Point Absorber Research Articles

Analysis on Evaluations of Monterey Bay Aquarium Research Institute’s Wave Energy Converter’s Field Data Using WEC-Sim and Gazebo: A Simulation Tool Comparison

Although many studies have validated wave energy converter (WEC) numerical models against scaled prototype experimental data, there remains a notable lack of validation using data from full-scale deployed WECs. This paper compares two numerical models of Monterey Bay Aquarium Research Institute’s Wave Energy Converter (MBARI-WEC), a two-body point absorber with an electro-hydraulic power take-off system (PTO). The models are implemented in WEC-Sim/Simscape and Gazebo Simulator. A statistical analysis of the models was performed, and field results were obtained to compare the models’ accuracy in predicting the RMS piston velocity, RMS motor speed, and mean electric power compared to field data for 56 observations across varying sea states. The Gazebo model demonstrated a closer agreement across all three parameters for a majority of the observations. When compared to the field data, the Gazebo and WEC-Sim models exhibited average mean electric power overestimations of 13% and 22%, respectively.

Optimal Control of Nonlinear, Nonautonomous, Energy Harvesting Systems Applied to Point Absorber Wave Energy Converters

Pursuing sustainable energy solutions has prompted researchers to focus on optimizing energy extraction from renewable sources. Control laws that optimize energy extraction require accurate modeling, often resulting in time-varying, nonlinear differential equations. An energy-maximizing optimal control law is derived for time-varying, nonlinear, second-order, energy harvesting systems. We demonstrate that sustaining periodic motion under this control law when subjected to periodic disturbances necessitates identifying appropriate initial conditions, inducing the system to follow a limit cycle. The general optimal solution is applied to two point absorber wave energy converter models: a linear model where the analytical derivation of initial conditions suffices and a nonlinear model demanding a numerical approach. A stable limit cycle is obtained for the latter when the initial conditions lie within an ellipse centered at the origin of the phase plane. This work advances energy-maximizing optimal control solutions for nonautonomous nonlinear systems with application to point absorbers. The results also shed light on the significance of initial conditions in achieving physically realizable periodic motion for periodic energy harvesting systems.

Life cycle environmental impact assessment of the “Sindhuja-I” wave energy converter

The life cycle assessment (LCA) is an inevitable part of ocean wave energy systems. This paper presents an LCA of the Sindhuja-I ocean wave energy converter (WEC). The WEC is a point absorber type WEC tested at the Tuticorin port in India. This study utilized the ISO 14044 standard and SimaPro LCA software to assess the environmental impact of the WEC in comparison to a coal power plant, offshore wind, and tidal energy devices. The functional unit considered is the generation of 1 kWh of electricity. The WEC has a global warming potential of 174 gCO2-eq/kWh, showcasing an impressive 81.9% reduction in emissions compared to coal power plants. Stainless steel contributes significantly to emissions, accounting for 93.7%, 94.6%, 99.4%, and 94.1% of total CO2, NOx, SO2, and PM2.5 emissions, respectively. The paper emphasizes the potential environmental benefits of recycling WEC materials at the end of their lifespan. Furthermore, the study suggests that the longevity of a point absorber device can positively impact its overall environmental footprint, given its minimal moving parts and low maintenance requirements. The WEC has a promising environmental footprint of ocean wave energy conversion, particularly compared to traditional fossil fuel-based power generation.

Wave-to-wire modelling and hydraulic PTO optimization of a dense point absorber WEC array

We investigate the hydrodynamic interactions and power extraction efficiency of a dense array of Point Absorber (PA) Wave Energy Converters (WECs) clustered around the fixed pillar of a wind turbine –the Ocean Grazer device– with a standard hydraulic Power Take-Off (PTO) system. Using potential flow theory, a detailed wave-to-wire model is developed in WEC-Sim with four distinct hydraulic PTO designs: i) Multi PTO-with individual hydraulic PTO systems for each buoy, ii) Shared PTO V1-with a unified PTO system for the entire array, iii) Shared PTO V2-with the accumulator volume split into two segments, and iv) Shared PTO V3-with four strategically distributed segments. Key parameters such as the diameter of the hydraulic pistons, volume and pre-charged pressure of the high-pressure accumulators, hydraulic motor displacement and the speed of the electric generator are optimized with a genetic algorithm and a parametric analysis across various sea states. The results highlight that strategically allocating the accumulators across the floaters of a dense WEC array can yield significantly higher power production and should be considered at the early design stages.

