The levellised cost of energy of wave energy converters (WECs) is not competitive with fossil fuel-powered stations yet. To improve the feasibility of wave energy, it is necessary to develop effective control strategies that maximise energy absorption in mild sea states, whilst limiting motions in high waves. Due to their model-based nature, state-of-the-art control schemes struggle to deal with model uncertainties, adapt to changes in the system dynamics with time, and provide real-time centralised control for large arrays of WECs. Here, an alternative solution is introduced to address these challenges, applying deep reinforcement learning (DRL) to the control of WECs for the first time. A DRL agent is initialised from data collected in multiple sea states under linear model predictive control in a linear simulation environment. The agent outperforms model predictive control for high wave heights and periods, but suffers close to the resonant period of the WEC. The computational cost at deployment time of DRL is also much lower by diverting the computational effort from deployment time to training. This provides confidence in the application of DRL to large arrays of WECs, enabling economies of scale. Additionally, model-free reinforcement learning can autonomously adapt to changes in the system dynamics, enabling fault-tolerant control.

We examined the heave motion of a spherical buoy during a free-decay drop test. A comprehensive approach was adopted to study the oscillations of the buoy involving experimental measurements and complementary numerical simulations. The experiments were performed in a wave tank equipped with an array of high-speed motion-capture cameras and a set of high-precision wave gauges. The simulations included three sets of calculations with varying levels of sophistication. Specifically, in one set, the volume-of-fluid (VOF) method was used to solve the incompressible, two-phase, Navier–Stokes equations on an overset grid, whereas the calculations in other sets were based on Cummins and mass-spring-damper models that are both rooted in the linear potential flow theory. Excellent agreements were observed between the experimental data and the results of VOF simulations. Although less accurate, the predictions of the two reduced-order models were found to be quite credible, too. Regarding the motion of the buoy, the obtained results indicate that, after being released from a height approximately equal to its draft at static equilibrium (which is about 60% of its radius), the buoy underwent nearly harmonic damped oscillations. The conducted analysis reveals that the draft length of the buoy has a profound effect on the frequency and attenuation rate of the oscillations. For example, compared to a spherical buoy of the same size that is half submerged at equilibrium (i.e., the draft is equal to the radius), the tested buoy oscillated with a period that was roughly 20% shorter, and its amplitude of oscillations decayed almost twice faster per period. Overall, the presented study provides additional insights into the motion response of a floating sphere that can be used for optimal buoy design for energy extraction.

Multiple wave energy converter (WEC) buoys can be used to establish a WEC array-powered microgrid collectively forming a Marine Energy Grid (MEG). An oceanic domain with gravity waves will have significant spatial variability in phase, causing the power produced by a WEC array to have high peak-to-average ratios. Minimizing these power fluctuations reduces the demand for large energy storage by WEC array-powered DC microgrids while also reducing losses in the undersea cable to the shore. Designs that reduce energy storage requirements are desirable to reduce deployment and maintenance costs. This work demonstrates that polyphase power in conjunction with an energy storage system can be used to maintain constant power. This work shows that an N WEC array geometry can be designed to reduce the energy storage requirements needed to mitigate the power fluctuations if the WEC array produces constant, polyphase power. Additionally, the conditions that identify the wave frequencies and control the effort needed to produce polyphase power are developed. This paper also shows that increasing the number of WECs in an array reduces aggregate power fluctuations. Finally, WEC array power profiles are investigated using simulation results to verify the mathematical conditions developed for the three and six WEC cases.

The motivation and focus of this work is to generate passive transfer function matrices that model the radiation forces for an array of WECs. Multivariable control design is often based on linear time-invariant (LTI) systems such as state-space or transfer function matrix models. The intended use is for designing real-time control strategies where knowledge of the model’s poles and zeros is helpful. This work presents a passivity-based approach to estimate radiation force transfer functions that accurately replace the convolution operation in the Cummins equation while preserving the physical properties of the radiation function. A two-stage numerical optimization approach is used, the first stage uses readily available algorithms for fitting a radiation damping transfer function matrix to the system’s radiation frequency response. The second stage enforces additional constraints on the form of the transfer function matrix to increase its passivity index. After introducing the passivity-based algorithm to estimate radiation force transfer functions for a single WEC, the algorithm was extended to a WEC array. The proposed approach ensures a high degree of match with the radiation function without degrading its passivity characteristics. The figures of merit that will be assessed are (i) the accuracy of the LTI systems in approximating the radiation function, as measured by the normalized root mean squared error (NRMSE), and (ii) the stability of the overall system, quantified by the input passivity index, $\nu$, of the radiation force transfer function matrix.

Oceans are harsh environments and can impose significant loads on deployed structures. A wave energy converter (WEC) should be designed to maximize the energy absorbed while ensuring the operating wave condition does not exceed the failure limits of the device itself. Therefore, the loads endured by the support structure are a design constraint for the system. Furthermore, the WEC should be adaptable to different sea states. This work uses a WEC-Sim model of a variable-geometry oscillating wave energy converter (VGOSWEC) mounted on a support structure simulated under different wave scenarios. A VGOSWEC resembles a paddle pitching about a fixed hinge perpendicular to the incoming wave fronts. The geometry of the VGOSWEC is varied by opening a series of controllable flaps on the pitching paddle when the structure experiences threshold loads. It is hypothesized that opening the flaps should result in load shedding at the base of the support structure by reducing the moments about the hinge axis. This work compares the hydrodynamic coefficients, natural periods, and response amplitude operators from completely closed to completely open configurations of the controllable flaps. This work shows that the completely open configuration can reduce the pitch and surge loads on the base of the support structure by as much as 80%. Increased loads at the structure’s natural period can be mitigated by an axial power take-off damping acting as an additional design parameter to control the loads at the WEC’s support structure.

Wave energy converter (WEC) buoys can be used for supplying electrical power for both terrestrial and marine energy grids. Marine applications include persistent sensing and refueling Underwater Autonomous Vehicles (UAVs). A WEC array is an attractive solution for marine energy grids where scalability is important, since evolving load requirements can be accommodated by adding or removing WECs from the array. The design space for a WEC array has many variables including inter-WEC spacing, individual WEC output capacity, WEC type, array geometry and the control approach[l]. Hydrodynamic decoupled analyses facilitate decentralized control, but miss a potential opportunity to exploit the hydrodynamic coupling of a more tightly packed array [2] [3]. A compact array model, parameterized with a non-dimensional WEC packing ratio, was proposed by Garnaud and Mei [1]. This paper extends those results to include the hydrodynamic coupling between individual WECs in the array showing an increase in the theoretical energy extraction.This work considers a 25-WEC, compact array example. The hydrodynamic radiation coefficients were generated using WAMIT (Wave Analysis MIT) and were incorporated into the dynamic equations introduced by Garnaud and Mei. An energy extraction efficiency metric, considering the energy dissipated due to the waves reflected by and transmitted through the array, was used to quantity the effect of the added terms. Incorporation of the hydrodynamic terms showed an increase of up to 28% in the low frequency range. This is important for wave energy conversion as it corresponds to waves with higher speeds and wavelengths.