Wave Energy Converter Research Articles

Approximate Dynamic Programming for Control of Wave Energy Converters With Implementation and Validation on a Point Absorber Prototype

It is recognized that the application of constrained optimal control for wave energy converters (WECs), represented by model predictive control (MPC), is hindered by its computation burden resulting from online optimization, especially when the model contains nonlinearities. In this article, a novel control solution based on approximate dynamic programming (ADP) is proposed, in which an explicit controller is solved by model sampling and neural network training. In this way, the major computation load is moved offline to enable fast online execution, and the need for wave prediction is eliminated. The effectiveness of ADP is verified by a simulation case study based on a nonlinear WEC system. Using nonlinear MPC as the performance benchmark, over 90% energy efficiency is achieved by ADP under various sea states with constraint satisfaction and dramatically faster computation. The ADP controller is further experimentally validated on a newly constructed WEC prototype through wave tank testing, where successful implementation and satisfactory performance are demonstrated.

Wave energy converter farm feasibility assessment in southwest Baja California, Mexico

This study evaluates the technical and economic feasibility of implementing a wave energy converter (WEC) farm on the southwest coast of Baja California, Mexico. The aim is to determine the theoretical installed capacity and the levelized cost of energy (LCOE) for a WEC farm, unlike most previous efforts that were limited to a single device. The availability of wave energy has been assessed using 40 years of wave data. The electrical power generation potential of the Archimedes Wave Swing and Wave Dragon devices was estimated using their power matrices. For the calculation of levelized cost of energy, the capital expenditure includes equity, debt, taxes, and the present value of the power generation over the project's lifespan. The results indicate that the Archimedes Wave Swing farms offer the most favourable pricing for end users, despite the Wave Dragon farms having a larger installed capacity. A sensitivity analysis was conducted for five variables, which revealed that site selection has the greatest impact on LCOE.

Optimal strategy of the asymmetric wave energy converter survival in extreme waves

Enhancing the survival performance of wave energy converters (WECs) in extreme wave conditions is crucial, and reducing wave loads is a key aspect of this. Placing the device underwater has been recognized as a beneficial strategy, yet the determination of the optimal submerged depth and the effects of varying wave conditions remain ambiguous. To address this, the study numerically analyzes the total forces in both horizontal and vertical directions, along with their harmonic components, across different wave configurations. A computational fluid dynamics method is employed to investigate a triangular-baffle bottom-shaped oscillating floater, which is known for its high energy conversion efficiency. The findings indicate that submerging the device to a depth equivalent to half the actual focused amplitude (1/2Ab) is the most effective strategy in the given sea state, offering superior wave force reduction vertically and robust performance horizontally. The analysis of harmonics reveals the significant contribution of high-order components to the total wave forces. Additionally, the study examines the impact of focused wave amplitudes and peak frequencies, showing that although force reductions are lessened in more extreme conditions, the optimal submerged depth of 1/2Ab still yields near 30% reduction in total vertical force and 22% in total horizontal force. This research provides theoretical insight that can guide the enhancement of WECs' survival capabilities in practical engineering applications.

Parametric Decay of a Kinked Alfvén Wave Packet: 3D Magnetohydrodynamic Simulations

Large amplitude Alfvénic fluctuations, sometimes leading to localized inversions of the magnetic field, called switchbacks, are a common but poorly understood phenomenon in the solar wind. In particular, their origin(s), evolution, and stability within solar wind conditions are yet to be fully understood. Simulations modeling switchbacks have previously studied their stability in 2D. Here, we investigate the decay process of Alfvén wave packets via MHD simulations in 3D by characterizing the effects of system size, aspect ratio, and propagation angle on the decay rate. We show that the initial wave packet is unstable to parametric instabilities that develop compressible and Alfvénic secondary modes in the plane of, and transverse to, the initial wave packet propagation direction. The growth of transverse modes, absent in 2D simulations, increases the decay rate of the wave packet. We finally discuss the implications of our results for lifetime estimates of switchbacks and wave energy conversion in the solar wind.