Nonlinear Model Predictive Control of Heaving Wave Energy Converter with Nonlinear Froude–Krylov Forces

Wave energy holds significant promise as a renewable energy source due to the consistent and predictable nature of ocean waves. However, optimizing wave energy devices is essential for achieving competitive viability in the energy market. This paper presents the application of a nonlinear model predictive controller (MPC) to enhance the energy extraction of a heaving point absorber. The wave energy converter (WEC) model accounts for the nonlinear dynamics and static Froude–Krylov forces, which are essential in accurately representing the system’s behavior. The nonlinear MPC is tested under irregular wave conditions within the power production region, where constraints on displacement and the power take-off (PTO) force are enforced to ensure the WEC’s safety while maximizing energy absorption. A comparison is made with a linear MPC, which uses a linear approximation of the Froude–Krylov forces. The study comprehensively compares power performance and computational costs between the linear and nonlinear MPC approaches. Both MPC variants determine the optimal PTO force to maximize energy absorption, utilizing (1) a linear WEC model (LMPC) for state predictions and (2) a nonlinear model (NLMPC) incorporating exact Froude–Krylov forces. Additionally, the study analyzes four controller configurations, varying the MPC prediction horizon and re-optimization time. The results indicate that, in general, the NLMPC achieves higher energy absorption than the LMPC. The nonlinear model also better adheres to system constraints, with the linear model showing some displacement violations. This paper further discusses the computational load and power generation implications of adjusting the prediction horizon and re-optimization time parameters in the NLMPC.

Experimental Implementation of Reinforcement Learning Applied to Maximise Energy from a Wave Energy Converter

Wave energy has the potential to provide a sustainable solution for global energy demands, particularly in coastal regions. This study explores the use of reinforcement learning (RL), specifically the Q-learning algorithm, to optimise the energy extraction capabilities of a wave energy converter (WEC) using a single-body point absorber with resistive control. Experimental validation demonstrated that Q-learning effectively optimises the power take-off (PTO) damping coefficient, leading to an energy output that closely aligns with theoretical predictions. The stability observed after approximately 40 episodes highlights the capability of Q-learning for real-time optimisation, even under irregular wave conditions. The results also showed an improvement in efficiency of 12% for the theoretical case and 11.3% for the experimental case from the initial to the optimised state, underscoring the effectiveness of the RL strategy. The simplicity of the resistive control strategy makes it a viable solution for practical engineering applications, reducing the complexity and cost of deployment. This study provides a significant step towards bridging the gap between the theoretical modelling and experimental implementation of RL-based WEC systems, contributing to the advancement of sustainable ocean energy technologies.

Design Optimization of a Point Absorber and Hydraulic Power Take-Off Unit for Wave Energy Converter

Design Optimization of a Point Absorber and Hydraulic Power Take-Off Unit for Wave Energy Converter

Comparative evaluation of floating OWC and BBDB wave energy converters by regular and irregular waves using numerical approach

ABSTRACT Point absorber wave energy converters (WECs) need to be predicted in order to estimate their durability in high sea states. Although little is known about hydrodynamics and there are few data available. Models of the wave conditions have been developed at the laboratory size using smooth particle hydrodynamics. To investigate how focused waves interact with a point absorber WEC, fixed OWC and BBDB type WEC are coupled. A validation research is evaluated by taking into account the wave amplitude and frequency. The hydrodynamic force and the motion response of the point absorber WEC have been measured throughout time. According to the numerical results, the hybrid configuration with the fixed OWC and BBDB has a significant impact on the motion response and hydrodynamic force. It is demonstrated that the position of hybrid OWCs affects the hydrodynamic force and intense motion response significantly.

Failure Consequence Cost Analysis of Wave Energy Converters—Component Failures, Site Impacts, and Maintenance Interval Scenarios

In the early stages of developing wave energy converter (WEC) projects, a quantitative assessment of component failure consequence costs is essential. The WEC types, deployment site features, and accessibility should all be carefully considered. This study introduces an operation and maintenance failure consequence cost (O&M-FC) model, distinct from conventional O&M models. The model is illustrated with case studies at three energetic Atlantic sites, each of which considers two types of generic floating WECs: a 300 kW point absorber (PA) with a hydraulic power-take-off (PTO) and a 1000 kW oscillating water column (OWC) with an air-wells-turbine PTO. This study compares 39 failure modes for PA and 27 for OWC in terms of direct repair costs and indirect lost production costs, examining the impact of location accessibility, capacity factors, and the mean annual energy production. The discussion revolves around the sensitive parameters. Recommendations for failure mitigations are presented, and the impact of planned maintenance (PM) during the operational phase is examined for 20 MW PA and OWC WEC projects. For a given WEC type, the method thoroughly evaluates how the location affects performance metrics. It offers a decision-making tool for determining optimal PM intervals to meet targets such as O&M costs, operating profit, or availability.

Impact of translator mass and buoy choice on a power absorption of point absorbing wave energy converter linear generator with linear generator power take off

