Model Of Wave Energy Converter Research Articles

Offshore Measurements and Numerical Validation of the Mooring Forces on a 1:5 Scale Buoy

Wave energy conversion is a renewable energy technology with a promising potential. Although it has been developed for more than 200 years, the technology is still far from mature. The survivability in extreme weather conditions is a key parameter halting its development. We present here results from two weeks of measurement with a force measurement buoy deployed at Uppsala University’s test site for wave energy research at the west coast of Sweden. The collected data have been used to investigate the reliability for two typical numerical wave energy converter models: one low fidelity model based on linear wave theory and one high fidelity Reynolds-Averaged Navier–Stokes model. The line force data is also analysed by extreme value theory using the peak-over-threshold method to study the statistical distribution of extreme forces and to predict the return period. The high fidelity model shows rather good agreement for the smaller waves, but overestimates the forces for larger waves, which can be attributed to uncertainties related to field measurements and numerical modelling uncertainties. The peak-over-threshold method gives a rather satisfying result for this data set. A significant deviation is observed in the measured force for sea states with the same significant wave height. This indicates that it will be difficult to calculate the force based on the significant wave height only, which points out the importance of more offshore experiments.

Numerical study on the hydrodynamic performance of a symmetrical dual-chamber oscillating water column wave energy converter

In this study, a novel floating oscillating water column (OWC) wave energy converter (WEC) with dual chambers is proposed, and its hydrodynamic performance and primary energy conversion characteristics are investigated by numerical calculation. It consists of a floating body and two long vertical pipes opening downward at the bottom, forming dual chambers at the top. These two rectangular pipes are fixed to the front and back ends of the buoyancy tank with the same width, and it can be regarded as an oscillating single floating body as a whole. Under the action of the incident wave, the WEC captures wave power by the heave motion and relative motion of the pipe and the water column in it to form an oscillating water column, outputting pneumatic power. The geometry size of the vertical pipes is optimized by comparing the hydrodynamic performance and capture width ratio (CWR) of the WEC models with several rectangular pipes of different sizes. The calculation results show that increasing the draft, which is positively correlated with the total mass of the WEC model, increases its optimal response period. By comparing the numerical calculation results of the hydrodynamic performance and CWR of the WEC models with three kinds of floater bottom shapes, semi-cylindrical, sharp-bottomed, and flat-bottomed, it is found that the flat-bottomed model has the best capture performance.

Representative linearised models for a wave energy converter using various levels of force excitation

In guiding the progression, development, and operation of wave energy converters (WECs) in a more efficient way, mathematical analysis and understanding of the dynamic process is essential. Mathematical WEC models, obtained either by numerical analysis or physical modelling, form the basis of most (model-based) energy maximising control strategies available in the literature, where experimental design and system identification methodology directly impact the resulting model. This study, using an experimental-based WEC model (which can be used for linear control design), investigates the dynamic behaviour of a WEC by analysing the dominant poles of the system, generated using fully nonlinear computational fluid dynamics (CFD)-based numerical wave tank (NWT) experiments. The aim is to effectively track the dominant dynamics of the WEC, using different force-input amplitude levels in the NWT setup, and perform a comparison with the classical linear boundary-element-methods (BEM) equivalent methodology. Thus, the presented case studies are shown to agree with previously proposed model assessment of linear WEC models, based on a free-decay NWT setup. In addition, the representative WEC models determined as part of this study can be used for WEC controller design, either singly, or using a form of model/controller gain scheduling.

Development of Dynamic Model of Wave Energy Converters Using Gaussian Process Regression

Development of Dynamic Model of Wave Energy Converters Using Gaussian Process Regression

Bayesian Actor-Critic Wave Energy Converter Control With Modeling Errors

This paper presents a comparison of a Reinforcement-Learning (RL) based wave energy conversion controller against standard reactive damping and model predictive control (MPC) approaches, in the presence of modeling errors. Wave energy converters (WECs) are under the influence of many non-linear hydrodynamic forces, yet for ease and expediency, it is common to formulate linear WEC models and control laws. Therefore it is expected that significant modeling errors may be present, which may degrade model-based control performance. Model-free RL approaches to control may offer a significant advantage in robustness to modeling errors, in that the model is learned by the controller by experience. It is shown that, for an annual average sea state, RL-based controllers can outperform model-based control – reactive control and MPC – by 19% and 16%, respectively, when significant modeling error is present. Furthermore, compared to similar studies of RL-based control, the proposed model can reduce the training time from 8.4 hr to 1.5 hr.

