Wave Energy Device Research Articles

Fully Coupled Analysis of a 10 MW Floating Wind Turbine Integrated with Multiple Wave Energy Converters for Joint Wind and Wave Utilization

The study focuses on a semi-submersible wind-wave integrated power-generation platform, which consists of an OO-Star semi-submersible platform equipped with a DTU 10 MW wind turbine and a set of wave energy converters. A hydrodynamic model was established using ANSYS-AQWA (2023 R1), and by incorporating upper wind loads and utilizing the open-source program F2A, a fully coupled time-domain model of the integrated power-generation platform was constructed. The primary objective is to explore the interaction mechanisms between the upper wind turbine and the lower wave energy devices under the combined effects of irregular waves and turbulent wind through a series of operational conditions. Additionally, the safety of the mooring system was assessed. The results indicate that, compared to the wave period, the power generation of the lower wave energy devices is more significantly affected by wave height. Overall, the integrated power-generation platform demonstrates optimal performance under the third operational condition. In survival conditions, the introduction of oscillating buoys can improve the motion responses of the platform in terms of sway, roll, pitch, and yaw to a certain extent, but it also increases the surge and heave motion responses and the associated mooring loads. The mooring system can ensure the safety of the integrated power-generation platform under extreme sea conditions.

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.

Performance analysis of a novel hybrid device with floating breakwater and wave energy converter integrated

As a kind of clean energy, wave energy has attracted increasing attention in recent years. However, due to its high cost and low efficiency, wave energy has not been widely commercialized worldwide. According to previous research works, the combination of wave energy devices and floating breakwaters can reduce the cost of wave power generation devices efficiently. In this paper, a hybrid device with wave energy converter (WEC) and flexible porous floating breakwater integrated is proposed. The hydrodynamic performance of this device is studied by numerical simulation based on Reynolds-Averaged Navier–Stokes (RANS) method which has been validated through experimental results. Based on this, a series of numerical simulations are performed under different power take-off stiffness (KPTO) and different power take-off damping coefficient (CPTO) to calculate the motion and transmission coefficient of the device. By comparing the numerical results, the influence of KPTO and CPTO of the hybrid device on its wave attenuation performance and energy conversion efficiency are analyzed. The results indicate that under the incident waves of period 0.56 s and 0.89 s, the recommended value of KPTO is 3.0 N/m and 0.5 N/m respectively. While for incident waves of period 0.56s, in order to achieve better wave attenuation performance and power generation efficiency, the recommended value of CPTO should be between 10.55 Ns/m and 14.23 Ns/m. On this basis, the influence of the size of breakwater on the wave attenuation performance and power generation efficiency of the hybrid device is also discussed. Moreover, through a cost analysis, it can be inferred that the utilization of the baseline model is more economically viable.

Characteristics of wave loading and viscous energy loss of a bottom-sitting U-OWC wave energy device: A validated numerical perspective

This study involves numerical simulations of regular waves interacting with a bottom-sitting circular OWC wave energy converter with a U-shaped duct (circular U-OWC). A numerical wave tank is built based on the RANS equation and is validated against experiments. The effect of water depth and the height of the outer tube of the U-shaped duct on capture efficiency, wave loading, and viscous energy loss is investigated numerically. Results show that the height of the outer tube of the U-shaped duct has a significant effect on the capture efficiency of the device. Wave loading analysis reveals a critical mode of stability that may threaten the operation safety of the device. It is found that increasing the height of the U-shaped duct opening increases the viscous energy loss inside the U-shaped duct. A semi-theoretical model between work done by waves to the device and the viscous energy loss in the U-shaped duct is established, numerical data indicates that a significant amount of work done by waves to the device is lost in viscous effects. This suggests that certain optimization for reducing wave loading could possibly also reduce viscous energy loss, thus improving the overall efficiency of the device.

