Heaving Wave Energy Converter Research Articles

A Comparison of the Capture Width and Interaction Factors of WEC Arrays That Are Co-Located with Semi-Submersible-, Spar- and Barge-Supported Floating Offshore Wind Turbines

This research paper explores an approach to enhancing the economic viability of the heaving wave energy converters (WECs) of both cylinder-shaped and torus-shaped devices, by integrating them with four established, floating offshore wind turbines (FOWTs). Specifically, the approach focused on the wave power performance matrix. This integration of WECs and FOWTs not only offers the potential for shared construction and maintenance costs but also presents synergistic advantages in terms of power generation and platform stability. The study began by conducting a comprehensive review of the current State-of-the-Art in co-locating different types of WECs with various foundation platforms for FOWTs, taking into consideration the semi-submersible, spar and barge platforms commonly employed in the offshore wind industry. The research took a unified approach to investigate more and new WEC arrays, totaling 20 configurations across four distinct FOWTs. The scope of this study’s assumption primarily focused on the hydrodynamic wave power performance matrix, without the inclusion of aerodynamic loads. It then compared their outcomes to determine which array demonstrated superior wave energy under the key metrics of total absorbed power, capture width, and interaction factor. Additionally, the investigation could serve to reinforce the ongoing research and development efforts in the allocation of renewable energy resources.

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.

Theoretical investigation on a heaving wave energy converter-dual-arc breakwater integration system array

The hydrodynamic performance of an array of heaving wave energy converter (WEC)-dual-arc breakwater integration systems was investigated using a theoretical model in the present paper based on the potential flow theory, with each dual-arc breakwater consisting of a bottom-mounted inner solid and outer perforated arc-shaped cylinder. The multiple scattering problem was solved using a hybrid iterative method. The mean transmission coefficient was introduced to quantify the wave attenuation performance. After successfully validating the theoretical model, the array effect and the hydrodynamic characteristics of the proposed integration system array are investigated. Focusing on the layout of a linear equidistant column, the calculation results indicate that the WEC and dual-arc breakwater array have mutual benefits in enhancing the wave energy extraction and wave attenuation performance. Compared to an array of bottom-mounted solid and porous cylinders, the proposed integration system array provides much better protection to the leeward region except at a very low wave frequency. In the considered frequency region, a closely arranged integration system array under the perpendicular incident waves has a very constructive array effect on the overall performance. For two staggered columns of integration systems, the wave energy absorption of the leeward column is improved and the sheltering effect to the leeward region is better at a high frequency as compared to the one-column layout; in contrast, the overall performance for two aligned columns is better at a low frequency.

A compressible degree of freedom as a means for improving the performance of heaving wave energy converters

A compressible degree of freedom (CDOF) can provide a means of improving wave power capture by adjusting the system stiffness and providing short-term energy storage, reducing or even eliminating the requirement for two-way electrical power flow as is typical in wave energy control systems. With the overarching goal of investigating and facilitating the application of a CDOF within wave energy converter (WEC) design, this paper focuses primarily on the case of heaving buoys, and on using air volumes to provide the compressible spring effect. Analytical formulae for the natural frequencies are used to gain fundamental insights into the main design considerations. Numerical methods are used to augment this understanding, helping to elucidate the effect of geometric parameters and scale on the required compressible volumes and the efficacy of the CDOF. Beginning with the WaveBot WEC, case studies are then used to demonstrate the design drivers in a more applied context, as well as highlighting the benefit of a self-reacting power take-off (PTO) system. The assimilation of these results with the findings of a detailed literature review culminates in a set of recommendations (or guiding principles) for designing a compressible degree of freedom to improve the performance of a heaving wave energy converter. These recommendations apply both to full-scale WECs, and to the design of scale physical modelling studies for validating the analytical and numerical models.

