Ex-post Analysis of the WEC Control Competition Results Using a Fourier Spectral Control Approach

Abstract The wave energy converter control competition (WECCCOMP) allowed several real-time control approaches to be assessed, both in numerical and physical experiments. The solution retained by IFP Energies Nouvelles (IFPeN), which won the numerical simulation and experimental evaluation phases, consists of a receding-horizon MPC algorithm, including an estimator and a predictor for the wave excitation torque. The control objective function, solved by a quadratic programming (QP) optimiser in the real-time implementation, is weighted over the receding time horizon by means of weighting coefficients, which are optimised off-line for each sea state, in order to take into account the non-ideal power take-off (PTO) efficiency. Given the potential complexity of the interaction between the different components involved in the control implementation (estimation, prediction, QP solution, choice of weightings), it is useful to carry out an ex-post analysis, in order to understand if, and how, the solution proposed by IFPEN could have been improved. To that end, a Fourier spectral control algorithm is implemented, which is able to calculate the optimal trajectory and control torque for the totality of a signal, simulated from WeCCCOMP sea states, taking the non-ideal PTO efficiency into account. By comparing MPC results with the theoretically optimal solutions provided by the spectral method, it is found that, in the studied WECCCOMP sea states, the IFPeN MPC algorithm performance lies within approximately 10% of the optimal solution, in terms of electric power.The influence of the MPC forecast accuracy and prediction horizon is examined. Finally, somechallenges associated with the offline MPC weighting optimisation are identified.