Two-body Wave Energy Converter Research Articles

Electric power prediction of a two-body hinge-barge wave energy converter using machine learning techniques

Investigating the electric power generated by wave energy converters (WECs) has attracted increasing attention along with the developments of wave energy converting technologies in recent years. Electric power estimation currently depends on wave-to-wire model-based numerical analysis and experimental studies of scale-down prototypes. However, traditional numerical simulations are time-consuming and expensive for power orediction of a full-scale WECs operated in real sea. More importantly, they cannot accurately predict WECs’ power performance in real time, thereby cannot be used for prediction-based real-time control. To address those problems, four machine learning techniques are employed as an alternative to traditional, complex physical modelling processes to evaluate and predict the generated electric power, based on historical experimental data of a two-body hinge-barge WEC. Comparative results of a Backpropagation (BP) Neural Network algorithm, a Long Short-Term Memory (LSTM) algorithm, a Support Vector Machine (SVM) algorithm and a Radial Basis Neural Network (RBFF) algorithm indicate that machine-learning-based approaches can accurately predict the electric performance of this complex multi-degree-of-freedom WEC, where the coefficient of determination (R2) of the BP Neural Network on the test dataset is up to 0.9987.

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.

Achieving optimum power extraction of wave energy converters through tunable mechanical components

Wave energy converters (WECs) play a significant role in harnessing the vast potential of marine renewable energy. To enhance the power extraction of WECs, it is necessary but challenging to design the parameters of the WECs for the time-varying wave conditions. This research explores the utilization of tunable mechanical components within both the power take-offs (PTO) and wave capturing structures. We first briefly review the tunable mechanisms and then conduct a theoretical analysis of their applications for maximizing power extraction under regular and irregular wave conditions. The study investigates the impact of PTO stiffness and inertance on power extraction through an analytical approach. The results reveal that both parameters exhibit a monotonic effect within specific frequency ranges, and showed the optimum power extraction can be achieved through the tunable mechanical components. Furthermore, the research highlights the importance of designing the frequency tuning limit for two-body WECs to coincide with the desired wave conditions, as it enables all PTO parameters to achieve an optimal power output. Based on the analysis, the paper gives insightful suggestions on the design of PTO and WEC systems, including mass ratio between the two bodies, mooring stiffness, and other relevant parameters. It is found that the tuning through the mechanical component can be significant for the single-body WEC yet less effective for the two-body WEC especially at irregular wave conditions.

Dimensional optimization of a two-body wave energy converter under irregular waves for the strait of hormuz

This study presents a method for designing an optimal two-body wave energy converter for offshore locations by choosing the Strait of Hormuz in southern Iran as the study site. To investigate wave behavior, the frequency and height of the waves were monitored over a two-year period. The collected data from the waves at this strait reveal a significant wave height of 0.8 m and a wave peak period of 4 s. Analyzing the obtained data shows an approximate power of 1.4 kW per meter width of the wave. The Design of Experiment method is employed to calculate the power that a wave energy converter can harvest under these conditions, using the converter parameters as the objective function. Moreover, the Response Surface Method is utilized to optimize the dimensions of the converter in order to achieve maximum output power. A mechanical power take-off system is considered to convert the wave-absorbed power into electricity. During the optimization process, ANSYS AQWA and WEC-Sim are employed to study the converter behavior under sea waves.

Performance of a Raft-Type Wave Energy Converter with Diverse Mooring Configurations

The development and utilization of wave energy, heralded as a potential leading source of clean energy worldwide, have garnered considerable attention from the global research community. Among the diverse array of wave energy converters (WECs), the raft-type WEC stands out for its potential to efficiently harness and utilize wave energy, offering high energy conversion rates and a broad frequency response range. This paper delves into the evaluation of a raft-type WEC’s performance in various mooring configurations under different wave conditions. Our analysis primarily focuses on the dynamics of the two-body WEC using a weakly nonlinear three-dimensional potential flow solver. The considered device comprises two interconnected floating barges, incorporating a power take-off system at the hinged connection point. This investigation involves the use of equivalent linear damping to model the power take-off (PTO) system. To validate the numerical simulations, we conduct physical model experiments with WECs. Additionally, the coupling of the raft-type WEC’s dynamics and its mooring dynamics was examined, highlighting the performance differences between various mooring systems through a comparative analysis.