Wave scattering and radiation by a surface-piercing vertical truncated metamaterial cylinder

In this paper, we study wave scattering and radiation by a surface-piercing vertical truncated metamaterial cylinder composed of a closely spaced array of thin vertical barriers, between which fluid can flow. A theoretical model is developed under full depth-dependent linearised water wave theory, where an effective medium equation and effective boundary conditions are employed, respectively, to describe the fluid motion inside the cylinder and match the flow between the fluid regions in and outside the metamaterial cylinder. A damping mechanism is introduced at the surface of the fluid occupied by the metamaterial cylinder to consider the wave power dissipation in narrow gaps between the thin vertical plates. The wave excitation forces acting on the cylinder and the hydrodynamic coefficients can be calculated straightforwardly in terms of the velocity potential inside the cylinder. An alternative way is by using the velocity potential outside the cylinder, the expression of which has the reduction of the integral and an infinite accumulation that are included in the straightforward expression. The results highlight the patterns of the radiated waves induced by the oscillation of the cylinder and the characteristics of the hydrodynamic coefficients. The metamaterial cylinder when fixed in place and with a damping mechanism included is found to capture more wave power than that of a traditional axisymmetric heaving wave energy converter over a wide range of wave frequencies.

Hydrodynamic analysis of a heave-hinge wave energy converter combined with a floating breakwater

Research interest in breakwater design has increased recently due to the impetus to develop marine renewable energy systems, as breakwaters can be retrofitted to harness wave energy at the same time as attenuating it. This study investigates a novel system of attaching a hinge baffle under a floating breakwater. The floating breakwater itself acts as a heaving wave energy converter, and meanwhile the hinge rotation provides a second mechanism for wave energy harnessing. A computational model with multi-body dynamics was established to study this system, and a series of simulations were conducted in various wave conditions. Both wave attenuation performance and energy conversion ratio were studied, using an interdisciplinary approach considering both coastal engineering and renewable energy. In particular, the performance of the proposed system is compared with contemporary floating breakwater designs to demonstrate its advantage. Overall, a useful simulation framework with multi-body dynamics is presented and the simulation results provide valuable insights into the design of combined wave energy and breakwater systems.

Nonlinear hydrodynamics of a heaving sphere in diffraction, radiation, and combined tests

We report on an experimental campaign designed to shed light on critical nonlinear hydrodynamic effects of heaving wave energy converter (WEC) buoys undergoing large-amplitude motions in operational conditions. The experiments carried out with a spherical model comprised radiation, diffraction and combined tests, where the vertical motion was prescribed and delivered via an actuator. As such, we had independent control of incident waves and motions, enabling isolation of different nonlinear terms by combining recordings from multiple phase- and amplitude-manipulated runs. All tests utilised short-duration wave groups and/or corresponding transient motion signals. We focus on analysis of nonlinear changes in the hydrodynamic forces, and free surface, in the first-harmonic frequency range - this is of most importance to WECs. In a series of radiation experiments, with progressively increasing imposed motions, the radiated wave field and the force in phase with the body velocity are found to decrease nonlinearly, pointing to the WEC's reduced ability to radiate waves under larger oscillations. In the combined tests, we are able to isolate various high-order cross-terms. We attempt to explain the observed trends through third-order potential flow interactions and consider a simple method to approximately describe these.

Power generation and wave attenuation of a hybrid system involving a heaving cylindrical wave energy converter in front of a parabolic breakwater

Deploying a cylindrical heaving wave energy converter (WEC) in front of a parabolic breakwater forms a basic module for synergetic coast protection and power generation. The interactions in the hybrid system are important to its performance but poorly understood. Here the power amplification effect of the parabolic breakwater on the WEC and the additional wave attenuation effect of the WEC on the parabolic breakwater are investigated based on the potential flow theory of linear regular waves. A parabolic breakwater and five WECs with optimized geometry and generator parameters are employed in comparative numerical studies conducted using an open-source code HAMS. Results show that the parabolic breakwater has similar power amplification effects on different WECs, despite the significant differences in their dimensions and power-take-off damping. The power of a WEC can be increased by more than 120% at its natural period. A WEC can shadow the region behind it and reduce the wave amplitude on the opening wall of the parabolic breakwater. It also slightly reduces the amplitude of the relatively high waves in the protection zone behind the breakwater. A flatter WEC with a larger diameter-to-draft ratio is recommended as it generates more power and has a stronger shadow effect.

