Point Absorber Wave Energy Converter Research Articles

A Numerical Study of the Performance of Point Absorber Wave Energy Converters

Free-floating and submerged wave energy converters (SWECs) are regarded as promising technologies for renewable energy production. These converters rely on a heave-motion buoy to capture the kinetic energy of ocean waves and convert it into electrical energy through power conversion systems. To better understand the impact of various factors on power generation and efficiency, the effects of different buoy shapes (rectangular, circular cylinder, and trapezoidal fin), submergence depths (0, 0.1, and 0.2 m), wave heights (0.04, 0.06, and 0.1 m), and spring stiffness (50 and 100 N/m) were investigated. A 2D numerical wave tank with a buoy was simulated, and the results were validated against experimental data. Information on vorticity, vertical displacement, power absorption, and efficiency are provided. The findings indicate that the buoy shape and wave height significantly affect power absorption and efficiency. Additionally, this study reveals that increasing submergence leads to higher power absorption and lower conversion efficiency.

Physical Modelling Of The Wave Field Around An Array Of Centrally Controlled Wave Energy Converters

To capture a substantial amount of wave energy, Wave Energy Converters (WECs) will be placed in arrays in a certain geometric configuration. WECs spaced closely together will interact, affecting the hydrodynamics of these devices and thus the total power absorption of the WEC array. These are called ‘near-field effects’. Furthermore, a WEC array will also influence the wave field in the wake zone behind the farm, the so-called ‘far-field effects’. This affects the coastline and other users of the sea near the WEC array. Both near- and far-field effects are caused by the modification of the incident waves due to wave radiation by and wave diffraction around the WECs. To understand these effects, it is therefore necessary to study the wave field in and around a WEC array. This study investigates the wave field modifications for an array of up to five heaving point absorber WECs that was tested at the Coastal & Ocean Basin Ostend. To optimize the absorbed power of the array, the Power Take-Off (PTO) devices are controlled using a centralized control algorithm, influencing the hydrodynamic behaviour of the WECs and hence the wave field. The research fits into the larger scope of the ‘WECfarm’ project, which has been initiated to address the lack of available realistic and reliable data covering large centrally controlled WEC arrays to validate numerical models (Vervaet et al., 2022).

SPH-based numerical modelling and performance analysis of a heaving point absorber type wave energy converter with a novel buoy geometry

Heaving point absorber (HPA) is one of the most promising technologies to absorb wave energy. Accordingly in this work, performance of a HPA in terms of capture-width-ratio (CWR) under the effect of hydrodynamics forces were analysed using the SPH-based open-source package: DualSPHysics. 395 cases of simulations, which include five different geometries with different densities of the buoy, different buoy height to wave height ratios, and damping coefficients of the WEC over a range of wave frequencies were studied and optimum operational parameters were found for the novel buoy geometry named: “Super cuboid”. Compared to other geometries, it produced up to 23 % of efficiency increment over a wide range of operational conditions. Furthermore, the flow patterns and pressure variation around different buoy geometries were studied and found that an increase in the projected area of the buoy in vertical direction tends to increase the pressure force which results in increase of CWR. The CWR is also slightly enhanced by the bottom shape of the buoy. Hence it is expected that the use of this novel buoy shape, will contribute to the design of more sustainable and reliable WECs in the future.

Physical Modelling Of A Centralized Controlled Array Of Five Wecfarm Wave Energy Converters

Point absorber wave energy converters (WECs) closely placed in array hydrodynamically interact through wave radiation and diffraction. The power absorption by these WECs is optimised by altering the WEC dynamics through the control of the Power Take-Off (PTO). As the WEC dynamics are changed, the hydrodynamic interactions change as well. Therefore, the PTO control should be optimized taking all these interactions into account, referred to as centralized control. The ‘WECfarm’ project has been initiated to study WEC arrays, and to address the research gap on available realistic and reliable data on WEC array tests to validate numerical models (Vervaet et al., 2022). This work discusses the experimental design, implementation and testing of a centralized controlled array of five ‘WECfarm’ heaving point absorber WECs, tested at the Coastal and Ocean Basin Ostend.

