Point Absorber Wave Energy Converter Research Articles

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.

Adaptive systematic optimization of a multi-axis ocean wave energy converter

Due to the growing global energy needs, renewable energy systems, particularly wave energy converters (WECs), are a feasible solution to satisfy current energy demand. Recently, wave farms with diverse technologies, geometries, and layouts have been developed; however, evaluating the performance of these devices is complicated and requires precise hydrodynamic modeling to efficiently deploy wave farms. This study proposes a multi-scenario model using boundary element method (BEM) solver, NEMOH, integrated with evolutionary many-objective algorithms to evaluate the performance of a multi-axis point absorber WEC with respect to cylindrical, triangular, quadrilateral, and octagonal geometries and varying dimensions, that is, radius, draft, and height. To this end, six objective functions were considered to maximize the energy absorption and significant velocity and to minimize the separation distance, levelized cost of energy, net present value, and q-factor. Accordingly, three EMnO frameworks were utilized: the non-dominated sorings genetic algorithm (NSGA-III), reference point-based NSGA-III (R-NSGA-III), and multi-objective evolutionary algorithm by decomposition (MOEA/D). The results of the three optimization algorithms indicate that R-NSGA-III converges faster than the other two and also found that the cylindrical and octagonal geometries produce more annual energy among other forms. Comparing the performances of the three different layouts for cylindrical and octagonal geometries reveals that the arrow layout with thirty buoys produced more energy and had a lower levelized cost of energy and net present value.

Fast time-domain model for the preliminary design of a wave power farm

This study presents a novel, fast time-domain model developed for an array of interacting point-absorber wave energy converters. The model is validated using experimental wave tank data. The point-absorbers, based on Uppsala University’s design, are arranged in a symmetric grid and interact with scattered and radiated waves while constrained to the heave motion. The model employs linear potential flow theory to solve the hydrodynamic coefficients in the frequency domain and employs Cummins’ formulation to solve the equations of motion in the time domain. Modeling an array of wave energy converters in the time domain yields a system of integro-differential equations, featuring convolution terms in the excitation and radiation forces. This implies that past waves radiated by the body continue to impact future dynamics. Irregular long-crested waves, generated from the Bretschneider spectrum, serve as the incident waves for the study. The model’s accuracy in capturing the dynamics and power absorption of the farm is demonstrated through validation against experimental data from a 1:10 scaled prototype of a six-point-absorber array. Despite inherent differences between the experimental and numerical set-ups, the model accurately represents the farm’s behavior. Furthermore, an efficiency test reveals that the numerical scheme approximates the performance of wave power farms comprising 6, 12, 24, 48, and 96 interacting devices within a maximum computational time of 20 s. Overall, this research presents a novel and accurate time-domain model for analyzing an array of point-absorber wave energy converters. The model’s ability to capture the dynamics and power absorption, along with its efficiency in simulating larger wave power farms, make it a valuable tool for the preliminary design stage.

A self-stabilizing point absorber wave energy converter with a top-shaped buoy and non-linear power take-off for oceanographic applications

Point absorber wave energy converters (PA-WECs) are considered an independent renewable energy resource in oceanographic research to study wave climate data, ocean navigation and maritime security. Their performance enhancement through optimally designed floats and power take-off (PTO) is a crucial challenge. The proposed study investigates the combined PA-WEC model, including (i) the hydrodynamic of the optimally designed top-shaped buoy, (ii) non-linear characteristics of power take-off and (iii) self-stability of PA-WEC under the real-time wave climate of XiaoMaiDao wave station, Shandong, China. The proposed mechanical power take-off comprises a double-sided rack with gear transmission and three-phase DC generators. The components of the power take-off are symmetrically oriented on both sides of the rack to make it statically and dynamically balanced for the self-stability of the PA-WEC. The floating buoy absorbs kinetic energy from waves relative to a fixed point and transfers it to the PTO system. The PTO module alters the forward and reverted strokes of heaving motion into uni-directional rotations on the output shaft, employing a mechanical gearing mechanism with one-way bearings. Subsequently, supercapacitors store the rectified electrical energy in the power conversion and storage modules. The mechanical power take-off was initially modeled in MATLAB/Simscape and verified through experimental investigations using mechanical testing and sensing machine. Secondly, the hydrodynamics of the floating buoy was studied using frequency- and time-domain simulations in ANSYS AQWA. Thirdly, the wave tank tests were performed on a 1:25 scaled buoy in a wave tank, and the test results were validated against the time-domain simulations. Finally, the combined effects of power take-off and buoy were studied on the prototype scale, and it is concluded that at 1m significant wave height, the power take-off system integrated with the Cyl-AS buoy can generate 247.76W (RMS) with PTO efficiency of ηpto_rms = 76.37% at PA-WEC efficiency of ηwec_rms = 12.10%. Installing the proposed point absorber wave energy converter system along the offshore platforms can promote the UN-SDG-2030 Agenda, specifically the 7 and 14 goals, by supplying electricity for oceanographic applications.