Coupled dynamic and power generation characteristics of a hybrid system consisting of a semi-submersible wind turbine and an array of heaving wave energy converters

A wind-wave hybrid system consisting of a semi-submersible floating wind turbine and an array of heaving wave energy converters (HWECs) provides a solution for co-located marine renewable energy extraction. The knowledge of the coupled dynamic and power features of the hybrid system is important to the design and operation but is poorly understood. This study proposes a comprehensive numerical model that can tackle the full couplings by bridging the aerodynamic module of OpenFAST and the hydrodynamic simulator WAFDUT through an in-house code based on multi-body dynamics. The coupled dynamic and power generation characteristics of the hybrid system are investigated, with an emphasis on the influence of the HWECs on the wind-induced motion, mooring tension, and wind power generation of the turbine. Results show that the HWECs do not produce negative effects on the wind-induced surge, heave, and pitch motions. The HWECs can slightly reduce the mooring tension and slightly improve wind power generation. The array of HWECs can generate over 500 kW wave power in the waves with periods of 6 s–10 s, which can be a qualified supplement to wind power. The findings offer useful knowledge about the key properties of the hybrid system for practical use.

Layout optimisation of the two-body heaving wave energy converter array

As the two-body heaving wave energy converter (TBH-WEC) moves toward more commercial and large-scale applications, it usually has to be deployed in the form of arrays to reduce costs and achieve better performance. However, hydrodynamic interactions in TBH-WEC arrays are highly complex and difficult to evaluate. The effect of array configuration on the performance and interactions of TBH-WECs within the array has not been fully investigated. To address this gap, the power output time-domain modeling of TBH-WEC arrays is first established using the enhanced MATLAB-APDL-AQWA unified simulation system. Based on this system, this work investigates the internal relationship between incident wave frequency, array size, array layout, and Power Take-Off (PTO) system, and array interaction factors in both unidirectional regular and irregular waves, as well as multidirectional real-wave scenarios. The energy redistribution properties of the array wavefield are then analyzed, as is the correlation between array layout and the disturbance wavefield of the devices. Results show that array layout optimisation and PTO configuration optimisation are relatively independent from each other, and that better array layouts can be quickly obtained by iteratively adding clusters or devices in the amplified region of the existing array disturbance wavefield.

Predicting hydrodynamic forces on heave plates using a data-driven modelling architecture

Prior work has modelled heave forces on surface piercing bodies in real time for 2D, convex and static geometries using a Hammerstein framework. In this work, the modifications needed to make that framework suitable for a representative heave plate geometry in irregular waves are investigated in order to facilitate force prediction for heaving wave energy converters. Two candidate models are compared. The first introduces a Bouc–Wen model to the conventional internal force calculation in the Hammerstein framework. The second further modifies the dynamic block by replacing the linear ARX dynamic calculation with a nonlinear Kolmogorov–Gabor polynomial (KGP) structure. The addition of the Bouc–Wen model introduces velocity and acceleration dependence and a new hysteresis contribution to the internal force predictions to capture the form drag and inertial loads known to occur around heave plates from the entrained fluid. This addition reduces the average error in the internal force calculation by up to 70% for kinematically controlled bodies in irregular waves. Using the revised internal force in the system dynamic block identification process, it was found that the resulting models provided significant improvements (up to 38%) in prediction of the hydrodynamic heave force when using both the linear and nonlinear ARX formulations.

A two-dimensional boundary element method with generating absorbing boundary condition for floating bodies of arbitrary shape in the frequency domain

A two-dimensional (2D) boundary element method is developed for the rapid assessment of the hydrodynamic performance of floating structures in waves. The boundary element method is based on potential flow and has panels along all boundaries of the fluid domain – not only along the boundary of the floater – to make the extension to second order feasible. Panels along all boundaries requires the development of generating absorbing boundary conditions for use at radiation boundaries to send incident waves into the domain while absorbing waves originating from the floating body at the same boundary, at the same time. The model is verified by means of conservation of energy of a heaving wave energy converter, and by means of the propagation of second-order waves. The performance in terms of conservation of energy with 12 panels per wave length is good, the generating absorbing boundary condition works according to expectation and the second-order wave propagation corresponds to theory.

