Design Of Wave Energy Converter Research Articles

Numerical investigation on the hydrodynamic performance of a land-based OWC system with multi-chamber modules

Modular design of wave energy converters (WECs) can offer a promising scheme to improve the economic competitiveness of wave energy by reducing the levelized cost of energy. In this study, the hydrodynamic performance of a land-based oscillating water column (OWC) system with multi-chamber modules is evaluated to optimize the layout and design of the system, the OWC structure is extended to five-chamber modules. A two-dimensional wave flume is developed using the high-order boundary element method to simulate the interaction of the incident waves with the OWC device based on the fully non-linear potential flow theory. The proposed numerical model is validated by published experimental data. It is concluded that the two-chamber installation provides superior hydrodynamic performance compared with the single-chamber OWC. The five-chamber OWC system is more suitable for energy capture in low-frequency wave conditions, where the first and last chambers are dominant in energy extraction. From the perspective of energy conversion efficiency and economy, the two- and three-chamber systems are most suitable for targeting low and high frequency waves in the tested conditions, respectively. Additionally, the resonant frequency of the single-chamber module plays a decisive role in the energy capture of the OWC system, and a chamber with a low resonant frequency and a small orifice opening ratio should be selected as the module unit. This paper provides valuable guidance for the modular application of OWCs and the arrangement of multiple chambers.

A bistable point absorber wave energy convertor with a mechanical motion rectifier

The design of novel wave energy converters (WECs) with the capability of low frequency energy capture is of great significance for the development of low frequency ocean wave energy. In this study, a novel point absorber WEC combined with a bistable mechanism and a mechanical motion rectifier (MMR) is proposed to achieve the goal of efficiently capturing wave energy in the low frequency range. In the WEC, the introduction of a rack-pinion-lever-spring (RPLS) bistable mechanism can not only enhance the capture efficiency in a low frequency range but also protect the system from excessive vibration amplitude through the nonlinear stiffness. Besides, one MMR based power take off (PTO) system is proposed to convert the bidirectional vibration into unidirectional rotation of the generator and extract more power via the mechanism of two one-way pinions. The dynamic model in the time domain for the nonlinear point absorber WEC with the RPLS bistable mechanism and the MMR based PTO system is established in which the convolution term is replaced by the state space method. The characteristics of the nonlinear dynamics and wave energy capture performance for the novel WEC are analysed in regular wave condition. The numerical results demonstrate that the peak capture width ratio of the proposed WEC can reach almost 2 times that of the traditional linear system in a lower frequency range.

An integrated system to significant wave height prediction: Combining feature engineering, multi-criteria decision making, and hybrid kernel density estimation

Accurate prediction of significant wave height is paramount for the effective design, operation, and maintenance of wave energy converters. However, current research falls short in achieving precise and stable point predictions, along with comprehensive uncertainty analysis of significant wave height. To address this gap, this study presents a comprehensive significant wave height combined prediction system. This integrated system encompasses outlier detection utilizing Autoencoders, sophisticated feature engineering, a multi-criteria decision-based model selection methodology, a multi-objective homogeneous nuclear molecular optimization algorithm, and a hybrid kernel density estimation technique. To tackle the critical issue of model selection within ensemble prediction, we introduce a multi-criteria compromise solution ranking algorithm known as VIKOR for the selection of sub-models. Additionally, a novel multi-objective homogeneous nuclear molecular optimization algorithm is proposed, which incorporates joint opposing selection and an elite retention strategy to effectively manage multiple objectives simultaneously, yielding Pareto optimal solutions for combining weights. Furthermore, a hybrid kernel density estimation approach is developed, surpassing previous methods reliant on a single kernel function and fixed bandwidth, thereby achieving a more precise fit to the distribution of wave height data. The effectiveness of the proposed model is rigorously evaluated using wave height datasets from three distinct locations. The experimental results convincingly demonstrate that the significant wave height combined prediction system outperforms existing solutions, excelling in both point and interval predictions of significant wave height.