Effect of piecewise damping torques and coefficients on power absorption of a point-absorber wave energy converter

Wave energy converters (WECs), especially point-absorber WECs, are of great interest in recent years due to the global energy crisis. The power take-off (PTO) control strategy plays a crucial role in the motion response and power absorption of the WEC. This study investigates a WEC on a multi-float power generation platform as a case study, and compares four different control strategies. These control strategies are classified into two types based on the method of generating PTO damping: Type-A, which applies damping torque, and Type-B, which applies damping coefficient. Furthermore, each type has two subtypes: continuous and piecewise, depending on whether the damping torque or coefficient is continuous in the upward and downward motions of the WEC. The results indicate that the Type-B control strategy improves the power quality compared with the Type-A control strategy. Among the subtypes, the piecewise control strategy achieves greater power absorption than the continuous control strategy, while keeping the motion performance at an acceptable level.

Nonlinear impedance matching control for a submerged wave energy converter

AbstractThe impedance matching control, also known as approximate complex conjugate control (ACC), is one of the main strategies for improving the capture of energy by point absorber wave energy converters. Such a strategy shapes the mechanical impedance related to the floater dynamics via the control law. Since the traditional ACC is given by a linear control law, this work proposes a generalization denoted as nonlinear complex conjugate control (NCC) that considers the presence of nonlinear viscous damping in addition to the usual linear damping and stiffness. The energy maximization conditions for the proposed NCC are derived in the frequency domain through the describing function method. These conditions show that the ACC is a special case of the NCC when the total damping on the floater is approximated as a linear function of its velocity. From numerical simulations of a point absorber wave energy converters with nonlinear damping, which is based on the Archimedes wave swing prototype, it is shown that the NCC provides greater energy conversion than the ACC, as well as a robust performance in the presence of variations of the damping coefficient and the excitation force peak frequency.

Experimental and CFD Assessment of Harmonic Characteristics of Point-Absorber Wave-Energy Converters with Nonlinear Power Take-Off System

The wave-energy excitation of point absorbers is highly associated with their resonant movement, and harmonic characteristics are of increasing concern in affecting resonance. However, the commonly used linearized power take-off (PTO) systems underestimate the impact of harmonics. The purpose of this study is to address the knowledge gap in assessing the contribution of hydraulic PTO systems to higher harmonic wave loads and velocities. In the present work, higher harmonics in point-absorber wave-energy converters (PA-WECs) with hydraulic power take-off (PTO) systems are investigated through both experimental and computational fluid dynamics (CFD) methods. The fast Fourier transform is used to decompose the high-order harmonics. To account for the influence of nonlinear wave–wave interaction on harmonics, the isolated PA-WEC is used as a basis for comparison with the paired PA-WECs. The influence of wave steepness is also estimated at two resonance periods. Results indicate that the additional resonance of the paired PA-WECs may be attributed to the harmonic wave loads at longer wave periods. Harmonic wave loads of paired PA-WECs typically have a more substantial impact and increase more rapidly with increasing wave steepness compared to isolated PA-WECs. Furthermore, as the wave steepness increases, there are significant enhancements in both the harmonic wave loads and heaving velocity, which strongly correlate with the instantaneous maximum hydraulic power. Consequently, our study will contribute to enhancing the maximum power output in the design of future point absorber arrays.