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.

Environmental-Sensing and adaptive optimization of wave energy converter based on deep reinforcement learning and computational fluid dynamics

This paper introduces a novel coupled model for real-time control of the point absorber wave energy converter (WEC) using parallelized deep reinforcement learning (DRL), where the WEC is situated within a numerical wave tank (NWT) built with the method of computational fluid dynamics (CFD). An in-house solver is developed to couple with the DRL and CFD to solve the interaction between WEC and the fluid environment. Validations on wave generation, wave-floater interaction, and power take-off (PTO) unit are carried out. Then, neglecting the detailed model for the PTO technologies, the DRL-based strategy dynamically adjusts the PTO force as a function of the wave features and floater motion. Based on the interaction data, the model-free DRL is outstanding in adaptability and robustness. Simulation results reveal that DRL control improves the wave energy absorption in irregular wave environments, resulting in improvement of 107.5 % compared to the resistive control, with better device protection performance than the model predictive control (MPC). An additional analysis of model-free characteristics of DRL demonstrates the optimization ability independent of floater modeling. This work is the first in-depth study of DRL control of WECs in CFD simulation, providing a more accurate simulation and an optimization process closer to the reality.

Improving the Amount of Captured Energy of a Point-Absorber WEC on the Mexican Coast

Although there are constant improvements in wave energy converter (WEC) technology, it is crucial to investigate site-specific sea conditions for optimal power absorption and efficiency. This study compares the efficiency of a floating buoy-type WEC device, with three differently shaped floats: a semi-sphere, a cylinder considered suitable for a location near Ensenada, on the Baja California peninsula, and a novel, rounded, semi-rectangular float. A statistical analysis of the wave climate of the last 42 years was performed to define the conditions to which the device is subjected. The WEC location was chosen for shallow waters, using a computational model that solves the modified mild slope equation. The hydrodynamic response of the three float designs was then analyzed in the frequency and time domains, using the software ANSYS AQWA 19.2, to assess the dynamics of the floating body, the forces exerted, and the power absorbed, as well as the suitability of the proposed power take-off (PTO) system. The findings show that the proposed float design absorbs the most energy, with an annual power of 135.11 MW, and that the PTO mechanism is appropriate.

Hydrodynamic response analysis of a hybrid TLP and heaving-buoy wave energy converter with PTO damping

In the present study, the numerical investigation is performed to analyse the hydrodynamic performance of circular and concentric arrangements of cone-cylinder-type heaving point absorber wave energy converter (WEC) around a Frustum Tension-Leg Platform (FTLP) based on potential flow theory. The responses of the single FTLP and the FTLP-WEC hybrid system are analysed for the rated wind speed of a 5 MW wind turbine to observe the influence of the WECs on wind power absorption of wind turbines supported on FTLP. The presence of the FTLP floating wind turbine platform and other WECs affects the hydrodynamic coefficients of the WEC. The influence of the hybrid system on the hydrodynamic coefficients is analysed on determining the ratio of the hydrodynamic coefficients for a single WEC system to those for a hybrid system. Further, the study analyses the instantaneous wave power absorption for the WECs arranged around the FTLP in a circular and concentric pattern. The hydraulic power take-off for the hybrid system with two different control strategies is then discussed to improve the wave power absorption of the WECs. The study observed higher wave power absorption of the WECs with the influence of the PTO system. The mean interaction factor and the capture width ratio of the hybrid system are further studied to understand the influence of array arrangement for the WECs. The hybrid system is noted to have favourable dynamic responses for different environmental factors and contributes positively in increasing power output.