Incorporating Mooring Dynamics into the Control Design of a Two-Body Wave Energy Converter

Mooring systems are a critical component of all floating wave energy converter (WEC) systems, yet the impact of amooring system on the WEC dynamics is often neglected during the initial assessment of candidate designs. The purpose of this study was to investigate how the inclusion of mooring dynamics in the early stages of the WEC design process influences decisions regarding hydrodynamic features and control strategies. The study was executed within a mechanical circuit framework to represent the WEC response in the frequency domain. Thevenin’s theorem was applied within this framework to transform a multi-body WEC into a single-body canonical form. This work specifically focused on self-reacting point absorbers and examined how four realistic mooring designs impact WEC intrinsic mechanical impedance across a range of common wave frequencies. We show how the mooring can easily be included in this framework, and a simple approach to identifying the mooring model parameters is described. It was observed that if mooring dynamics are considered within the WEC control design process, a 40% reduction in the required range of the controller physical variable can be achieved while yielding up to 16% more useful power. These results suggest that considering the mooring system early can enhance WEC design.

Experimental study of a floating two-body wave energy converter

Experimental study of a floating two-body wave energy converter

Improving the power capture performance of deep-sea two-body counter-rotating wave energy using frequency domain optimization in regular and irregular waves

This paper presents a novel two-body counter-rotating wave energy converter (CR-WEC) designed to power deep-sea exploration equipment. In contrast to conventional two-body structures, which employ relative motion, the CR-WEC powers the Power Take-Off (PTO) via absolute motion to circumvent the issue of a limited working stroke. We present the power equation of CR-WEC in the frequency domain, based on the actuator disk model from the wind turbine field, in order to elucidate the energy absorption characteristics of this type of two-body absorber and investigate the influence of parameters on power acquisition. Experiments conducted as part of this study have confirmed this theory's applicability to the CR-WEC. Through an approximation, we derive the frequency point corresponding to the maximum value of the equation, which we refer to as the Power Maximum Frequency Point (PM-FP) in this paper. Under the external excitation of both regular and irregular waves, we investigate how parameter modification can enhance the absorber's capture characteristics in specific cases. After modifying the parameters according to the principles derived from the aforementioned research, the system's theoretical power output can more than double. In addition, this study's conclusions emphasize the benefits of CR-WEC with cascade expansion. By connecting multiple PTOs in series, power generation can be enhanced.

Semi-analytical and CFD formulations of a spherical floater

Today, humanity is facing the great pressure of fossil fuels exhaustion and environmental pollution. This obliges governments and industries to make accelerated efforts on producing green energy. The focus is spotted on marine environment which is a vast source of renewable energy. Among several classes of designs proposed for wave energy conversion, spherical Wave EnergyConverters (WECs) have received considerable attention. The problems of water wave diffraction and radiation by a sphere has been examined by a substantial amount of literature, i.e., [1]–[4], whereas in [5]–[8] linear hydrodynamic effects on a spherical WEC have been examined. All these research works are based on potential flow methodologies. Nevertheless, overthe last decade there has been a significant interest on Computational Fluid Dynamics CFD modelling due to its detailed results, focusing also to spherical WECs [9]–[10].In the present work a semi-analytical model is applied to solve the wave radiation problem around a spherical WEC (Figure 1), in the context of linear potential theory. The outcomes of the theoretical analysis are supplemented and compared with high fidelity CFD simulations (Figure 2 for a semi-submerged sphere). Furthermore, the two methodologies are compared with a theoretical approach for the hydrodynamic analysis of floating bodies with vertical axis as being presented in [11]. The method is based on the discretization of the flow field around the body using coaxial ring elements, which are generated from the approximation of the sphere’s meridian line by a stepped curve.Numerical results are given from the comparison of the three formulations, and some interesting phenomena are discussed concerning the viscous effects on the floater.
 [1] Havelock, T. H. 1955. Wave due to a floating sphere making periodic heaving oscillations. R. Soc. London,A231, 1-7.[2] Hulme, A. 1982. The wave forces acting on a floating hemisphere undergoing force periodic oscillation. J. FluidMech., 121, 443-463.[3] Wang, S. 1986. Motions of a spherical submarine in waves. Ocean Engng., 13, 249-271.[4] Wu, G.X. 1995. The interaction of water waves with a group of submerged spheres. Appl. Ocean. Res., 17, 165-184.[5] Srokosz, M.A. 1979. The submerged sphere as an absorber of wave power. J. Fluid Mech., 95, 717-741.[6] Thomas, G.P., Evans, D.V. 1981. Arrays of three-dimensional wave energy absorbers. J. Fluid Mech., 108, 67-88.[7] Linton, C.M. 1991. Radiation and diffraction of water waves by a submerged sphere in finite depth. Ocean Engng.,18, 61-74.[8] Meng, F., et al. Modal analysis of a submerged spherical point absorber with asymmetric mass distribution.Renew. Energy 130, 223-237.[9] Shami, E.A., et al. 2021. Non-linear dynamic simulations of two-body wave energy converters via identificationof viscous drag coefficients of different shapes of the submerged body based on numerical wave tank CFD simulation.Renew. Energy, 179, 983-997.[10] Katsidoniotaki, E., et al. 2023. Validation of a CFD model for wave energy system dynamics in extreme waves.Ocean Engng., 268, 113320.[11] Kokkinowrachos, K., et al. 1986. Behaviour of vertical bodies of revolution in waves. Ocean Engng., 13, 505-538

