Enhancing Decentralized Control of Wave Energy Arrays by Predicting Optimal Array Motion

Forming multiple wave energy converters (WECs) into arrays is an inevitable trend to achieve high-capacity, low-cost wave energy generation. Advanced control has been recognized to play a central role in improving array energy production. However, control for WEC arrays is significantly more difficult than for single WECs. Within an array, the motion of devices is tightly coupled with each other through radiation effects and, unlike wind farms, these coupling effects can be both constructive and/or destructive. Consequently, an ideal controller needs to manage all radiation forces simultaneously, which corresponds to centralized control, represented by centralized model predictive control (C-MPC) in the literature. However, since the control actions of all devices are planned together, C-MPC, despite its optimal performance, leads to significantly increased computational complexity, which can become prohibitive for a large array. Accordingly, decentralized MPC (D-MPC) has been developed, which controls each device independently, enabling fast computation. However, unsurprisingly, the energy performance is degraded due to failure in modelling mutual radiation effects. To tackle this performance-computation dilemma, an effective decentralized MPC (eD-MPC) controller is proposed in this paper. The basic control structure is the same as D-MPC, in which each device is equipped with a local controller that solves for its own control actions. However, in eD-MPC, the control objective is to maximize the total energy production of the array, instead of the individual device energy production as in D-MPC. To achieve this, each local controller needs to predict the behaviour of other devices. It is proposed to calculate a suboptimal array velocity profile, from wave excitation force information, to serve as the motion prediction. This profile is calculated using a causal, single-frequency approximation of the optimal unconstrained velocity, yielding simple computation without increasing the wave excitation force prediction requirement. By using this motion prediction to assist the decentralized control planning process, each local controller of eD-MPC can align its actions, to a certain degree, with other devices, so that constructive radiation interactions are enhanced, and destructive effects are mitigated, improving overall energy production. On the other hand, eD-MPC possesses the same control complexity as D-MPC, enabling fast online computation. Numerical simulation, based on a four-body WEC array, are conducted to validate the proposed control method. The relatively close spacing between the devices results in pronounced radiation effects, under which D-MPC performs significantly poorer than C-MPC in terms of energy production. However, C-MPC requires 20 times more computation time compared to D-MPC. Notably, it is shown that, with a computation time similar to that of D-MPC, eD-MPC can significantly improve the energy production across various sea states, sometimes achieving performance comparable to C-MPC. This highlights eD-MPC as a promising and efficient solution for WEC array control.