Wave energy converter with multiple degrees of freedom for sustainable repurposing of decommissioned offshore platforms: An experimental study

Targeting at the sustainable repurposing of decommissioned offshore platforms, a novel wave energy converter with a distinct mechanical-motion-rectifier power take-off system is developed to provide renewable energy. A scaled prototype is constructed and experimentally investigated in a large wave tank, as an essential step before sea trials. A new phenomenon of parametric oscillation is observed and explored, as physical evidence of chaotic instabilities of wave energy devices. Several advantages of the multi-degree-of-freedom device over its single-degree-of-freedom counterpart are disclosed physically for the first time. Releasing the pitch and roll degrees of freedom helps enlarge the heave amplitude of the energy-absorbing buoy, receive a larger hydrodynamic force from water waves to the power take-off system, reduce structural deflection and friction of the transmission machinery, and eliminate spiky and noisy vibrations of the internal force. Accordingly, the maximum efficiencies in the energy absorption and transmission stages increase from 45% and 11% to 90% and 30%, respectively; the overall efficiency of energy conversion is increased by up to three times in a broad spectrum of wave conditions.

Numerical Simulation Method of Hydraulic Power Take-Off of Point-Absorbing Wave Energy Device Based on Simulink

Wave energy has a high energy density and strong predictability, presenting encouraging prospects for development. So far, there are dozens of different wave energy devices (WECs), but the mechanism that ultimately converts wave energy into electrical energy in these devices has always been the focus of research by scholars from various countries. The energy conversion mechanism in wave energy devices is called PTO (power take-off). According to different working principles, PTOs can be classified into the linear motor type, hydraulic type, and mechanical type. Hydraulic PTOs are characterized by their high efficiency, low cost, and simple installation. They are widely used in the energy conversion links of various wave energy devices. However, apart from experimental methods, there is currently almost no concise numerical method to predict and evaluate the power generation performance of hydraulic PTO. Therefore, based on the working principle of hydraulic PTO, this paper proposes a numerical method to simulate the performance of a hydraulic PTO using MATLAB(2018b) Simulink®. Using a point-absorption wave energy device as a carrier, a float hydraulic system power-generation numerical model is built. The method is validated by comparison with previous experimental results. The predicted power generation and conversion efficiency of the point-absorption wave energy device under different regular and irregular wave conditions are compared. Key factors affecting the power generation performance of the device were investigated, providing insight for the subsequent optimal design of the device, which is of great significance to the development and utilization of wave energy resources.

Multi-phase SPH-FDM and experimental investigations on the hydrodynamics of an oscillating water column wave energy device

In this paper, the hydrodynamic performance of a bottom-seated type oscillating water column (OWC) device is investigated by numerical and experimental methods. A coupled SPH (Smoothed Particle Hydrodynamics) - FDM (Finite Difference Method) is proposed to simulate the interaction between waves and the OWC device. The current SPH-FDM model improves grid encryption method, and expand the single-phase SPH-FDM to multiphase SPH-FDM. The results from SPH-FDM align closely with those from the published experimental measurements. Following the successful validations, SPH-FDM and experiment are employed for a series of simulations to investigate the performance of the OWC device. Compared to experimental method, SPH-FDM can obtain global flow field information and avoid the influence of free surface identification and capillarity on vortex determination. In addition, SPH-FDM can naturally captures free surfaces, so it supports further studies on the non-uniformity of water surface in the chamber of OWC which cannot be studied by PIV or pneumatic model.

Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians

This paper presents a generalized and efficient method for quasi-static analysis of mooring systems, including complex scenarios such as when shared mooring lines interconnect multiple floating wind or wave energy devices. While quasi-static mooring models are well established, most published formulations are focused on specific applications, and no publicly available implementations provide efficient handling of large mooring system networks. The present formulation addresses these gaps by: (1) formulating solutions for edge cases not typically supported by quasi-static models; (2) creating a fully generalized model structure such that any combination of mooring lines, point masses, and floating bodies can be assembled; and (3) deriving analytic expressions for the system Jacobians (stiffness matrices) so that systems with many degrees of freedom can be solved efficiently. These techniques form the theory basis of MoorPy, an open-source mooring analysis library. The model is demonstrated on nine scenarios of increasing complexity with features of interest for offshore renewable energy applications. When compared with steady-state results from a lumped-mass dynamic model, the results show that the quasi-static formulation accurately calculates profiles and tensions and that its analytic approach provides more efficient and reliable computation of system stiffness matrices than finite-differencing methods. These results verify the accuracy of the MoorPy model.