Material Selection Framework for Lift-Based Wave Energy Converters Using the Fuzzy Technique for Order Preference by Similarity to Ideal Solution

Material selection is a crucial aspect in the design of reliable, efficient and long-lasting wave energy converters (WECs). However, to date, the development of tailored methodologies applied to the material selection of WECs remains vastly unexplored. In this paper, a material selection framework for the case of lift-based WECs is developed. The application of the methodology is demonstrated with the hydrofoils of the device. Offshore steel, high-strength offshore steel, aluminium alloys, and carbon- and glass-fibre-reinforced composites are considered and evaluated subject to relevant criteria for wave energy converters, namely structural reliability, hydrodynamic efficiency, offshore maintainability, total manufacturing cost and environmental impact. Candidate materials are assessed via fuzzy TOPSIS for three scenarios of the life cycle of the WEC: conceptual, commercial and future projection stages. Results show that the choice of optimal materials could change from present to future and that multi-criteria decision-making tools aided by a fuzzy approach are useful design tools for novel WECs when field data are scarce. Hence, methodologies such as the ones presented in this work can help in reducing the probability of mechanical failures of emerging WEC technology.

Control co-design of power take-off and bypass valve for OWC-based wave energy conversion systems

Wave energy is a significant source of renewable energy harnessed by wave energy converters (WECs). However, due to the relatively high levelised cost of energy (LCoE), wave energy has not attained a commercial stage yet. To minimise the LCoE, since the optimum (uncontrolled) WEC design typically differs from the optimum controlled WEC design, control co-design (CCD) techniques are essential. With CCD, the WEC control-related aspects are taken into account from the start of the WEC design phase and, ideally, the best control-informed WEC design is then achieved. This paper specifically focuses on CCD for an oscillating-water-column (OWC) WEC, equipped with a Wells turbine and a bypass valve. In essence, a parametric CCD approach is devised to find the optimum (control-informed) turbine rotor diameter, and bypass valve diameter, for the considered OWC WEC. In particular, the optimum design parameters minimise a ‘simplified’ LCoE, which is chosen as a suitable performance function. Despite the LCoE is primarily sensitive to the power take-off size, rather than to the bypass valve size, peak-shaving control with a bypass valve potentially increases the capacity factor and, consequently, can minimise the LCoE for small-to-medium sized turbines.

Research and concept design of wave energy converter on ocean squid jigging ship

Wave power capture applied on a squid jigging ship is assessed in this paper; this would decrease the operating cost of ships and reduce carbon emissions. Firstly, the history of wave energy devices and wave energy generation on ships are briefly reviewed. Then, a new wave energy device on an ocean squid jigging ship is designed. The linear mathematical system model of the device, and WAMIT software are used to calculate wave energy captured. The floating bodies of the device is designed to take advantage of resonance. By comparing wave capture width ratio of the float with arm hinged on the ship, it is found that wave capture width ratio of the device is highest when the arm length is half a wavelength. The numerical method is validated by experimental tests which are presented in details from setup, data treatment to wave energy capture ratio calculated. Based on a resonance criterion, 20 wave energy device layouts of the ocean squid jigging ship are designed. From numerical simulation the optimum radius of the floating body is 2 m, and the maximum annual average power among these devices is 136 kW at Northwest Pacific fishery ground, which can provide about 10 % of the power consumption for the ocean squid jigging ship.

Period and length of high surface gravity waves measured in the coastal waters of eastern Arabian Sea and its variations in 10 years

Information on the period and length of waves is required for the planning and design of marine facilities and wave energy converters. In this article, the period and length of the waves measured during the peak monsoon (June–July) in the coastal waters of the eastern Arabian Sea for 10 years are examined. The most typical wave periods (T) are within 3.9 s and 5.5 s and about 25 % are above 9 s. The peak wave period (Tp) indicates that during the peak monsoon months, long-period waves dominate the eastern Arabian Sea. Significant wave period and integral wave period show a good linear relationship with energy wave period with a slope value close to 1. There are inter-annual variations of up to 15 % in the 90-percentile value of the Tp. From 2010 to 2019, the average wavelength during peak monsoon varied from 61.3 m to 67.6 m and the maximum wavelength from 216.6 m to 248.8 m. Interannual variations in the 90-percentile values for wavelength corresponding to maximum wave height is only 7 %.