Dynamic modeling of the motions of variable-shape wave energy converters

In the recently introduced Variable-Shape heaving wave energy converters, the buoy changes its shape actively in response to changing incident waves. In this study, a Lagrangian approach for the dynamic modeling of a spherical Variable-Shape Wave Energy Converter is described. The classical bending theory is used to write the stress–strain equations for the flexible body using Love’s approximation. The elastic spherical shell is assumed to have an axisymmetric vibrational behavior. The Rayleigh–Ritz discretization method is adopted to find an approximate solution for the vibration model of the spherical shell. A novel equation of motion is presented that serves as a substitute for Cummins equation for flexible buoys. Also, novel hydrodynamic coefficients that account for the buoy mode shapes are proposed. The developed dynamic model is coupled with the open-source boundary element method software NEMOH. Two-way and one-way Fluid–Structure Interaction simulations are performed using MATLAB to study the effect of using a flexible shape buoy in the wave energy converter on its trajectory and power production. Finally, the variable shape buoy was able to harvest more energy for all the tested wave conditions.

Development and Wave Tank Demonstration of a Fully Controlled Permanent Magnet Drive for a Heaving Wave Energy Converter

One option for converting the energy in sea waves into renewable electricity is the development of floating wave energy converters coupled to electrical generators. For this to work, bespoke slow-speed electrical machines coupled to bidirectional power smoothing power electronic converters are required. This paper reports on the successful design and wave tank validation of an electric machine, power converter and fully controlled direct drive power take-off system coupled to two small scale heaving wave energy converters. The design, development and demonstration of linear generators and power converters is presented including some simulated and laboratory results. Demonstration of wave energy converters with pure electric drives, fully automated control, bidirectional power flow and active force management is almost unique and essential for future wave energy development. The results presented prove that direct-drive power take-off for wave energy devices is technically possible and can be used to implement an automated control system with bidirectional power flow in both resonant and non-resonant wave energy systems.

A novel two-objective optimization computational framework for a two-body heaving wave energy converter

The present research introduces a novel two-objective optimization computational framework, named H∞ optimization criterion-constrained Two-Objective Optimization Genetic Algorithm (H∞ − cTOOGA). Within this optimization framework, the objectives considered are: (i) the sprung mass isolation, and (ii) the wave energy extraction of a heaving buoy coupled with a sprung (overlying) mass. In such a two-body heaving wave energy converter (WEC), the satisfaction of both objectives is pursued by proper selection of the buoy geometry (i.e., radius r and draft Dr) and the characteristics of the power take-off (PTO). The interrelation among potential buoy geometries and PTO characteristics is performed on the basis of a critical condition. The critical condition refers to the formation of equal double peaks in the sprung mass acceleration response curve and is imposed as the sprung mass acceleration limit that is not allowed to be exceeded throughout the entire frequency range of interest. The two-objective optimization is realized with r, Dr and the tuning ratio δOPT being the decision variables. The value of δOPT is constrained by the value of the critical tuning ratio δcrit, that is, δOPT <δcrit. This ensures the minimization of the maximum sprung mass acceleration response. Then, the Pareto-optimal solutions result to optimal wave energy extraction.

Absorbed power density approach for optimal design of heaving point absorber wave energy converter: A case study of Durban sea characteristics

This work proposes an approach for the optimal sizing of a cylindrical heaving wave energy converter (WEC). The approach is based on maximising the absorbed power density (APD) of the buoy, with the diameter being the decision variable. Furthermore, two types of buoy shapes were compared to get the best option. The two buoy shapes are the cone cylinder buoy (CCB) and the hemisphere cylinder buoy (HCB). The aim was therefore to determine the best shape and as well as the optimal size of the cylindrical point absorber. To validate the approach, the simulation was performed under Durban (South Africa) sea characteristics of 3.6 m wave significant height and 8.5 s peak period, using the openWEC simulator. The buoy diameter range considered was from 0.5 m to 10 m for both shapes. Simulation results revealed that a diameter of 1 m was the optimal solution for both buoy shapes. Furthermore, the APD method revealed that the HCB was more efficient than the CCB. The power density of the HCB was 1070 W/m2, which was almost double the power density of the CCB, while the two shapes present almost the same absorbed power.