Electric power prediction of a two-body hinge-barge wave energy converter using machine learning techniques

Investigating the electric power generated by wave energy converters (WECs) has attracted increasing attention along with the developments of wave energy converting technologies in recent years. Electric power estimation currently depends on wave-to-wire model-based numerical analysis and experimental studies of scale-down prototypes. However, traditional numerical simulations are time-consuming and expensive for power orediction of a full-scale WECs operated in real sea. More importantly, they cannot accurately predict WECs’ power performance in real time, thereby cannot be used for prediction-based real-time control. To address those problems, four machine learning techniques are employed as an alternative to traditional, complex physical modelling processes to evaluate and predict the generated electric power, based on historical experimental data of a two-body hinge-barge WEC. Comparative results of a Backpropagation (BP) Neural Network algorithm, a Long Short-Term Memory (LSTM) algorithm, a Support Vector Machine (SVM) algorithm and a Radial Basis Neural Network (RBFF) algorithm indicate that machine-learning-based approaches can accurately predict the electric performance of this complex multi-degree-of-freedom WEC, where the coefficient of determination (R2) of the BP Neural Network on the test dataset is up to 0.9987.

Energy Transport and Conversion Within Earth's Supercritical Bow Shock: The Role of Intense Lower‐Hybrid Whistler Waves

AbstractDetailed analysis of a high Mach number quasiperpendicular Earth bow shock crossing by the Magnetospheric Multiscale (MMS) spacecraft fleet reveal that lower‐hybrid (LH) whistler waves generated in the shock foot region transport energy predominately along the shock surface and slightly toward the shock ramp in the shock normal incidence frame, where wave energy accumulates and is dissipated into the plasma. This suggests the LH whistlers play an integral role in energy reconfiguration at high Mach number collisionless shocks with ramifications to plasma heating. The multipoint observations are used to quantify the wave characteristic parameters (via interferometry), Poynting fluxes, and energy conversion rates D, and to assess their scale dependencies and spatial and temporal properties. The whistler associated energy transport and conversion are found to depend on scale and location within the layer. High‐frequency electrostatic waves yield largest values of D. However, the dominant net energy exchange contribution is from the LH whistlers. In the foot spatially temporally coherent net energy exchange from the plasma to whistlers is observed, whereas deeper in the ramp net wave energy dissipation to the plasma is observed exhibiting significant space‐time variability. These results are consistent with the modified two stream instability driven by the relative drift between reflected ions and electrons as the mechanism for wave growth in the foot. Owing to strong electron heating, whistler energy dissipation in the ramp is attributed to Landau damping, which out‐competes the destabilizing effect of the reflected ion and electron drift.

Hydrodynamic Interactions and Enhanced Energy Harnessing amongst Many WEC Units in Large-Size Wave Parks

Interactions between wave energy converters (WECs) can significantly affect the overall energy-harnessing performance of a wave park. Although large-size wave parks with many WEC units are commonly considered in practical applications, it is challenging to simulate such parks due to huge computational costs. This paper presents a numerical model that uses the boundary element method (BEM) to simulate wave parks. Each wave energy converter (WEC) was modelled as a comprehensive system, including WEC buoys, power take-off, and mooring systems, with hydrodynamic interactions included. Two classical layouts for arranging 16 units were simulated using this numerical model. The energy-harnessing performance of these array layouts was analyzed for both regular waves and a selection of irregular sea state conditions with different wave directions, wave heights, wave periods and water depths. For each layout, three WEC separation distances were studied. An increase of up to 16% in the power performance of the WEC under regular waves was observed, which highlights the importance of interaction effects.

Wave energy resource classification system for the China East Adjacent Seas based on multivariate clustering

This study based on the 25-year wave hindcast database of the western Pacific and used three unsupervised learning clustering algorithms to classify the wave energy resources in the China East Adjacent Seas. Five wave energy characteristic parameters are comprehensively considered in the calculation process of the clustering algorithm. According to the analysis of the classification results, it can be seen that the Class Ⅳ is the most suitable for wave energy development in the China East Adjacent Seas, followed by the Class Ⅲ and Class Ⅴ. The Class Ⅵ is too far away from the coast to be used as the intended area for wave energy development. The Class Ⅰ is mostly located in inland seas and harbors, which are not suitable for wave energy development. By analyzing the annual average captured power, it can be seen that the optimal capture interval of the existing wave energy converters with mature technology is too large compared with the wave conditions in the China East Adjacent Seas. We should vigorously develop wave energy converters that are more suitable for the wave conditions of Class Ⅲ, Class Ⅳ and Class Ⅴ, and improve the capture efficiency of the wave energy converters.