Relevance of Robustness and Uncertainties Analysis in the Optimal Design of Wave Energy Converters

The optimisation design of Wave Energy Converters (WEC) to reduce the cost of energy of the technology is a widely investigated topic. In literature classical optimisation strategies have been presented and applied to identify the optimal system parameters of WECs to optimise specific techno-economic metrics. The performance of the optimal identified devices relies on these nominal parameters and it can be strongly affected by construction and modelling uncertainties. In this context, the concept of robustness of the optimal solution plays a relevant role in the identification of a device whose performance is affected as little as possible by uncertainties of various kinds. In the first part of this paper different declinations of robustness concept are derived from other fields of application and described. The identified robustness indexes are then applied to optimal solutions obtained via classical optimisation to evaluate its importance in the design process of WECs.
 Strictly related to this kind of methodology is the Sensitivity Analysis (SA) technique, it aims to investigate how the input variation (due to uncertainties or external noise or additional environmental parameters) influences the output results of a defined numerical model and highlight the relative input parameters relevance. Sensitivity Analysis, therefore, can be a valuable tool applicable in the uncertainty set estimation to identify the variables most subject to such uncertainties and their prominence.
 The main objective of the work is to underline the importance of introduce the robustness evaluation of WECs during the optimisation process since classical optimisation techniques can lead to solutions that are affected by uncertainties.

Hybrid linear potential flow - machine learning model for enhanced prediction of WEC performance

Numerical models based on the linear potential flow equations are of paramount importance in the design of wave energy converters (WECs). Over the years methods such as wave stretching, nonlinear Froude-Krylov and Morrison drag have been developed to overcome the short-comings of the underlying assumptions of small amplitude wave, small motion and inviscous flow. In this work we present a different approach to enhance the performance of the linear method: a hybrid linear potential flow – machine learning (LPF-ML) model. A hierarchy of high-fidelity models – Reynolds-Averaged Navier-Stokes, Euler and fully nonlinear potential flow – is used to create training data for correction factors targeting nonlinear hydrodynamics, pressure drag and skin friction, respectively. Long short-term memory (LSTM) networks are then trained and added to the LPF model. LSTM networks are heavy to train but fast to evaluate so the computational efficiency of the LPF model is kept high. Simple decay tests of generic bodies (sphere, box, etc) are used to validate the LPF-ML model. Finally, the LPF-ML is applied to a model-scale point-absorber WEC to assess the power production.

Tuning Wave Energy Converters to local wave conditions

A Wave Energy Converter (WEC) cannot operate efficiently if left alone floating to the mercy of the random sea surface. Moreover, high waves may impose destructive forces while contributing nil energy production in return. For a WEC to be efficient, its natural frequency should be close to the peak frequency of a wave spectrum. At the resonance or another lower natural frequency, dynamic responses are more regular, and thus, the power take-off system (PTO) can operate in a more efficient manner. This paper introduces a general systematic methodology for tuning the natural frequency of a resonant WEC for the desired degree of freedom and converting dynamic responses into power. A barge is used as a case study to tune its roll and heave natural period, which in general are much lower than the peak period of swells. The roll natural period is increased by hanging subsea structures to the sides of the vessel by means of mooring lines, see Fig. 1. The size of the structures and their entrapped water increase the roll mass moment of inertia to achieve the desired period. For the heave response, the natural period raises by adding skirts to the sides of the vessel, increasing the entrapped water. The resonant motions are significantly suppressed by means of the drag force acting on the subsea structures. Thus, the extreme drag forces acting on the structures act as a damper to the vessel response. These forces are transferred to the mooring lines, which can be converted into a rotary motion of a shaft of the PTO. Our application focuses on the Galapagos Islands, where narrow, low-frequency southerly swells with a typical 13 s peak period dominate the wave climate. This study allows for a systematic design of resonant-type WECs, which is necessary for the development of technical and economic feasibility studies of various novel and existing concepts.
 