The study on the force analysis model of wave energy devices in heaving and pitching motion

The study on the force analysis model of wave energy devices in heaving and pitching motion

Evaluating the economic viability of near-future wave energy development along the Galician coast using LCoE analysis for multiple wave energy devices

The economic profitability of future wave energy production along the Galician coast is assessed by analyzing the Levelized Cost of Energy (LCoE) under different Capital Expenditure (CapEx) scenarios and two discounts rates (5% and 10%). Wave resources for the near future under the RCP8.5 scenario are downscaled using SWAN, providing up to 75 m spatial resolution in coastal areas. The study’s goal is to enhance the cost-effectiveness by selecting the most suitable wave energy converter (WEC) for each location. Fourteen WECs operating at different depths are considered. This analysis reveals that the Atargis device boasts the lowest LCoE for 64.2% of the coastal area, mainly in deep waters, with an LCoE of 77 €/MWh. In addition, the Oyster and Wave Dragon devices exhibit the lowest LCoE for 12.4% and 15.0% of the coastal area, respectively, excelling in shallow waters and near the coast, with values of 50 €/MWh and 97 €/MWh. These findings demonstrate the profitability of wave energy production along the Galician coast, even when considering a more conservative CapEx of 3 M€/MW, resulting in a cost of 140 €/MWh. This conclusion takes into account the evolving electricity prices in Spain, which reached 0.2068 €/kWh in the second half of 2023.

The study on the force analysis model of wave energy devices in heaving motion

The study on the force analysis model of wave energy devices in heaving motion

Analysis of Hydrodynamic Loads by a Vertical Hollow Cylindrical Structure in A Two-Layer Fluid of Finite Depth

This paper aims to study the effect of surge radiation by a vertically hollow cylinder floating in a two-layer fluid of finite depth. Since most of the important characteristics of the oscillating water column are preserved by the hollow cylindrical structure, so the proposed device can be considered as an oscillating water column (OWC) which is one of the important wave energy device. In this two-layer fluid system, the upper layer is bounded above by a free surface and the lower layer is bounded below by a solid impermeable bottom, and the submerged hollow cylindrical structure allows it to oscillate in a surge mode of motion in the upper layer. On the assumption that wave amplitudes are small in comparison to wavelengths, hence the linear water wave theory is applied to formulate boundary value problems by dividing whole domain into 2 sub-domains. The formulated boundary value problems for surge radiated potentials in each sub-domain; we execute to obtain solutions in each sub-domain by using variable separation and matched eigenfunction expansion methods. With the help of obtained surge radiated potentials, we derive the radiation forces by the device in terms of added mass and damping coefficients. A set of influences of different parameters of the device on the added mass and damping coefficients are demonstrated in both surface and internal wave modes of motion. Hydrodynamic coefficients oscillate highly near a particular frequency, which leads to the resonance phenomena. In addition to that, the 3D plots of the free surface elevation in surface and internal wave modes are presented. A density ratio γ = 0.97 has a higher oscillation than a density ratio γ = 0.93, 0.95. High oscillations occur around a particular frequency ω = 3.83 due to the resonance phenomenon in which the waves incoming match with the natural motion of the object. HIGHLIGHTS A floating hollow vertical cylindrical structure is considered in a two-layer fluid system having finite depth The separation of variables and matched eigenfunction expansion methods are utilized to obtain the solutions to the boundary-value problems The diffracted velocity potentials under the surge mode of motion are evaluated in the identified regions The added mass, damping coefficients, free surface and interface elevations in surface and internal wave modes are evaluated with different set of parameters of the device A number of results are presented regarding the effect of parameters of the device on the added mass, damping coefficients, free surface and interface elevations It is observed that the density ratio of the two-layer fluid has significant effect on the added mass, damping coefficient and the elevations GRAPHICAL ABSTRACT

