, two main actions have been identified: (i) the energy absorption capability of the devices must be enhanced, for which the design of advanced energy maximising control strategies is crucial; and (ii) cost reduction is a key action, meaning that more reliable prototypes must be designed with an economic perspective. In the traditional design process, the most critical aspects of WECs, the floater, the power take-off system, and mooring lines, are optimised based on the energy absorption capabilities and the loading on critical elements under a simplified control strategy: commonly, an unconstrained passive resistive control. Once the design is determined, an advanced control strategy is developed for that design to maximise energy absorption and generation capabilities.
However, the implementation of more advanced control actions significantly alters the behaviour of the device, substantially enhancing its motion. As a consequence, the pre-defined system may not suit the behaviour of the WEC under such control strategies. As a solution to this design imbalance, the control strategy is adapted so that it can extract the maximum energy allowed by the design, which is far from optimal. However, it is likely that the characteristics of the design include unnecessary overdesigns.
To avoid such problems, an alternative design approach has been suggested, which articulates the information about advanced control actions from the early stages of the design: Control co-design (CCD). The design of the WEC can be decided considering the behaviour of the device under the final control actions. However, analysing and redesigning geometry variations within a CCD loop requires a recomputation of hydrodynamic coefficients, which implies running a boundary element method (BEM) software at each iteration, which can render the computational demand of the CCD optimisation loop prohibitive. In that case, the only solution may be reducing the resolution of the BEM simulation in order to make the CCD optimisation numerically feasible. Another potential solution is computing an extensive pre-defined hydrodynamic coefficient database covering all the potential geometry variations in advance or having a reduced database combined with an interpolator.
The present paper suggests an efficient solution for the computation of hydrodynamic coefficient in CCD loops, which avoids the need for using BEM methods in CCD schemes. Based on an advanced data-based interpolation model for identifying the hydrodynamic coefficients for any variation of a base case geometry. To that end, the interpolation model is provided with hydrodynamic data for an extended base case, including the coefficients for the base case geometry and a limited range of expected variations. Based on this extended space, the data-based interpolator provides accurate information on any variations beyond the original base case, significantly reducing the computational cost of the CCD approach.