 Figure 1: Schematic representation of resonant WEC with tuned roll natural period

Spectral control co-design of wave energy converter array layout

Wave energy systems are designed to maximise energy absorption from the oscillatory motion of waves, which can make a crucial contribution in a new carbon free generation matrix [1]. Thus, the global ocean energy market (including wave and tidal) is expected to grow by more than 700\% by 2028 [2]. However, the harsh conditions faced in the ocean, the strong variability of the resource, and the high force/velocity ratios pose significant challenges to the development of the different ocean energy technologies. Therefore, to date, wave energy converter (WEC) technology is still under development and still needs a significant progress to enhance the energy conversion efficiency and, consequently, to become commercial viable. Crucially, to meet these existing challenges, there are a number of key considerations to progress the effectiveness and efficiency of WEC technologies. In particular, energy maximising control systems, to maximise energy absorption, and the optimisation of WEC array schemes, to take advantage of constructive interaction effects, are currently considered as some of the key drivers for the development of efficient WECs [1]. Recent studies have shown that total design of WECs, analysing the impact of each individual component on the rest of the system, is a key methodology to achieve effective designs. For example, the levelised cost of energy (LCoE) is considered in the objective function in [3], analysing the interplay between the control system based on a spectral controller and the specifications of the power take-off (PTO) system defined as the maximum stroke and force. This methodology has been generally labelled as `co-design', or, when the development is carried out in a control-aware manner, `control co-design'. Similarly, in [4], the interaction between control and optimal WEC geometry is studied. In addition, as discussed before, another key driver in achieving effective wave energy system is the operation of WEC arrays. In particular, in [5] and [6] different array layouts are analysed in terms of computational efficiency and control, respectively. Considering the results in [5], where methods based on harmonic balance techniques are used to analyse the computational demand related to different array layouts, an assessment of the impact of different array layouts on the LCoE, is performed in this study. Figure 1 illustrates different array layouts (a), and the impact of different separation and number of WECs on the resulting LCoE (b). (Figure in PDF abstract)For the implementation of this study, a spectral control methodology is considered to virtually achieve optimal control solutions, even in constrained scenarios. In tandem, different layout templates, composed of multiple point absorber WECs, are considered. To achieve a clear global indicator based on the LCoE, each layout is analysed, in terms of the separation distance and the number of WECs, as well as capital and operation expenditure (CapEx and OpEx, respectively). Following the methodological guidelines considered in [3], a general co-design scheme is designed, essentially based on an exhaustive search method, indicating the interplay between different array layouts and LCoE.