Robust Tube-Based Model Predictive Control for Wave Energy Converters

This paper proposes an efficient robust tube-based model predictive control (RTMPC) strategy for energy-maximization control of wave energy converters (WECs) subject to constraints due to safety considerations. Compared with the existing MPC strategies developed for the WEC control problem, the RTMPC method provides an effective approach to explicitly handle plant-model mismatches with guaranteed constraint satisfaction, contributing to improved energy capture efficiency. The fundamental idea is to integrate disturbance invariant sets into the MPC scheme for energy-maximization control to form a tube-based predictive controller, which enhances the robustness of MPC for a WEC without increasing online computational complexity. The resulting RTMPC controller can bound the WEC plant trajectories in a tube centered around a nominal WEC model trajectory, and uncertainties from un-modeled WEC dynamics and unmeasured disturbances can be mitigated by an error feedback portion. Numerical simulations demonstrate the effectiveness of the proposed control strategy.

Dynamical modeling and parametric analysis of an electret-based wave energy converter

Carbon neutrality and the Internet of Underwater Things have injected new impetus into the development of wave energy converters (WECs) albeit most of WEC projects have ended in failure due to low cost-effectiveness. Hereupon we present the dynamical modeling and parametric analysis of a novel electret-based WEC that has a distinct power take-off system compared to the conventional ones and has exhibited high power density in our previous study. Linear wave theory and Morison equation are applied for wave field and forces, respectively. WEC motions parallel with incident waves are modeled, and the electrical subsystem of the generator is treated as a current source and a capacitor. With these simplifications, the governing equations of the nonlinear and non-smooth electromechanical system are obtained and then numerically solved using an event-driven algorithm. The new power take-off system is experimentally validated. We find that the power output varies nonlinearly with wave parameters under regular wave excitation but linearly under irregular ones, and that superharmonic resonance can significantly enhance energy conversion performance at relatively low frequencies, based on which the optimum parameters are obtained. A peak average power of around 2 mW (at a matched load resistance) is generated from each generator encapsulated in the WEC of a diameter of 15 cm. The findings shed light on the characteristics of electret-based WECs and provide support for the development of wave energy farm; moreover, the methodologies of modeling and analysis can be extended to the design and optimization of the scaleups of the proposed electret-based WEC.

Power output estimation of a two-body hinged raft wave energy converter using HF radar measured representative sea states at Wave Hub in the UK

For the physical model testing of wave energy converters (WECs) in the wave basin, it is necessary to test the models in a small number of sea states. Previously, the H – T binning method was widely used to determine the sea states that are representative of an ocean area. However, it omitted much useful information such as the wave directionality. In this paper, a novel method, the K-means clustering technique is used in combination with High Frequency (HF) radar measured data from Wave Hub, UK. The results show that K-means clustering method better preserves the characteristics of the ocean area than the binning method. Furthermore, the impact of different regrouping methods on assessing the annual energy output of the model is investigated, by applying the K-means clustering method to a 1:25 two-body hinged raft WEC. It is found that although non-linear performance can be clearly observed in the model both physically and numerically. Due to the fact that most sea states from Wave Hub are out of the non-linearity range of the model, the non-linear effect on the overall performance of the WEC model in this ocean area is limited. It allows the annual energy output to be accurately predicted by using only a small number of representative sea states (defined as K) ≤15, based on K-means clustering method.

Numerical and experimental study of the hydrodynamic coefficients and power absorption of a two-body point absorber wave energy converter

This study compares the hydrodynamic coefficients of a two-body point absorber wave energy converter (WEC) model obtained by three methods, namely the experimental method, the finite volume method (FVM), and the boundary element method (BEM). The BEM and FVM numerical simulations of the WEC motion are done using ANSYS AQWA and OpenFOAM, respectively. An experimental method for the accurate calculation of the added mass, damping coefficient, and wave excitation force for the WEC is introduced. The experiments are carried out in a wave tank with a scaled-down WEC model. A comparison of the results shows that – although the BEM is computationally fast, inexpensive, and able to estimate the added mass of the WEC with a reasonable accuracy – it is not able to accurately calculate the damping coefficients. The power absorbed by the WEC is calculated using the hydrodynamic coefficients obtained by all methods. The results show that the viscous damping dramatically decreases the absorbed power. A practical range of dimensionless damping coefficients is proposed to estimate the viscous damping of a two-body point absorber WEC, based on the experimental and FVM results. The upper bound of the absorbed power is also discussed in this paper.