On the spectral wave climate of the French Atlantic Ocean

The accurate description of wave climate at different spatio-temporal scales requires the application of advanced statistical models together with a good knowledge of geophysical processes. Furthermore, accurate modelling of multimodal sea states is of primary importance for most of offshore and coastal activities, such as wave energy device optimization, maritime design practice and for safety at sea. The present manuscript is conceived within this scientific framework proposing to assess wave climate of a complex area of French Atlantic Ocean bordering seas. The main “Spectral Climatology Types” of the area are identified as resulting of defined combinations of wave systems detected through directional spectra and partitioned wave systems analysis. The presence of swell systems is evaluated quantitatively on the whole area, characterized by different regimes of multimodal sea-states at strong regional variability and put into relation with main meteorological forcing active on the area at different spatial scales. Celtic Sea exhibits a marked regional characterization with a prevalence of multimodal conditions given by different combination of wave systems with increasing contribution of swell systems moving from North-West to South. A significant presence of crossing sea states is observed in South Celtic Sea especially in proximity of bathymetric slope. The South Bay of Biscay is influenced by fully developed swell systems enhanced by refraction effects caused by both the coastline and bathymetry gradients. English Channel and North Sea show complex sea-states conditions induced by local topography features together with wind channelling and tide effects able to trigger geophysical processes at a sub-scale responsible for the development of multimodal seas. Crossing and bimodal seas are also found to be influenced by bathymetry gradients acting directly on the directional spectrum shape as well as by tide due to tidal current-induced refraction effect on wave propagation. No generalized significant trends are detected within the investigated spatial domain for the wave spectrum integral quantities; locations sited at northern Celtic Sea show a downward Significant Wave Height, while only locations confined at eastern English Chanel only shows a Peak Period upward trend.

Calculation on maximum output power of wave energy-PTO system

The energy conversion efficiency of wave energy device is one of the key problems in the large-scale utilization of wave energy. The study of the maximum output POWER of PTO (Power-Take-Off) system provides a theoretical reference for the efficient utilization of energy. In this paper, genetic algorithm and adaptive differential evolution algorithm based on neighborhood search are used to optimize the two-objective multi-order differential equations for the maximum output power of PTO system, and the global optimal solution is obtained. Compared with the traversal algorithm, the algorithm involved in this paper is efficient and the optimal output power obtained can provide a scientific basis for the structural optimization design and material selection of the wave energy device.

Wave Energy Conversion through Oscillating Water Columns: A Review

An oscillating water column (OWC) is designed for the extraction and conversion of wave energy into usable electrical power, rather than being a standalone renewable energy source. This review paper presents a comprehensive analysis of the mathematical modeling approaches employed in OWC systems, aiming to provide an in-depth understanding of the underlying principles and challenges associated with this innovative technology. A prominent classification within the realm of wave energy devices comprises OWC systems, which exhibit either fixed or floating configurations. OWC devices constitute a significant proportion of the wave energy converter prototypes currently operational offshore. Within an OWC system, a hollow structure, either permanently fixed or floating, extends below the water’s surface, creating an enclosed chamber where air is captured over the submerged inner free surface. This comprehensive study offers a thorough assessment of OWC technology in conjunction with air turbines. Additionally, the investigation delves into theoretical, computational, and experimental modeling techniques employed for analyzing OWC converters. Moreover, this review scrutinizes theoretical, computational, and experimental modeling methodologies, providing a holistic understanding of OWC converters. Ultimately, this work contributes a thorough assessment of OWC technology’s current state, accentuating its potential for efficient wave energy extraction and suggesting future research avenues.

Dual‐Float‐Based Triboelectric Nanogenerator for Low‐Frequency Wave Energy Harvesting

Electromagnetic induction generator is not the best choice for collecting low frequency wave energy, since waves have the characteristics of low frequency and variable amplitude. In contrast, triboelectric nanogenerator (TENG) has an absolute advantage in collecting low‐frequency mechanical energy. Based on this, a dual‐float‐based triboelectric nanogenerator (DF‐TENG) for harvesting low‐frequency wave energy is proposed in this article. In this device, the TENG is mounted in the lower float, and its slider component is connected to the upper float by a cable. On the one hand, the motion of the slider is consistent with the relative motion of the dual floats, which is easy to analyze; on the other hand, the TENG is located in the lower float, which avoids damage to the TENG caused by extreme sea conditions. The physical model of the device was established, and the motion characteristics, electrical output characteristics, and its influencing factors of TENG were analyzed using finite element simulation software. The numerical calculations were verified by experimental tests. The calculated results show that the optimal matching resistance of the system is 500 MΩ. The research work in this article provides a research basis and reference for the development and application of such wave energy devices.