Reducing the uncertainty of ULS load estimates in offshore structural design

The design process of any offshore structure, including Wave Energy Converters (WECs), aims to assess a series of critical conditions, often encapsulated in the concept of ‘limit states’, that define the ‘design boarders’ across which a structure is unlikely to respond satisfactorily, potentially leading to functional failure(s). The Load and Resistance Factor Design (LRFD) method aims to quantify such ‘design boarders’ with adequate safety margins on both the loading and the resistance sides of the design inequality. An inherent risk of such approach is that the definition of ‘adequate’ may be clouded by multiple sources of uncertainty, making it challenging to assess if a system is likely to be under- or over-designed from inception.
 Although overall guidance for the design process of a WEC can be sought from related industries – see e.g. [1], and while noting that generic guidance for WEC design is available in e.g. [2], there is at present limited (practical) guidance on how to derive estimates of long-term return period loads. In recent work, comparative assessments of different load estimation methods have been made, illustrating the dependence of the outputs on the underlying method – see e.g. [3]. Additionally, and in connection with the assessment of extreme loads acting on WECs, the load post-processing methodology was identified in [4] as the major contributor to the uncertainty in Ultimate Limit State (ULS) load estimates.
 This paper presents a novel post-processing methodology to assess the uncertainty when estimating ULS loads acting on an offshore structure. To assess which statistical distributions are best suited to estimate long-term extreme loads, goodness-of-fit tests were performed using a series of input load time-series. The methodology was applied to evaluate the 50-year return load acting on the foundation of a generic Submerged Pressure Differential (SPD) WEC, based on the generic configuration originally defined in [5]. Results suggest that current conventional practices based on visual inspection(s) may lead to the selection of non-representative fitting functions which, in turn, likely lead to inaccurate extreme load estimations.
 Ultimately, the methodology described in this paper aims to contribute to a probabilistic approach to the definition of suitable safety factors, which in turn is expected to reduce the uncertainty in key design metrics and the risk of either under- or over-design.
 This study was conducted as part of the H2020 VALID and H2020 IMPACT projects.
 References
 [1] DNVGL-ST-0437. (2016). Loads and site conditions for wind turbines.
 [2] IEC/TS 62600-2. (2019). Marine energy — Wave, tidal and other water current converters Part 2: Design requirements for marine energy systems.
 [3] Michelen, C., Coe, R. Comparison of Methods for Estimating Short-Term Extreme Response of Wave Energy Converters, Sandia National Laboratories, SAND2015-6890C.
 [4] Atcheson, M., Cruz, J., Martins, T., Johannesson, P., Svensson, T. (2019). Quantification of load uncertainties in the design process of a WEC, Proc. 13th European Wave and Tidal Energy Conference (EWTEC 2019), Naples, Italy.
 [5] Babarit, A., Hals, J., Muliawan, M.J. et al. (2012). Numerical benchmarking study of a selection of wave energy converters. Renewable Energy 41, 44-63.

Quantification of uncertainty in linear wave energy hydrodynamic models from experimental data

Considerable testing and modeling are required in order to fully realise, efficiently develop, and successfully industrialise the wave energy converters (WECs). Numerical modeling, full-scale measurements, and scaled prototype testing are the various methodologies that can be applied to model WECs and predict the dynamic response. Mathematical WEC models form the basis of model-based energy maximising control and directly affect the ability of model-based controllers to maximise energy capture. Linear WEC models are attractive in leading to simpler control designs, but may not cover the complete operational space. One solution is to identify a range of linear models at different operating points, which give a measure of the underlying nonlinear behaviour [1], [2]. This model set can then be used to extract a nominal model, and an associated uncertainty region, which can be used as a basis for a robust WEC controller synthesis process, such as articulated in [3].
 Recently, such an approach has been adopted using data generated from a high-fidelity numerical computational fluid dynamics (CFD) model [4]. However, numerical wave tanks (NWTs) and physical wave tanks differ significantly in terms of the range of tests which can be performed, and the contamination which can affect the measurements used to determine the data-based models e.g. measurement noise, numerical effects, wave reflections, etc [5]. As a result, the determination of nominal models and uncertainty regions in a physical wave tank may provide some advantages (and disadvantages) which need to be examined carefully. In addition, the range of post-processing techniques which could, or should, be applied to the different experimental/numerical domains, to improve the fidelity of the identified models, may differ between domains.
 In this paper, experimental testing of a WEC, by recreating a wave field similar to real-life conditions and a small-scale version of the device, is used to understand the hydrodynamic behaviour and to obtain an accurate dynamic model for WECs, which are considered to be essential towards optimal WEC design. Physical wave tank experiments, even though having their own disadvantages, overcome some difficulties of CFD-based NWT experiments, most notably huge computation time, problems in accurate representation of viscous fluids, uncertainty in the specification of an appropriate turbulence model, and propagation of incident waves [6]. 
 In this study, representative linear models of a point-absorber type WEC from a physical wave tank in the wave basin at Aalborg University are determined which give insight into the system dynamics and provide a basis for robust control of WECs. Among different stimulation techniques to excite the system dynamics in physical wave tank tests, the particular types of excitation signals covering the complete range of frequencies and amplitudes of the system dynamics, while considering limitations on the range of excitation signals or the wave tank reflections, are adopted for the determination of representative linear models. Moreover, a full investigation is carried out to ascertain the appropriate post-processing needed to optimise the signals as the basis for model identification. The model identification includes the non-parametric frequency response by means of empirical transfer function estimate (ETFE). 
 