Multi-freedom effects on a raft-type wave energy convertor- hydrodynamic response and energy absorption

This research delves into the effects of multiple degrees of freedom on a raft-type wave energy converter (WEC), using both experimental and computational methods. The WEC features two interconnected floating bodies linked by a specialized parallelogram joint, allowing for distinct heave, pitch, and surge motions. The power take-off (PTO) system, integrating Coulomb damping, is analysed for its impact on energy absorption. Despite varying damping amplitudes, peak energy absorption is consistent across different wave periods, as shown in scaled model tests. Computational simulations further investigate the multi-freedom effects by imposing constraints on various degrees of freedom, thus elucidating their individual and combined influences on energy absorption. Preliminary results indicate that the addition of degrees of freedom can enhance the WEC's efficiency, especially through coordinated release of the bodies' relative pitch and surge motions. The study also finds that the energy absorption efficiency from pitch motion depends on the release of surge motion. Moreover, the energy distribution among each degree of freedom is significantly affected by the device's multi-freedom characteristics. This research provides valuable insights and practical guidelines for the development of advanced multi-freedom WEC technologies.

Hydrodynamic Performance of Two Types of Floating Breakwaters Integrated With a Wave Energy Converter

Hydrodynamic Performance of Two Types of Floating Breakwaters Integrated With a Wave Energy Converter

Multi‐mode converter control for linear generator‐based wave energy system

AbstractThe electrification of remote islands has long been a subject of research interest, primarily because of their historical reliance on fossil fuels, leading to a significant carbon footprint. Recent advancements in wave energy converters offer a promising avenue to make these islands more self‐sustainable while considerably reducing carbon emissions. However, the persistent issue of voltage dips due to weaker grids continues to pose a challenge. This study introduces a multi‐mode converter control strategy with the goal of electrifying remote islands, employing a linear generator‐based wave energy converter in a unified electrical model. Various scenarios, including voltage dips and mainland grid disconnection, are simulated using MATLAB/Simulink. The study demonstrates the converter's ability to transition swiftly and smoothly in response to these scenarios, ensuring an uninterrupted power supply. Furthermore, the analysis indicates that the power quality at the point of common coupling remains well within acceptable standards.

Research on Maximum Power Control of Direct-Drive Wave Power Generation Device Based on BP Neural Network PID Method

Ocean wave energy is a new type of clean energy. To improve the power generation and wave energy conversion efficiency of the direct-drive wave power generation system, by addressing the issue of large output errors and poor system stability commonly associated with the currently used PID (proportional, integral, and derivative) control methods, this paper proposes a maximum power control method based on BP (back propagation) neural network PID control. Combined with Kalman filtering, this method not only achieves maximum power tracking but also reduces output ripple and tracking error, thereby enhancing the system’s control quality. This study uses a permanent magnet linear generator as the power generation device, establishes a system dynamics model, and predicts the main frequency of irregular waves through the Fast Fourier Transform method. It designs a desired current tracking curve that meets the maximum power strategy. On this basis, a comparative analysis of the control accuracy and stability of three control methods is conducted. The simulation results show that the BP neural network PID control method improves power generation and exhibits better accuracy and stability.

Wave excitation force prediction for arrays of wave energy converters in directional waves

The implementation of advanced control strategies is an effective means of maximizing the energy production of wave energy converters (WECs), and most of them require future wave excitation forces to determine the optimal control sequence. The WECs deployed in arrays can enable a significant reduction in the cost of wave energy and improve prediction performance by incorporating excitation forces from the array. In this paper, a critical comparison of the excitation prediction methods, including the time series, machine learning, and neural network, for a two-body heaving point absorber WEC is presented. Considering the symmetry of the WEC and arrays, the directional spectrum is utilized to determine the reference measurement of wave excitation. The prediction methods are applied to isolated WEC and different array layouts. Moreover, additional sensitivity analyses are performed to evaluate the performance. The results show that the autoregressive with extra input (ARX) model has the best performance in short-term wave excitation force prediction. In most cases, the ARX model is weakly influenced by the sampling period and can adapt well to changes in the directional distribution and sea states of irregular waves, and the ARX model requires the least amount of computational time in the simulations.