Parametric analysis of a two-body floating-point absorber wave energy converter

In the evolution of floating-point absorber wave energy conversion systems, multiple-body systems are gaining more attention than single-body systems. Meanwhile, the design and operation factors affecting the performance of multiple-body systems are much greater than those of single-body systems. However, no systematic study has yet been presented. In this article, a theoretical model is proposed by using a coupled oscillator system consisting of a damper-spring system to represent a two-body system (the floating body and the reacting body). Dimensionless expressions for the motion response and wave power absorption efficiency are derived. With the newly developed model, we prove that an appropriately tuned two-body system can obtain a limiting power absorption width of L/2π (L is the incident wavelength) as much as a single-body system. The generic case of a two-body system is presented with numerical simulations as an example. The results show that increasing the damping coefficient can reduce the wave frequency at which the peak of power absorption efficiency occurs. Increasing stiffness can make the wave frequencies for high power absorption efficiency move to a higher frequency region and can also make the spectrum bandwidth for high power absorption efficiency become narrower. Further, we show that the two-body system can absorb more wave energy at low wave frequencies than the single-body system.

Hybrid Model Predictive Control of a Two-Body Wave Energy Converter with Mechanically Driven Power Take-Off

In this paper, a variable damper is proposed to regulate the efficiency of a two-body wave energy converter (WEC) with mechanically driven power take-off (PTO). The variable damper introduces logic constraints into the WEC system, which can be translated into a mixed logical dynamical form with the dynamics of real-valued variables, the dynamics of logic variables, and their interactions. A hybrid model predictive control (MPC) method is used to determine the control inputs, which has the capacity to handle various constraints. The performance is assessed through simulations to evaluate the effectiveness of the proposed method. The achievable performance improvements of the proposed hybrid MPC are shown by means of comparative analysis with uncontrolled WEC devices. The results show that the proposed hybrid MPC has a high requirement on the lower bound of the variable damper and the maximum damping is used only at low relative velocities to achieve the optimum phase, like latching control. The hybrid MPC performs exceptionally well under wave conditions with a small significant wave height and long wave period, improving the power generation of the uncontrolled system up to 22.5%. And, the prediction error has a significant effect on hybrid MPC performance, especially for long prediction horizon.

Performance prediction and design parameters sensitivity analysis of two-body point absorber wave energy harvesters

This paper introduces a novel model for predicting the performance and conducting sensitivity analysis of design parameters in two-body point absorber wave energy converters. The key novelty lies in the examination of design parameter sensitivity and their interaction effects on performance. The model utilizes the response surface method (RSM) in conjunction with central composite design to establish analytical equations for efficiently predicting the resonance frequency and peak generated power of the two-body wave energy converters based on geometric parameters and wave height. This eliminates the need for complex analytical solutions and boundary element simulations. The accuracy and reliability of the RSM prediction models are validated through state-of-the-art numerical simulations and analysis of variance (ANOVA). Using these RSM prediction models, the study proceeds to design and optimize two-body point absorbers for locations along the coastlines of the six Australian states, focusing on two objectives: maximizing peak output power and maximizing the power-to-weight ratio at each location. By incorporating the second optimization target, it is observed that impressive power output with smaller device dimensions or a higher power-to-weight ratio can be achieved across all six Australian states. The developed response surface method prediction model is a versatile mathematical framework applicable to all two-body point absorber wave energy converters and can be adapted for optimizing other types of wave energy converters with expansive search spaces. Australia was selected as a case study due to its abundant wave energy density along its southern shorelines. Notably, no similar studies addressing these specific aspects have been reported in the literature, making this work the first of its kind.

