Optimal control for wave energy converters: Non-linear model predictive control approach

Obtaining cost competitiveness is the major challenge facing ocean wave energy technology. Reducing the structural cost of wave energy converters (WEC) and improving energy capture are two ways to decrease its levelised cost of energy (LCOE). This research aims to contribute to the second route by enhancing energy capture using an advanced control strategy tailored for WEC applications to optimise their power performance.

In this study, a moving window blocking technique is proposed for reducing the size of the optimal control problem (OCP) arising at each time step. Using a Moving Window Blocking (MWB) technique reduces the number of decision variables, thereby reducing the time required to solve each OCP. Through numerical simulations, the advantages of the MWB-model predictive controller are demonstrated.

Moving to advanced energy-maximising control strategies, a non-linear model predictive control (NMPC) approach based on the real-time iteration (RTI) scheme is introduced to maximise the energy recovered from the ocean waves. The proposed controller incorporates the efficiency of the Power Take-Off (PTO) system when solving the optimal control problem at each time step. This controller differentiates from others in that it does not require offline computations to solve the non-linear programming problem that arises from incorporating the PTO's efficiency into the optimal control problem.

Numerical simulations of the proposed RTI-NMPC controller indicate that the RTI-NMPC approach can significantly improve wave energy converter performance. The proposed controller outperformed the other two controllers used for comparison, i.e., a resistive controller and linear MPC while keeping the amount of power "borrowed" from the grid to a bare minimum. The proposed RTI-NMPC strategy is later evaluated using a Kalman filter paired with a random-walk model to estimate the wave excitation force and a linear autoregressive (AR) model to forecast the wave excitation force over the prediction horizon where similar results are obtained.

A further contribution of this research is the derivation of a computationally efficient algorithm O(N^2) for "only-output" cost functions. For large prediction horizons, the algorithm O(N^2) significantly reduces the time required to calculate the hessian, which is the primary time driver in solving an optimal control problem numerically.