Control co-design optimization of nonlinear wave energy converters

This paper presents a study in which both the control and the shape of a Wave Energy Converter (WEC) are optimized simultaneously. A heaving point absorber WEC is assumed. To optimize the shape of the WEC’s buoy, nonlinear hydrodynamics need to be evaluated. One main contribution of this paper is the integration of nonlinear hydrodynamics and nonlinear control during the optimization of the WEC’s buoy shape. This approach is referred to as Control Co-Design (CCD). In this work, we present a control co-designed nonlinear heaving point absorber WEC that leverages the nonlinear dynamic, static Froude–Krylov (FK) forces to maximize power extraction. The nonlinear FK forces are approximated using a variation of the algebraic solution; the hydrodynamic forces of the body are computed using an analytic formulation leveraging the methods of eigenfunction expansion and separation of variables. The nonlinear geometry of the buoy is modeled as a series of inclined panels; the inclination angles are optimized to arrive at the optimal shape. The performance of the optimized shape is compared to that of a nonlinear spherical WEC. It is found that an average of 20% improvement is achieved by the optimized geometry over the spherical device.

A comprehensive review on scour and scour protections for complex bottom-fixed offshore and marine renewable energy foundations

Due to the marine environment's complexity, optimising offshore foundations' design is still a major focus of the scientific and industrial community, since foundations represent a large portion of the total investment. Scour is one of the main causes that lead to ultimate, and service limit states, impacting design optimization and costs. Scour at monopile foundations has been extensively studied. However, advances in scour protections for hybrid structures, and other bottom-fixed foundations for offshore renewable energy harvesting technologies are often kept confidential by stakeholders, and knowledge gaps must be covered. Thus, the present paper provides a summary of the most recent physical and numerical studies related to scour and riprap scour protections for complex bottom-fixed foundations, such as jackets, tripods, gravity-based foundations (GBF), high-rise structure foundations (HRSF), and suction buckets, while covering other marine energy harvesting technologies as well, including wave energy converters (WEC) and tidal energy converters (TEC). This manuscript presents knowledge gaps, recent improvements, and potential studies on hybrid foundations – offshore wind turbine foundations combined with WECs or TECs. It is shown that offshore scour protection is a study field with a wide margin of development, but crucial for the future of the offshore renewable energy sector, thus pointing out key challenges and major opportunities for future research.

Control co-design for wave energy farms: Optimisation of array layout and mooring configuration in a realistic wave climate

This paper presents a novel Control Co-Design (CCD) methodology aimed at economically optimising the layout of wave energy converter (WEC) arrays. CCD ensures the synergy of optimised WEC and array parameters with the final control strategy, resulting in a comprehensive and efficient design of the array. By integrating a spectral-based control strategy into the array layout design, this study pursues the twin objectives of maximising energy absorption while reducing costs. To prove the performance of the proposed CCD methodology, an application case is proposed where the inter-device distance, alignment, and mooring configuration of a five-device array, considering realistic wave scenarios, are optimised. Energy capture and system cost evaluations are conducted, with results emphasising the significance of incorporating advanced control strategies in the design phase to improve energy absorption and reduce costs. With the application case, the study demonstrates that the optimal layout of a WEC array considering economic factors may differ from the optimal from purely technical factors, such as energy absorption, in the analysed case.