Experimental and numerical study of a novel unidirectional mechanical power take-off system for two-body wave energy converters

Experimental and numerical study of a novel unidirectional mechanical power take-off system for two-body wave energy converters

New Strategy on Power Absorption of a Concentric Two-Body Wave Energy Converter

The wave energy converter (WEC) system, which extracts electricity through the relative heave motion of two concentric cylinders, comprises an inner cylinder and a torus-type outer cylinder sliding along the inner cylinder. To maximize the relative heave motion between two cylinders, the natural frequencies of the two cylinders must be precisely tuned to resonate and be situated on each side of the peak frequency of the wave spectrum. However, the demerit of this strategy is that it demands a deep draft of each cylinder for tuning, and a large-scale PTO damping device is necessary for mechanical power amplified by resonance. As an alternative to efficient and stable WECs, we adopt a new strategy in which the outer cylinder follows the incoming waves and the motion of the inner one is restricted to be minimal using a heave disk. The viscous damping due to formation of vortices at the disk edge is realized by the drag force in the Morison equation. The developed hydrodynamic model of two-body WEC based on a matched eigenfunction expansion method (MEEM) is applied to irregular waves characterized by significant wave height and peak period. It is found that the present two-body WEC with heave disk produces wave energy stably across a wide range of wave frequencies compared to the previous two-body WECs using resonance.

A rectified unidirectional rotary PTO for two-body wave energy converters

This work presents a new mechanism for a mechanical power take-off (PTO) system that can be used in a variety of wave energy converters (WECs). This mechanism uses two ball screws to convert the relative linear motion of the WEC bodies into unidirectional rotary motion. The resulting rotary motion finally causes a generator to rotate and generate electricity. Due to the oscillatory nature of the wave, the relative velocity of the WEC bodies will have a sinusoidal motion; therefore, the angular velocity of the ball screw becomes zero at two moments during one period of movement. The designed mechanism prevents the generator shaft from changing its direction of rotation at these moments. This mechanism also decouples the generator shaft from the ball screw when the angular velocity of the generator shaft exceeds the angular velocity of the ball screw due to its rotational moment of inertia. As the relative velocity of the bodies increases, the generator shaft is re-coupled to the ball screw and, in consequence, rotates at the angular velocity of the ball screw. This article examines the effect of using the present mechanism on increasing the electrical output power of the WEC at different wave frequencies.

On improving the wave-to-wire efficiency of a two-body hinge-barge wave energy converter

The multi-body hinge-barge wave energy converter has the advantages of high capture width ratio and wide bandwidth of wave-excited response, which is the current hotspot of studies on wave energy converters. However, to correctly and throughfully analyse its overall efficiency, hydrodynamics, mechanical dynamics and electrical dynamics, a fully coupled wave-to-wire approach by numerical analysis and physical validation is required, which is not concerned by current studies. The work conducted in this study improves the overall wave-to-wire efficiency by optimising the mooring system, the structure and geometry of the primary capture system, and the external electric load. Results show that an optimised prototype achieves a wave-to-wire efficiency up to 25% in flume experiments, where a significant improvement of 53% is contributed by employing a damping plate to the right barge. Numerical results indicate that a wave-to-wire efficiency of up to 53% is obtained by further optimisation of the damping plate.

A designed two-body hinged raft wave energy converter: From experimental study to annual power prediction for the EMEC site using WEC-Sim

The present study aims at providing more data and insights for the hinged type WEC, especially focusing on the two-body hinged raft WECs. Two WECs are considered: a well-studied generic hinged raft WEC (G-HRWEC) and a 1:25 scale designed hinged raft WEC (D-HRWEC). The open-source tool WEC-Sim is employed in numerical studies. Referring to the published numerical data for G-HRWEC, corrections are proposed to the WEC-Sim model which are shown to realise the ability of WEC-Sim to model the two-body hinged WEC. For the 1:25 scale D-HRWEC, the physical results show that the relative hinge motion between the rafts is predominately linear under small waves, but significant nonlinearities like viscosity, submergence and overtopping exist under large oscillations. The updated WEC-Sim model is used to simulate this D-HRWEC and is validated with experiment data, showing good representation of the nonlinear behaviour observed in physical experiments with low computation expense. Annual average power of ∼83 kW is predicted for the D-HRWEC in full scale at EMEC site, using the validated WEC-Sim model. The power performance of D-HRWEC is shown to be dependent on the wave steepness. The updated WEC-Sim is provided and can be directly used to model any two-body hinged WECs dominated by linear hydrodynamics. For realistic devices, representative nonlinear terms need to be carefully identified via physical data or computational fluid dynamic simulations and then added into the updated WEC-Sim to improve the modelling accuracy. Following the theory and method given in this work, the updated WEC-Sim for two body hinged raft WEC can be re-developed to extend the WEC-Sim application for WECs or platforms with numbers of hinge connections.

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.