Wave Spectral Analysis for designing Wave Energy Converters

When designing a Wave Energy Converter (WEC) it is inappropriate to consider overall bulk parameters, like for instance, the typical scatter diagrams Hs-Tp. The reason is that in most of the world wave conditions are complex and involve several long-term wave systems, each with different characteristics (Fig. 1a). This is true even for apparently simple basins like the Mediterranean or the North Sea, in the open ocean this is certainly the case with swells arriving from remote places. Naturally, each Wave System (WS) has different characteristics, like their seasonal variability, typical wave height, but most importantly, the wave period and the spectral width are fundamental design parameters. As WECs must resonate on the exciting force to effectively convert energy, that resonance depends on the wave period. On the other hand, the spectral width indicates how disperse is energy in frequency and direction, the broader the spectrum (more entropy) the more difficult to tap its energy. Therefore, a smart WEC’s design cannot aim to the full spectrum, but to the particular WS with the more favorable characteristics (high energy, narrow spectral band, low frequency). For the present application we focus on a site in the Galapagos Islands. Apart from the aforementioned spectral conditions, this tropical site offers a couple of additional advantages, namely a small seasonal variability, and the absence of high extremes (to be withstood by the device even if idle), with still an interesting average resource (~20 kW/m). At this site we find three main WSs (see Fig. 1, a and b). WS1 belongs to the southerly swells, from the Antarctic extra-tropical storms. WS2 corresponds to swells from the northern hemisphere. WS3 is due to the southern trade-winds, active locally in the area (wind-sea). Clearly, the target for energy conversion is WS1, but for a non-directional device (e.g., point absorber), WS2 is also interesting due to the similar peak frequency. In addition, WS1 and WS2 are seasonally complementary, as they are mainly active in the austral and boreal winters respectively. The identification and separation of these different WSs allows us to determine their characteristics and to obtain specific design parameters. The modulation strategy for the WEC design is the subject of a parallel paper.
 
 Fig. 1. a) (left) Spectral wave conditions in the Galapagos Islands. WS1: Antarctic swells, WS2: northern swells, WS3: southern trade-winds, WS4: Central America wind jets. The colorbar indicates number of occurrences within 1979-2015. b) (right) Average one dimensional spectra for the WSs in panel a. Data obtained from GLOSWAC: https://modemat.epn.edu.ec/nereo/.

Control co-design and uncertainty analysis of the LUPA’s PTO using WecOptTool

Control co-design has been shown to significantly improve the performance of wave energy converters (WEC). By considering the control and WEC design concurrently, the space searched by the optimization routine is greatly expanded which results in better performing devices. Recently, an open-source WEC co-design code, WecOptTool, was released to perform control co-design research and facilitate its adoption in the community. In this study, we use WecOptTool to perform control co-optimization and uncertainty analysis of the LUPA device. The Laboratory Upgrade Point Absorber (LUPA) is a new open-source laboratory-scale WEC that provides a platform for testing new concepts, innovating control schemes, and validating numerical models. The LUPA can be adjusted to different configurations, including changing the number of bodies, the degrees of freedom (DOF), the float and spar geometry, and the diameter of the drive sprocket pulley in the power take off (PTO) system, as well as providing different control algorithms and input waves. The drive sprocket diameter influences the torque vs speed of the generator, which allows for more flexibility in operating under different wave conditions or with different control schemes. In this study we optimize the drive sprocket diameter, while considering the optimal control algorithm for each potential design, to identify the optimal diameter for electric power production at the PacWave South WEC test site. This case study demonstrates several new capabilities of WecOptTool including a multi-body multi-DOF system and multi-directional irregular waves. The PTO dynamics are modeled using first principle methods for a parametrized model of the mechanical subcomponents in combination with generator model obtained using a power-invariant Park transform. The case-study will be made available to serve as a design tool along the LUPA hardware. Users can readily use this model to perform their own design optimization prior to testing with the physical LUPA device. Finally, we use the automatic differentiation capability of WecOptTool to perform a sensitivity and uncertainty analysis of the LUPA device.