AbstractOcean waves have the potential to contribute to future renewable electricity production. A wave energy converter (WEC) is a technology developed to absorb the energy of the wave and convert it to another form of energy. The Uppsala University WEC (UU WEC) is a point absorber with a direct drive permanent magnet synchronous linear generator power take off. Among other parameters affecting the value of absorbed power for UU WEC are the buoy size, mass of the system consisting of the buoy and translator, and available wave energy at the site of interest. This study reviews the earlier static model that considered only static forces as the buoyancy and gravity forces and neglected all dynamic forces. The static model was proposed to simplify the early‐stage design decision. Although the static model was applied to two UU WECs of different dimensions, the present study shows that the static model is not held for certain buoy and translator dimensions. As an alternative, the dynamic model which accounts for the impact of hydrodynamic forces and various translator masses is proposed. The dynamic model is based on Cummins' equation and the linear potential flow theory, and the damping force is approximated as a viscous damper with the constant damping coefficient optimizing the absorbed mechanical power under a particular sea condition. The dynamic model is applied to four fixed buoy geometries of two shapes (cylinder and cylinder with a moonpool), each of two different dimensions, but the method can be extended to other buoy shapes and dimensions. In addition, the impact of translator mass was assessed for two sites located on the west coast of Sweden and near Gran Canaria, Spain. A translator of 10–11 t promotes 16.8% higher annual average power absorption for a cylindrical buoy compared to a translator of 6 t for the same buoy. However, heavier translators up to 15 t provide only 1.1% increase in average annual absorbed power.

Nonlinear modelling of arrays of submerged wave energy converters

Studies of arrays of wave energy converters (WECs) with respect to power absorption and array interactions are often performed using linear models. However, nonlinear effects can be important and may change power estimates and optimal array designs. In this study, we have compared linear predictions of the behaviour of a shallowly submerged, buoyant point absorber with predictions from the nonlinear model SWASH with a WEC incorporated (WEC-SWASH). The latter was first comprehensively validated against 1:20 Froude scaled measured data from physical experiments. WEC-SWASH predictions of body motions and mean power absorption were generally in good agreement with measurements (absolute bias within 25%), although some discrepancies were observed in the body motions, especially when the device exhibited motion instabilities. The validated WEC-SWASH model was then compared with a linear frequency-domain model, as the latter is well-known and widely used because of its computational efficiency. Model comparisons were carried out for both an isolated WEC and small arrays (up to 5 devices). The mean power estimates from the linear model and WEC-SWASH for two representative wave farms showed good agreement for mild waves, with a difference of less than 5%. However, for larger waves, the disagreement increased to about 75 to 85% between the models (for the two wave farms tested). We found that array interactions for these arrays depend on wave amplitude and not just wave frequency. Furthermore, we discovered that the power take-off coefficients optimized using the linear model were not the optimum coefficients for the nonlinear model (WEC-SWASH).

Harnessing Vietnam's coastal potential: Prioritizing marine energy technologies with an objectively weighting decision-making approach

Vietnam's potential to harness marine energy for sustainable development is significant due to its long coastline, yet this potential remains underutilized as current renewable energy efforts focus mainly on wind and solar power. This study addressed the challenge of selecting optimal Marine Energy Technologies (METs) for Vietnam's specific environmental and socio-economic context. A streamlined methodology, integrating the Method based on the Removal Effects of Criteria (MEREC) and the Spherical Fuzzy Combined Compromise Solution (SF CoCoSo) methods, facilitated a multi-criteria analysis that distilled expert opinions into a decision-making framework. The study identified Point Absorbers (PAB) as the most promising MET for Vietnam, with Overtopping Devices (OTD) and Salinity Gradient Power (SGP) also ranking well based on key factors like readiness and cost. This study introduces a methodology that, with a more comprehensive data set including various marine energy technologies, could provide valuable insights for decision-makers in Vietnam's marine energy sector.

Experimental and numerical investigation of breakwater-integrated heaving point absorber device under irregular waves

Integrating wave energy devices with coastal structures is a promising solution to reduce the cost of wave energy development along with additional shared benefits. In this study, the performance of a heaving spherical point absorber wave energy converter model in irregular waves is analysed and compared experimentally and numerically. After the fundamental investigation of models in regular waves, it is important to advance the testing in more realistic conditions before the sea trial phase. The investigations are conducted in irregular waves on a 1:30 scale model under two scenarios, (1) model heaving alone and (2) model heaving in a chambered breakwater. Irregular waves are generated based on the JONSWAP spectrum with modified parameters to suit the Indian coastal conditions. Results indicate that the wave energy converter model in the chambered breakwater produces 40.25 % higher power than the model heaving alone in irregular sea conditions. The performance of the model is found to be less compared to that in regular waves.

The role of size and inertia on the hydrodynamics of a self-reacting heave single point absorber wave energy converter

We propose a detailed numerical study of a self-reacting floating point absorber, resembling the Ocean Power Technologies device PB3 PowerBuoy, for a possible installation in the Adriatic Sea. A simplified model of the mentioned device, composed of a floater sliding along a reacting body, which supports the floater, is studied, reproducing and analysing the most complex nonlinear phenomena, such as the wave overtopping and the out-of-water motion of the floater. Three different sizes of the device have been simulated, each with three different masses of the floater, deriving the time evolution of the wave in the surrounding of the floater, its frequency dispersion and energy content, the generated exciting force, the wave overtopping over the floater, and the out-of-water motion of the floater. The results highlight that the linear response is favoured by small floater density and optimal floater thickness. Additionally, large-sized devices are characterized by linear, but dissipative, response, while the response of medium-sized devices is only apparently linear.

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.

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.

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 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.