The application of the spectral domain modeling to the power take-off sizing of heaving wave energy converters

The power take-off (PTO) system is a main component in wave energy converters (WECs), and it accounts for a notable proportion in the total cost. Sizing the PTO capacity has been proven to be significant to the cost-effectiveness of WECs. In the numerical modeling, the PTO size is normally represented by a force constraint. Therefore, to accurately evaluate the power performance of WECs with various PTO sizes, it is necessary to take the PTO force limitation, a nonlinear effect, into consideration. In this paper, a computationally-efficient spectral domain model of the PTO force saturation is developed for a heaving point absorber, and the nonlinear term is included by statistical linearization. For comparison, a frequency domain and nonlinear time domain model are implemented, and the developed spectral model is verified with the results of the nonlinear time domain model. Compared with the frequency domain model, the spectral domain model remarkably reduces the relative errors in predicting the power performance of WECs with force constraints, while the computational demand is much lower than the nonlinear time domain model. Furthermore, a case study is conducted to size the PTO capacity for reducing the levelized cost of energy (LCOE) in a chosen wave site. Three different numerical models are applied respectively. The frequency domain model could lead to a misestimate of the optimal PTO capacity, with a maximum relative error on the prediction of the annual energy production (AEP) of 24%. In contrast, the spectral domain model indicates the same optimal PTO size with the time domain modeling, and its relative errors on the prediction of the AEP are within 4.3%.

Theoretical study on arranging heaving wave energy converters in front of jarlan-type breakwater

A hybrid wave energy extraction (HWEE) system consisting of a heaving wave energy converter (WEC) and a Jarlan-type breakwater was theoretically investigated using the linear potential theory. The law of wave energy flux conservation was used for verification. The effect of several critical geometry parameters on the hydrodynamic performance of the HWEE system was discussed. Then, appropriate parameter ranges were recommended in terms of the stability of the structure and the wave energy capture performance. The contribution of the wave radiation force to the total force was discussed, it was found that, compared with the wave excitation force, the wave radiation force can be ignored in most frequency ranges, except near the natural frequency of the heaving WEC. By a contrastive study, it was found that the hydrodynamic performance of the heaving WEC is greatly adjusted by the rear perforated breakwater, and the wave attenuation performance of the proposed HWEE system is much better than an isolated perforated breakwater. Furthermore, it was also found that, in irregular waves, the proposed HWEE system can still maintain a rather good wave energy capture performance.

Power Absorption of A Two-Body Heaving Wave Energy Converter Considering Different Control and Power Take-off Systems

Power Absorption of A Two-Body Heaving Wave Energy Converter Considering Different Control and Power Take-off Systems

Hydrodynamics of Moonpool-Type Floaters: A Theoretical and a CFD Formulation

Moonpool-type floaters were initially proposed for applications such as artificial islands or as protecting barriers around a small area enabling work at the inner surface to be carried out in relatively calm water. In recent years, a growing interest on such structures has been noted, especially in relation to their use as heaving wave energy converters or as oscillating water column (OWC) devices for the extraction of energy from waves. Furthermore, in the offshore marine industry, several types of vessels are frequently constructed with moonpools. The present paper deals with the hydrodynamics of bottomless cylindrical bodies having vertical symmetry axis and floating in a water of finite depth. Two computation methods were implemented and compared: a theoretical approach solving analytically the corresponding diffraction problem around the moonpool floater and a computational fluid dynamics (CFD) solver, which considers the viscous effects near the sharp edges of the body (vortex shedding) as non-negligible. Two different moonpool-type configurations were examined, and some interesting phenomena were discussed concerning the viscous effects and irregularities caused by the resonance of the confined fluid.