A CFD-FEM analysis for Anaconda WEC with mooring lines

Anaconda wave energy converter (WEC) [1] is a typical flexible tube WEC design. In the past decade, the hydro-elastic performance of Anaconda model has been studied through experiments [2-3] and reduced-order numerical simulations [4-5]. However, to date, most of the undertaken research assumes that both ends of the tube are fixed, neglecting mooring lines that exist at designed conditions. The tube is allowed to move freely head to waves when mooring lines are considered. This is evident by an experiment conducted by Checkmate Flexible Engineering Ltd., where they observed a significant heave motion of Anaconda WEC, which may impact the dynamic response of WEC and further the energy conversion [6]. In our previous work [7], supported by the EPSRC project BASM-WEC (No. EP/V040553/1), a coupled numerical analysis tool using computational fluid dynamics (CFD) and finite element method (FEM) has been proposed to perform a numerical study for an Anaconda WEC model without considering mooring lines.In this paper, the coupled fluid-structure interaction (FSI) analysis tool [7] based on CFD-FEM method will be used to investigate Anaconda WEC with mooring lines. To account for the effects of free motion of WEC, we develop a sub-module to be embedded into the existing tool. The fluid and structure are solved by a two-phase CFD solver developed based on OpenFOAM and a three-dimensional FEM code CalculiX, respectively. The strong coupling between OpenFOAM and CalculiX is achieved by a multi-physics coupling tool preCICE.For the flexible tube, a commercial Natural Rubber material is studied. The hyper-elastic model YEOH is utilized to describe the nonlinear behaviour of material, and the model constants are calculated from the bi-axial tests. With the tool developed, numerical simulations are performed for different given regular waves. The flow details, velocity and pressure variation, structure deformation and stress distribution will be fully examined to better understand energy conversion performance of Anaconda WEC with mooring lines.
 References[1] Farley F J M D, Rainey R C T. Distensible tube wave energy converter: U.S. Patent 7,980,071[P]. 2011-7-19.[2] Chaplin J R, Heller V, Farley F J M, et al. Laboratory testing the Anaconda[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, 370(1959): 403-424.[3] Heller V, Chaplin J R, Farley F J M, et al. Physical model tests of the anaconda wave energy converter[C]//Proc. 1st IAHR European Congress. 2000.[4] Farley F J M, Rainey R C T, Chaplin J R. Rubber tubes in the sea[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, 370(1959): 381-402.[5] Babarit A, Singh J, Mélis C, et al. A linear numerical model for analysing the hydroelastic response of a flexible electroactive wave energy converter[J]. Journal of Fluids and Structures, 2017, 74: 356-384.[6] Checkmate Flexible Engineering, https://www.checkmateukseaenergy.com/, accessed 15th December 2022.[7] Huang Y, Xiao Q, Idarraga G, et al. Numerical analysis of flexible tube wave energy converter using CFD-FEA method[C]//International Conference on Offshore Mechanics and Arctic Engineering. American Society of Mechanical Engineers, 2023 (submitted).

Maximizing Wave Energy Converter Power Extraction by Utilizing a Variable Negative Stiffness Magnetic Spring

Complex conjugate impedance matching is a key concept for wave energy converter design. Matching the impedance of the power take-off (PTO) system to the complex conjugate of the wave energy converter's (WEC) impedance ensures efficient transfer of energy from the WEC body motion to electrical power. In low frequency waves, impedance matching often requires a negative PTO stiffness. In this paper, an adjustable stiffness magnetic torsion spring will be presented and modeled to understand its potential to improve WEC performance. The spring has the ability to provide a negative stiffness, allowing the PTO impedance to more closely match the complex conjugate of the WEC impedance at low frequencies. The spring also supports an adjustable stiffness value, meaning it can be tuned according to the incoming wave conditions. The spring's tunability may put less stress on the rest of the PTO system in wave conditions outside its normal operation zone without sacrificing electrical power output. The adjustable magnetic spring's effects are modeled and explored in this paper by examining the resultant average annual electrical power and capacity factor. The study suggests that the tunable magnetic spring has the potential to significantly improve capacity factor while maintaining a high average electrical power.