A new method for analysis of marine sustainable energy systems

This paper proposes to utilise a new adaptive kernel density estimation (KDE) methodology based on linear diffusion processes for predicting the probability distribution tails of sea-state parameters. A key conclusion was reached that the proposed new methodology can lead to more accurate prediction results than traditional methods based on fittings to a measured significant wave height data set at National Data Buoy Center station 46014. This proposed methodology was subsequently utilised for deriving an accurate 50-year environmental contour line that was used in the dynamic analysis of a two-body point absorber wave energy converter. After systematically analysing the calculation results, another key conclusion was drawn that it is advantageous to use a more reliable contour line derived using the proposed new methodology for long-term dynamic analysis of wave energy converters. In summary, the proposed new adaptive KDE methodology is recommended to be utilised and to be refined continuously in future research work in the field of long-term reliability analysis of marine sustainable energy systems.

Two-Way Coupling Simulation of Fluid-Multibody Dynamics for Estimating Power Generation Performance of Point Absorber Wave Energy Converters

The objective of the present study is to develop and validate a two-way coupling simulation method between viscous fluid and multibody dynamics to estimate the power generation performance of point absorber wave energy converters. For numerical analysis of fluid dynamics, an enhanced density correction model was proposed to improve the accuracy and stability of the pressure calculation in DualSPHysics, an open-source code based on smoothed particle hydrodynamics (SPH). Through 2D hydrostatic and wave generation simulations, it was seen that the relative error in the average pressure was reduced from 11.81% to 1.64%. In addition, an interaction interface was developed to enable coupling simulation with RecurDyn, a commercial software for the simulation of multibody dynamics. Simulations were performed for a 3D single-body cylinder with a simple shape and a two-body floating wave energy converter (WEC) in regular waves, varying the linear damping coefficient of the power take-off (PTO) system to verify the proposed coupling simulation method for fluid-multibody dynamics. The results were benchmarked against experimental data, revealing a relative error of 1.05% with the experimental results when employing a high damping coefficient for the PTO system. Furthermore, to improve the efficiency of the two-body WEC, two design modifications were suggested; their impact on power generation performance improvement was examined. The developed method is anticipated to contribute to research aiming to enhance the power generation efficiency of various wave power devices with multiple elements and joints, pending further validation and refinement of the simulation approach.

Performance analysis of two generations of heaving point absorber WECs in farms of hexagon-shaped array layouts

ABSTRACT Numerical analyses are presented for two generations of a floating heaving point absorber wave energy converter (WEC) installed with different farm array layouts. The wave farm configurations are based on WECs developed by Waves4Power. The numerical models are developed in the DNV software package, Sesam. Parametric studies of the isolated WEC configurations and farm array layouts are conducted under typical environmental conditions and various incident wave directions to understand the hydrodynamic power performance and the levelised cost of energy (LCoE). Hexagonal layouts are proposed for deploying the WEC units and compared with a 10-unit layout termed StarBuoy, which has been reported in previous work. The results of the present study confirm that the interactions between arrayed units in a farm can have either positive or negative effects on the LCoE, which is dependent on the array layout and environmental conditions. The hexagonal array layouts lead to lower LCoE owing to constructive interaction effects.

Analytical study on dynamic performance of a hybrid system in real sea states

A mathematical model is developed to investigate the performance of a hybrid system comprising semi-submersible floating offshore wind turbines (FOWT) coupled to an array of point-absorbing wave energy converters (WECs) under irregular waves and dynamic winds. In this study, the hydrodynamic interaction of the hybrid system is conducted by applying the matching-method of eigenfunctions to solve the diffraction and radiation velocity potentials. Non-linearities of the hybrid system are taken into account in the Cummins framework, covering aerodynamic, catenary mooring, PTO system, fluid viscosity modeling, and frequency–time domain transformation of hydrodynamic coefficients. After running the convergence analysis and model validation, the present model is employed to perform a multiparameter effect analysis. Case studies are presented to clarify the effects of WEC parameters (including radius, draft, PTO damping, and layout) on the performance of a hybrid system. Nevertheless, a significant aspect of this work revolves around the development of a precise and efficient mathematical model, capable of accurately computing hydrodynamic coefficients for specific marine structures and evaluating the motion response of the interconnected floaters. Additionally, the study offers valuable insights into the preliminary design of hybrid systems and lays a mathematical foundation along with corresponding code for hybrid system projects.