Multi‐Track Triboelectric Nanogenerator Toward Omnidirectional Ocean Wave Energy Harvesting

AbstractTriboelectric nanogenerators (TENGs) present a great potential approach for low‐frequency blue energy harvesting due to their unique advantages, however, omnidirectional wave energy harvesting remains challenging in complex marine environments. Herein, an omnidirectional multi‐track spherical structure TENG (OMS‐TENG) based on eight‐track fan type TENG (FTENG) is developed for harvesting low‐frequency ocean energy. The diameter and number of PTFE balls are optimized theoretically for boosting individual FTENG output and verified experimentally. The connection mode between different tracks and layers of OMS‐TENG is further investigated for efficient omnidirectional ocean energy harvesting. The motion parameters including translation and oscillation on electrical output performances of OMS‐TENG are systematically investigated and optimized. OMS‐TENG has proved to be an efficient device for harvesting omnidirectional wave energy with excellent stability and durability in complex marine environments. The maximum instantaneous power of 1270 µW can be obtained by individual OMS‐TENG. This work provides an effective approach toward omnidirectional ocean energy harvesting and important guidance for designing sustainable energy harvester.

Modification method and impact analysis of aerodynamic loads for fixed wind-wave hybrid devices

Aerodynamic load is one of the important loads that must be considered for wind-wave energy hybrid devices. In this study, the effects of blade angle and foundation structure vibration on aerodynamic loads are considered, and the traditional blade element momentum (BEM) is dynamically modified by the method of coordinate matrix transformation and vibration function analysis, starting from the relative inflow angle and the instantaneous wind speed of the wind turbine, and the aerodynamic loads of the wind turbine were simulated by using the improved BEM theory. The correctness of the proposed method in this study is verified by comparing the data of a large number of researchers and the computational results of OpenFast. A simulation study has been carried out using AQWA, combining the modified aerodynamic load of the wind turbine and the hydrodynamic load of the wave energy device, to analyze the variation trend of the base structure response of the wind-wave hybrid device under general and extreme conditions. The results show that the method developed in this paper can provide theoretical reference for the development and stable operation of wind-wave hybrid device.

Kinematic Characterization of Marine Wave Energy Devices Based on Immune Particle Swarm Algorithm

This paper explores the optimization of motion characteristics and energy output in an ocean wave energy device. The displacement and velocity of the device in pendant oscillatory motion are explored by simplifying the device model and simulating it using Simulink. Numerical methods are employed to solve the dynamics model. Subsequently, an optimization model for the average output power of the damper is developed based on this exploration. Both the grid search method and particle swarm algorithm are utilized to optimize the damping coefficients. These two methods are compared, revealing the particle swarm algorithm's superior efficiency.

Design an Optimum Air Duct for Oscillating Water Column Wave Energy Device

Oscillating Water Column (OWC) is a technology that harvests wave energy to generate electricity. It works by harnessing the wave-induced pressure oscillation in the opening mouth of OWC. The oscillation of the pressurised air is extracted using a turbine placed at the top of the OWC structure. Although OWC has been studied for many years, designing an optimum air duct for such devices is still an open research area. The air duct plays a crucial role in the energy conversion process, as it is responsible for directing the airflow towards the turbine, and its design can greatly affect the performance and efficiency of the system. The article aims to study how the air duct design impacts the power output form. Moreover, the result will be compared with the conventional air duct design. The OWC performance is analysed using Computational Fluid Dynamic (CFD) software to identify which shape of the air duct has high efficiency. Autodesk Inventor is used to design the OWC devices modified from the basis design. Then these designs are imported into CFD software to simulate and obtain the energy extraction result. The CFD software is chosen to simulate the hydrodynamics problem. In this study, the oval design shows significant improvement in the energy extraction performance compared to the basis design. The oval design managed to produce 9.81, 10.02, and 11.66 J/kg of mechanical energy compared to 9.81, 9.82, and 10.04J/kg as prompted by the basis air duct design at the wave height of 0.2505, 0.75, and 2.25m, respectively. The result shows that the non-edge produces higher air pressure than the sharp edge of the air duct shape. Thus, the oval air duct design is more efficient, and it may increase the performance of the OWC wave energy converter device at a low wave height of 0.75 m.