Analysis of an innovative compact point absorber wave energy converter concept suitable for small-scale power applications

In response to the need for efficient, small-scale power sources for applications such as ocean observation and navigation, this paper presents the design, modeling, fabrication, testing, and analysis of a compact point-absorber wave energy converter (PAWEC) equipped with a mechanical direct-drive power takeoff (PTO) mechanism. The motivation is to address the mismatch between the natural frequencies of conventional PAWECs and dominant ocean wave frequencies, which limits energy capture. The primary objective is to enhance the efficiency of small-scale wave energy converters (WEC) without increasing the buoy size. To achieve this, we introduce a novel design element: an added mass plate (AMP) attached to the buoy. The AMP is devised to increase the WEC added mass and natural period, thereby aligning its natural frequency with dominant ocean wave frequencies. In our case study of a scaled model (1:2.2), the AMP effectively doubled the added mass of the WEC and increased its natural period by 32%. The WEC incorporates a rack and pinion mechanical motion rectifier-type PTO to convert the heave oscillations of the buoy into unidirectional rotation. The scaled model was tested in a wave basin facility with regular waves at zero angle of incidence. The WEC with AMP achieved a maximum root mean square power of 9.34 W, a nearly 30% increase compared to the conventional configuration without AMP, which produced 7.12 W under similar wave conditions. Numerical analysis using the boundary element method in the frequency domain for regular waves confirmed these findings. Finally, it has been derived that the proposed WEC, equipped with an AMP, offers enhanced efficiency in longer wave periods without the need for a larger buoy, establishing its viability as a power source for navigational buoys. This paper also offers a comprehensive guide to experimental techniques for characterizing a PAWEC in a laboratory setting, contributing valuable insights into the wave energy community.

Design and performance evaluation of novel magnetic tristable wave energy converter

To realize efficient broadband wave-energy conversion, this study proposes a point-absorber wave energy converter with a novel magnetic tristable mechanism (NMT-PAWEC). The tristable mechanism consists of coaxial inner and outer magnetic rings. The outer magnetic ring features two types of sector magnets with opposite poles. The motion control equations of the NMT-PAWEC are established using the Cummins equation and the equivalent magnetic charge method. The preferred parameter region of the novel tristable mechanism was investigated, and the energy-conversion performance of the NMT-PAWEC under regular waves was analyzed. The results show that the NMT-PAWEC with shallower potential wells can easily achieve inter-well oscillation under low-amplitude waves, with higher energy harvesting efficiency, and a wider frequency and work-damping band. Through a nonlinear bifurcation dynamics analysis, the causes of fluctuations and sudden changes in the output power under low-amplitude waves were revealed. Furthermore, the capture width ratio and annual average power of the South China Sea were considered. The influence of optimized PTO parameters on the energy-conversion performance of the NMT-PAWEC in regular and irregular waves was further discussed. In general, the efficient broadband power output capabilities demonstrate the excellent applicability of NMT-PAWEC.

The impact of climate change on the wave energy resource potential of the Atlantic Coast of Iberian Peninsula

This study investigates the impact of climate change on the wave energy potential along the Atlantic coast of the Iberian Peninsula, a region acknowledged for its high wave energy resource. The research focuses on the annual and intra-annual variations in wave power for the high-emission RCP8.5 global warming scenario over different time frames: historical, near-future, and far-future. The results show a decreasing trend in the wave energy resource throughout the study area, with the most notable reductions observed in the northwestern region. The reduction in maximum annual power ranges from 15.1 to 7.2 kW/m. Changes in atmospheric circulation patterns and ocean surface temperature gradients induced by climate change effects could explain these results. This study also discusses the impacts of wave power projections on the design of wave energy converters and their future operation. The outcomes are of high interest to adapt the renewable energy infrastructure to a changing climate, ultimately also aiding in the strategic planning and cost-effective design of future wave energy projects.