Model-Predictive Control Strategy for an Array of Wave-Energy Converters

Abstract

To facilitate the commercialization of wave energy in an array or farm environment, effective control strategies for improving energy extraction efficiency of the system are important. In this paper, we develop and apply model-predictive control (MPC) to a heaving point-absorber array, where the optimization problem is cast into a convex quadratic programming (QP) formulation, which can be efficiently solved by a standard QP solver. We introduced a term for penalizing large slew rates in the cost function to ensure the convexity of this function. Constraints on both range of the states and the input capacity can be accommodated. The convex formulation reduces the computational hurdles imposed on conventional nonlinear MPC. For illustration of the control principles, a point-absorber approximation is adopted to simplify the representation of the hydrodynamic coefficients among the array by exploiting the small devices to wavelength assumption. The energycapturing capabilities of a two-cylinder array in regular and irregular waves are investigated. The performance of the MPC for this two-WEC array is compared to that for a single WEC, and the behavior of the individual devices in head or beam wave configuration is explained. Also shown is the reactive power required by the power takeoff system to achieve the performance.

Towards Real-Time Reinforcement Learning Control of a Wave Energy Converter

“…In addition, the robust and computationally efficient MPC strategy described in [6,8] is selected to initialise the training and benchmark the results of the DRL scheme. The method is implemented in the MATLAB/Simulink framework using the quadratic-programming solver quadprog, after discretising the matrix equation in (6) with a zero-order hold.…”

“…The method is implemented in the MATLAB/Simulink framework using the quadratic-programming solver quadprog, after discretising the matrix equation in (6) with a zero-order hold. Similarly to [6,8], the future wave elevation is assumed here to be known exactly, as prediction methods with 90% accuracy up to 10 s into the future have been proposed [41,43].…”

“…As a result, no constraints on either the buoy displacement or the PTO force are set on the MPC controller. The penalty on the slew rate is expected to be sufficient for the achievement of a suitable WEC response, by setting r MPC = 10 −5 to ensure convexity according to [8].…”

“…An even more efficient implementation cast in a quadratic programming form has been proposed by Zhong and Yeung [6]. Fundamentally, the convex form enables the strategy to be generalised to the control of multiple WECs in real-time [7,8]. However, linear MPC relies on a linear model of the WEC dynamics.…”

“…After sufficient data samples are collected, the controller can move to the proposed data-driven model, whose computational cost at deployment does not increase if nonlinearities are present and can adapt to changes in the system dynamics or noncritical faults if retrained regularly. Hence, first of all, the WEC is operated in a range of representative sea states under the convex MPC proposed in [6,8]. Data samples are collected from 15-minute-long wave traces in each sea state.…”