Data-based modelling of arrays of wave energy systems: Experimental tests, models, and validation

One of the key steps towards economic feasibility of wave energy conversion technology concerns scaling up to farms of multiple devices, in the attempt to reduce installation costs by sharing infrastructure, and a consequent drop in levelised cost of energy. Moreover, whenever wave energy systems are deployed in proximity (in so-called arrays), the exploitation of the hydrodynamic interactions between single devices is fully enabled, potentially increasing the final energy outcome. To achieve this in real (operational) time, the employed energy-maximising control strategies require control-oriented array models, able to efficiently describe the dynamics of these interconnected systems in a representative fashion. This can be, nonetheless, a difficult task when considering first principles alone, under small motion assumptions, for modelling purposes. Recognising the uncertainty associated to array numerical models obtained from the linearisation of simplified system equations around their equilibria, this paper presents models of several array configurations identified following a frequency domain approach on the basis of experimental data. Tailored tests on laboratory-scale devices have been designed and conducted in the Aalborg University (Denmark) wave tank facility, with the purpose of performing representative system identification of the wave energy systems arrays. The obtained models are validated on different representative sea states configurations, in controlled and uncontrolled motion operational conditions. The validation results are fully discussed and analysed in terms of standard error measures and time lag, while the obtained models are made freely accessible via a linked repository (named OCEAN), in the attempt to openly provide validated models for different array configurations.

Stochastic optimization framework for hybridization of existing offshore wind farms with wave energy and floating photovoltaic systems

Due to the complementarity of renewable energy sources, there has been a focus on technology hybridization in recent years. In the area of hybrid offshore power plants, the current research projects mostly focus on the combinational implementation of wind, solar, and wave energy technologies. Accordingly, considering the already existing offshore wind farms, there is the potential for the implementation of hybrid power plants by adding wave energy converters and floating photovoltaics. In this work, a stochastic sizing model is developed for the hybridization of existing offshore wind farms using wave energy converters and floating photovoltaics considering the export cable capacity limitation. The problem is modeled from an investor perspective to maximize the economic profits of the hybridization, while the costs and revenues regarding the existing units and the export cable are excluded. Furthermore, to tackle the uncertainties of renewable energy generation, as well as the energy price, a scenario generation method based on copula theory is proposed to consider the dependency structure between the different random variables. Altogether, the hybridization study is modeled in a mixed integer linear programming optimization framework considering the net present value of the project as the objective function. The results showed that hybrid-sources-based energy generation provided the highest economic profit in the studied cases in the different geographical locations. Furthermore, the technical specifications of the farms have also been considerably improved providing more stable energy generation, guaranteeing a minimum level of power in a high share of the time, and with a better utilization of the capacity of the cable while the curtailment of energy is maintained within the acceptable range.

Power Generation Enhancement through Latching Control for a Sliding Magnet-Based Wave Energy Converter

A Surface-Riding Wave Energy Converter (SR-WEC) featuring a sliding magnet inside a pitching cylindrical hull is investigated as an easily deployable small power device to support small-scale marine operations. This study extends the earlier development of the system by authors to enhance power performance through the application of end spring and latching control. The inclusion of springs at the tube’s end enhances the magnet release and travel speeds as well as the average power output compared to systems without them. Further improvement of power output can also be achieved by employing optimal latching control. We introduced constant-angle and variable-angle unlatching strategies to determine optimal parameters in combination with passive and reactive power take-off (PTO) controls to assess their effectiveness. The optimized latching control and end spring can increase 60–80% more power output compared with the case without them under certain PTO damping. Additionally, we discussed the effects of limiting peak powers and associated energy leaks with latching.

Energy Efficiency Analysis of a Deformable Wave Energy Converter Using Fully Coupled Dynamic Simulations

Deformable wave energy converters have significant potential for application as flexible material that can mitigate structural issues, while how to design the dimensions and choose an optimal deployment location remain unclear. In this paper, fully coupled computational fluid dynamics and computational solid mechanics were used to simulate the dynamic interactions between ocean waves and a deformable wave energy converter. The simulation results showed that the relative length to wave, deployment depth and aspect ratio of the device have significant effects on the energy conversion efficiency. By calculating the energy captured per unit width of the device, the energy efficiency was found to be up to 138%. The optimal energy conversion efficiencies were achieved when the structure length was 0.25, 0.5 or 0.75 of the dominating wavelength and submerged at a corresponding suitable depth. The aspect ratio and maximum stress inside the wave energy converter showed a nonlinear trend, with potential optimal points revealed. The simulation approach and results support the future design and optimisation of flexiable wave energy converters or other marine structures with notable deformations.