Validation of a numerical wave tank based on overset mesh for the wavestar-like wave energy converter in the South China Sea

The CFD-based numerical wave tanks (CNWTs) have become a valuable numerical tool for research and development (R＆D) of wave energy converters (WECs) with improvements in computational efficiency. Verification and validation are crucial during the development of a CNWT to demonstrate the precision of the numerical results. The CNWT was utilized to conduct model tests on a designed point-absorber wavestar-like WEC at a scale of 1:17.5. A model of the wavestar was tested at the physical wave tank (PWT) at the Tianjin Research Institute. Verification and validation investigations were carried out on the variation wave strategies of the CNWT, which involved test cases with varying wave encounter angles (WEAs), wave steepnesses (WSTs), and wave periods. The results indicate that the amplitude of the float motion response increased with the growth of the WEA, and the motion response of the model under WEA of 180 deg is 17.3 % larger than the 0 deg. The phenomenon of cut jet flow and gas-liquid mixing that occurred in both PWT and CNWT for sea states with larger WST. The detailed error and deviation analyses and frequency domain study of numerical and experimental results were conducted. The experimental measurements indicate that the numerical results for the motion displacement of the WEC and the free-surface elevation surrounding the WEC are in satisfactory agreement.

Real-Time Model Predictive Control Framework for a Point Absorber Wave Energy Converter With Excitation Force Estimation and Prediction

Real-Time Model Predictive Control Framework for a Point Absorber Wave Energy Converter With Excitation Force Estimation and Prediction

Study on the power performance of wave energy converters mounted around an offshore wind turbine jacket platform

With the deepening of renewable energy research, the economic-friendly multi-energy coupling development method is gradually favored. This paper proposes a jacket-mounted hybrid wind-wave energy converter, which includes a bottom-fixed offshore wind turbine (OWT) and a microarray composed of three point-absorbing wave energy converters (WECs). Numerical simulations were conducted to study the power performance of the wave energy converter array, and a model test with a scale of 1:8 was carried out to calibrate and validate the numerical model. The array converts wave energy through a hydraulic system, and a dynamic-link library was created to simulate the hydraulic power take-off (PTO) system that can take into account the real-time pressure changes of the accumulator. The time domain simulation results show that the maximum capture width ratio (CWR) of the WEC array exceeds 0.5 when the wave period is nearly to the natural period, and the optimal CWR of a single WEC exceeds 0.8. When the wave period is less than 2 times the natural period, the energy capture behavior of WEC is sensitive to the change in wave direction, and this sensitivity is weakened when the device forms an array. Specifically, a single WEC prefers waves to be incident from the back side, while the WEC array prefers waves to be incident obliquely. This work will provide design guidance for the engineering application of stationary hybrid wind-wave energy concepts.

Energy capture performance enhancement of point absorber wave energy converter using magnetic tristable and quadstable mechanisms

This paper proposes two magnetic multistable (tristable and quadstable) mechanisms to enhance the energy capture performance of point absorber wave energy converters (PAWECs) for low-amplitude waves. Accordingly, two mechanisms consisting of several coaxial magnetic rings are designed based on the superposition effect of magnetic fields. Compared with conventional magnetic bistable mechanisms, the proposed tristable and quadstable mechanisms feature lower potential barriers and greater distances between two outermost potential wells, facilitating the occurrence of large-amplitude interwell motions in low-amplitude waves. A mathematical model is established using the Cummins equation and equivalent magnetic charge approach to depict the dynamic behavior and performance of PAWECs. The energy capture performance and average annual output power of PAWECs with tristable and quadstable mechanisms are evaluated for regular and irregular waves. The findings demonstrate that the two mechanisms significantly improve the energy conversion efficiency, enhancing their robustness against low-amplitude waves and damping detuning. The design concept of nonlinear multistable PAWECs using the superposition effect of magnetic fields provides a promising alternative for exploiting wave energy resources with low energy densities.