Design, modeling and performance analysis of a deployable WEC for ocean robots

Ocean robots have important application value in both military and civil fields. However, ocean robots powered by batteries need to be launched and recovered frequently during mission due to the lack of continuous power supply. Capturing wave energy is a promising method to provide sustainable energy for ocean robots, despite that the existed wave energy converters (WECs) designed for ocean robots have limited power generation capacity. In this paper, we propose a deployable WEC for ocean robots to increase the wave energy capture performance in power generation mode and reduce the drag force in motion mode. The structure design and the power generation principle of deployable WEC are firstly introduced. Then, we establish the frequency domain and time domain dynamics models of wave energy harvesting. After that, a simulation platform based on the time-domain model is established to reveal the influence of wave amplitude, wave period, generator damping and the location of robot center of gravity (COG) on the dynamic response characteristics and wave energy capture performance. The results show that the highest capture width ratio of WEC can reach about 0.5 under the excitation of regular wave (T = 1.6 s, A = 0.02 m). The WEC proposed in this paper uses the deployable mechanism for on-board wave energy generation and overcomes the constraint of the size of the ocean robot on the power generation performance of WEC, which provides a new solution to the energy supply problem of ocean robots in the future.

Improving Computational Efficiency in WEC Design: Spectral-Domain Modelling in Techno-Economic Optimization

Wave energy converter (WEC) optimization often underlines incremental and iterative approaches that result in suboptimal solutions, since all the elements that concur with a techno-economical evaluation are optimized separately due to computation constraints. A design process should rely on precise WEC models to ensure high result accuracy while minimizing the computational demand. These conflicting objectives can be addressed with non-linear time-domain models, known to be numerically accurate, and frequency-domain models due to their high computational efficiency. This work pursues the development of an all-encompassing optimization tool for a gyroscopic-type WEC called ISWEC that applies a new modelling technique named spectral-domain technique as a substitution to the complex time-domain model previously employed. In particular, the spectral-domain technique provides accurate and fast performance predictions of the ISWEC system and offers the possibility to model a hydraulic power take-off, not representable in the frequency domain. The article illustrates techno-economic trends associated with an early-stage design of the ISWEC in high-energy sea-sites, where the low-speed and high-torque profiles call for the use of hydraulic transmissions as opposed to the old electro-mechanical transmissions. The design tool proposed could facilitate the development of WEC technologies via efficient and accurate power assessment and via the possibility of carrying out advanced techno-economic optimisation that goes beyond linear models.

Validated analytical model for a cyclorotor wave energy device

We present a new analytical model for a horizontal axis cyclorotor-based wave energy converter (WEC). A number of cyclorotor-based WEC concepts and models, with different numbers of hydrofoils, have previously been studied. Our model is derived for a horizontal cyclorotor with 2 hydrofoils. The governing equations are optimised and converted to the polar coordinate system. The mechanical model is based on Newton's second law for rotation. Rotation is considered in two-dimensional potential flow, for both monochromatic and panchromatic waves, including waves generated by the rotating rotor, and viscous losses. The developed model is very convenient for modelling, analysis and control design for a cyclorotor based WEC.
 The authors of this work have derived new, exact, analytic functions for the free surface perturbation and induced fluid velocity field caused by hydrofoil rotation. These new formulae significantly decrease the model calculation time, compared to previous models, and increase the accuracy of the results. We present the results of free rotation simulations for the rotor in monochromatic and panchromatic waves obtained with the use of the newly derived equations.

Deep reinforcement learning based coastal seawater desalination via a pitching paddle wave energy converter

Wave energy has the potential to become a significant contributor to the future seawater desalination thanks to its high-power density. However, the intermittent characteristics of wave energy are the main issues to be overcome in the seawater desalination process. In this paper, a spiral wave energy converter (WEC) powered desalination system is proposed by utilizing a bottom flanged pitching spiral pump based WEC to directly convert the pressurized seawater into freshwater. The dynamic model of the spiral WEC powered desalination system is established. In order to mitigate the uncertainties and fluctuations in the fresh water supply, a deep reinforcement learning (DRL) control of the WEC is also designed for smoothing freshwater production, and a prioritized experience replay mechanism is employed for improving training efficiency. The test results indicate that the freshwater flowrate can be maintained at the desired value of 1200 m3/day by using the trained DRL control and the DRL training process converges to the stable value of around −18.