Design and Control of Hydraulic Power Take-Off System for an Array of Point Absorber Wave Energy Converters

The development of wave energy converter (WEC) arrays is an effective way to reduce the cost of levelized energy and facilitate the commercialization of WECs. This study proposes a hydraulic power take-off (PTO) system for an array of point absorber wave energy converters (PA-WECs) and designs a control system using a novel algorithm called the improved simplified universal intelligent PID (ISUIPID) controller and the adaptive matching controller including an improved artificial gorilla troops optimizer (IGTO) to improve and stabilize the output power of PA-WEC arrays. Simulations under varying irregular wave states have been carried out to verify the validity of the mathematical model and the control system. The results show that the designed IGTO has faster convergence speed and better convergence accuracy in solving the optimal linear damping coefficient of the generator, and the proposed ISUIPID controller provides superior performance in tracking the speed of the hydraulic motor under the changing sea states. In addition, the capture power and output power of the array of PA-WECs are improved and the electrical energy can be output stably under the designed control system. The array of PA-WECs with the proposed control system will become an independent, stable, efficient, and sustainable power supply system.

A bistable point absorber wave energy convertor with a mechanical motion rectifier

The design of novel wave energy converters (WECs) with the capability of low frequency energy capture is of great significance for the development of low frequency ocean wave energy. In this study, a novel point absorber WEC combined with a bistable mechanism and a mechanical motion rectifier (MMR) is proposed to achieve the goal of efficiently capturing wave energy in the low frequency range. In the WEC, the introduction of a rack-pinion-lever-spring (RPLS) bistable mechanism can not only enhance the capture efficiency in a low frequency range but also protect the system from excessive vibration amplitude through the nonlinear stiffness. Besides, one MMR based power take off (PTO) system is proposed to convert the bidirectional vibration into unidirectional rotation of the generator and extract more power via the mechanism of two one-way pinions. The dynamic model in the time domain for the nonlinear point absorber WEC with the RPLS bistable mechanism and the MMR based PTO system is established in which the convolution term is replaced by the state space method. The characteristics of the nonlinear dynamics and wave energy capture performance for the novel WEC are analysed in regular wave condition. The numerical results demonstrate that the peak capture width ratio of the proposed WEC can reach almost 2 times that of the traditional linear system in a lower frequency range.

High efficiency and wideband wave energy capture of a bistable wave energy converter with a displacement amplifier

Ocean wave energy is a kind of renewable energy with huge reserves, which can play an important role in the future construction of smart oceans. The low capture efficiency and narrow bandwidth of traditional wave energy capture devices seriously restrict the large-scale application of wave energy. To address these issues, a rack-pinion-lever-spring (RPLS) adaptive bistable Power Take-Off (PTO) mechanism with a time-varying potential barrier is proposed and applied to a point absorber wave energy converter (WEC). In the proposed nonlinear PTO system, a rack-pinion-lever (RPL) mechanism, as a displacement amplifier, has an effect on enhancing the poor amplitude sensitivity issue of the negative stiffness mechanism. Based on linear wave theory, a special nonlinear one-and-half-degree of freedom dynamic model is developed to describe the adaptive bistable wave energy converter (AB WEC). In comparison with the traditional bistable WEC (TB WEC) and equivalent linear WEC, the numerical results show that the AB WEC can greatly enhance the capture efficiency of lower frequency energy, especially at small wave excitations. The energy capture efficiency of the AB WEC is close to that of the TB WEC even at large wave amplitudes and is higher than that of the equivalent linear WEC. Finally, the wave energy capture characteristics of the three kinds of systems are studied based on the wave distribution diagram of a certain sea area in the South China Sea. The results show that the AB WEC has a large wave height adaptability in the low frequency region. The AB PTO mechanism with a displacement amplifier proposed in this paper can provide a technical reserve for the highly efficient and wide bandwidth capture of low frequency ocean wave energy.