A Review of the Linear Generator Type of Wave Energy Converters’ Power Take-Off Systems

The traditional wave energy converters (WECs) use hydraulic or turbine-type power take-off (PTO) mechanisms which consist of many moving parts, creating mechanical complexity and increasing the installation and maintenance costs. Linear generator-based direct-drive WECs could be a solution to overcome this problem, but the efficiency of the single conventional linear generator is not high enough, and it cannot work satisfactorily in the low-frequency range. This article reviews the recent research developments of the linear permanent magnet (PM) generator-based WEC to harness maximum energy from ocean waves. It starts with a brief introduction and background of wave energy converters using linear generators. Following this, the working principle of the WECs with linear PM generators is briefly outlined. Subsequently, the analytical model of the linear PM generator-based WEC is studied. After that, the up-to-date developments of the linear PM generator-based PTO systems are studied. Despite some modifications resulting in complexity in the linear PM generator’s structure and a rise in manufacturing costs, the study shows the systems’ efficiencies increased by increasing magnetic flux and reducing cogging force. The key parameters and improvement issues that can increase the performances and efficiencies of the PTO systems are identified to help future researchers for further development. Moreover, the review discusses the numerical and experimental analysis tools, the typical control systems used by the researchers and the challenges of the linear generator-based wave energy conversion system. Finally, conclusions about the significant beneficial characteristics and design choice of the WEC linear generator structure are provided and related to the application conditions.

A Multi-Filter Based Dynamic Power Sharing Control for a Hybrid Energy Storage System Integrated to a Wave Energy Converter for Output Power Smoothing

The output power fluctuations from the wave energy converters (WECs) with a high peak-to-average ratio need to be smoothed out before supplying power to electric loads or power grids. Usually, short-term energy storage is used to smooth out the output power fluctuations of WECs. In this article, a novel multi-filter-based dynamic power-sharing control is devised for a hybrid energy storage system (HESS) integrated with a grid-connected WEC. An advanced model of HESS-integrated WEC consisting of a direct-drive permanent magnet linear generator, a supercapacitor, and a battery system is developed to test the proposed multi-filter-based dynamic control strategy under realistic conditions. The distinguishing features of this study are as follows; 1) the power-sharing strategy is based on a dynamic filter that is designed to change its corner frequency depending upon the incoming ocean wave, 2) the low and the high-frequency power components are allocated based on ocean wave conditions, 3) the proposed strategy is suitable for the real-time control of the proposed HESS integrated with the WEC, and 4) a detailed model of the WEC is used instead of using a pre-saved power profile. The results suggest that with the implementation of the proposed multi-filter-based dynamic power-sharing scheme in the HESS integrated WECs, the output power can be effectively smoothed out before supplying the power to the grid.

A Detailed Investigation Into the Wave Energy Resource at a Small-Scale Ocean Energy Test Site in China

During the R&D of marine renewable energy converters, scale models are usually used in the early stages of development of marine renewable energy converters. China’s National Ocean Integrated Test Site (NOITS) is being developed by the National Ocean Technology Center (NOTC) in Weihai, Shandong Province, to facilitate testing of scaled wave and tidal energy converters in an open sea environment. This research aims to gain a detailed understanding of the wave characteristics and the wave energy resource at this site. A nested modeling system has been implemented using Simulating WAves Nearshore (SWAN) to provide a 10-year high-resolution wave hindcast between 2009 and 2019 with an approximately 60 m resolution covering the test site. Analysis of the spatio-temporal distribution of wave energy resource in NOITS reveals its strong seasonality, with the mean wave power density of >1.5 kW/m during winter and <0.2 kW/m during summer. We also performed a statistical analysis of the high and extreme wave conditions and their occurrence. By applying scaling methods to wave resources, four WECs were selected to demonstrate the testing at different scale ratios in NOITS. The results of this study provide engineering references for the design of scale wave energy converter models which target to perform open sea trials in NOITS.

Data-Driven Model Predictive Control for Wave Energy Converters Using Gaussian Process

The energy harvested by an ocean wave energy converter (WEC) can be enhanced by a well-designed wave-by-wave control strategy. One of such superior control methods is model predictive control (MPC), which is a nonlinear constrained optimization control strategy. A limitation of the classical MPC algorithm is its requirement of an accurate WEC dynamic model for real-time implementation. This article overcomes this challenge by proposing a data-driven MPC scheme for wave energy converters. The data-based WEC model is developed by a Gaussian process (encompassing mean predictions and symmetric uncertainties) for a more accurate description of nonlinear and unmodeled system dynamics. A cross-entropy solver for data-driven MPC is employed for rapid, high-performance results, which samples trajectories from Gaussian distributions based on the concept of the symmetry principle. The proposed strategy is verified numerically by simulations which demonstrate its superior performance over a classical complex-conjugate controller.

Effect of mooring mode and internal mass block layout on eccentric rotating wave energy converter model

Reliability and energy conversion ability are the most concerned performance indexes of Wave Energy Converter Eccentric Rotating Wave Energy Converter (ERWEC) with closed shell can protect energy conversion unit away from seawater, which has shown excellent reliability. However, energy conversion ability of Eccentric Rotating Wave Energy Converter is poor and the method to improve performance of ERWEC is still not clear. The objective of this work is to improve mooring security, motion attitude stability and energy conversion ability of ERWEC. In this paper, experimental model of ERWEC was developed, and energy conversion mechanism was clarified. Experiments on various mooring modes and various internal mass block layouts were carried out. Besides, breaking coefficient, instability coefficient and energy conversion coefficient were calculated to evaluate performance of ERWEC. The result showed that the effect of mooring mode on mooring security, motion attitude stability and energy conversion ability was coupled to the effect of internal mass block layout on those three indexes. Furthermore, under determined mooring mode condition, internal mass block layout was optimized by multi-objective genetic algorithm. This paper provides basis for conceptual design of mooring mode and real-time control of mass block layout to achieve better mooring security, motion attitude stability and energy conversion ability of ERWEC.

A Hybrid Multiobjective Optimization Based on Nondominated Sorting and Crowding Distance, with Applications to Wave Energy Converters

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) has attracted a lot of attention since it can handle multiobjective problems (MOP) with a complicated Pareto front. The procedure involves decomposing a MOP into single subproblems, which are eventually optimized simultaneously based on the MOP neighborhood information. However, the MOEA/D strategy tends to produce a distributed optimization that is not of good quality in some problems with complex Pareto optimal front, such as problems with a long tail and sharp peak, common in real-world situations. This paper proposes an improved MOEA/D to enhance the distributed optimization quality and minimize its complexity while accelerating the optimization to get a better solution. The improved method is achieved by incorporating a Hybrid Differential Evolution/Particle Swarm Optimization algorithm and a hybrid operator based on nondominated sorting and crowding distance algorithm. This incorporation takes place in the mutation generator and initial population part of the original MOEA/D algorithm. Simulations and comparisons are carried out based on some MOP benchmark functions to verify the proposed method’s performance. The experimental results show that the proposed method achieves better performance compared to other algorithms. Furthermore, the proposed method is also applied to optimize the multiobjective wave energy converter model to maximize power per year and minimize cost per unit power.

Research on Energy-Capture Characteristics of a Direct-Drive Wave-Energy Converter Based on Parallel Mechanism

Aiming at the capture and conversion of multidirection wave energy, a multifreedom direct-drive wave-energy converter (WEC) based on a parallel mechanism is studied. The dynamic model of WEC was conducted based on force analysis and hydrodynamic theory, and the inverse kinematic solutions of each branch chain of the mechanism were obtained following the space vector method. Furthermore, the kinetics response of the linear generator branch chain was obtained. Moreover, the influence on the capture efficiency of the device’s geometric structure scale was investigated under different sea conditions. To evaluate the performance of the WEC, a linear generator model was simulated and analyzed by COMSOL Multiphysics. A laboratory prototype was manufactured. The test results indicated that the multifreedom device can achieve better power conversion performance than traditional single degree of freedom (DOF) devices. This study provides ideas for the design and development of large multi-DOF wave-energy-conversion devices.