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DOE OSTI2023

Mooring structure for ocean wave energy converters

A mooring system for an Ocean Wave Energy Converters (OWEC) includes multiple structural members such as legs and braces that are linearly extendible and connected using mobile joints, each joint providing two degrees of freedom for rotations about the joint. Mobile joints also attach bottom ends of the legs to mooring points. A jacking system can change lengths of the extensible structural members to adjust depth of the OWEC for operation or for storm safety, to lift the OWEC out of the water for maintenance, or to align the OWEC to an incoming wave direction.

Siegel, Stefan G.↗

DOE OSTI2020

Revisiting Theoretical Limits for One-Degree-of-Freedom Wave Energy Converters: Preprint

This work revisits the theoretical limits of one-degree of freedom wave energy converters (WECs). This paper considers the floating sphere used in the Ocean Energy Systems (OES) Task 10 Wave Energy Converter modeling and verification effort for analysis. Analytical equations are derived to determine bounds on the motion amplitude, time-averaged power, and power take-off (PTO) force. A unique result was found that shows the time-averaged power absorbed by a WEC can be defined solely by the inertial properties and the radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force amplitude was derived which has provided upper and lower bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression can only provide a lower bound as there is theoretically no upper bound. These bounds are used to compare the performance of a floating sphere if it were to extract energy using surge or heave motion. The analysis shows that because of the differences in hydrodynamic coefficients of each oscillating mode there will be different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on power absorption while also utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate the time-averaged power with a nonideal PTO is modified by the mechanical-to-electrical efficiency and the ratio of the PTO spring and damping coefficients. These were separated in the expression which allows for limits to be set on the possible values of PTO coefficients to ensure a net flow of power to the grid.

50 EE - Wind and Water Power Program - Water (EE-4↗

DOE OSTI2025

Co-design of a wave energy converter through bi-conjugate impedance matching

As with other oscillatory power conversion systems, the design of wave energy converters can be understood as an impedance matching problem. By representing the wave energy converter as a multi-port network, two separate but related impedance matching conditions can be established. Satisfying these conditions maximizes power transfer to the load. In practice, these impedance matching conditions may be used to influence the design of the system (including the hull, power take-off, controller, mooring, etc.). To this end, this paper considers some example applications of wave energy converter design with the help of the impedance matching framework.

WEC↗

DOE OSTI2023

Design of a Two-Body Wave Energy Converter Featuring Controllable Geometry: Preprint

While the field of wave energy has been the subject of numerical simulation, scale model testing, and precommercial project testing for decades, wave energy technologies remain in the early stages of development and must continuing proving themselves as a promising modern renewable energy field. A wave energy converter (WEC) concept, currently being explored, is hoping to add an extra control option to WEC design is the variable-geometry WEC (VGWEC). These VGWECs attempt to incorporate controllable geometric features to adjust the floating body hydrodynamics to favor either power absorption, load shedding, or other operational goals. These variable geometry components have been proposed to be controlled on a sea-state-to-sea-state or wave-to-wave time scale depending on the force (or toque) and bandwidth limitations of the actuators required to manipulate just the controllable geometric hull features. The opportunities of having control over both the WEC geometry components and the power-take-off (PTO) have the potential to improve overall system performance and reliability if a cost-effective solution can be found for a given WEC architecture. This paper will present the recent developments and results of a VGWEC concept that incorporates variable geometry modules into a two-body WEC. In the proposed VGWEC concept, the variable geometry modules consist of air inflatable bags in the surface float and a water inflatable ring in the subsurface body. The surface float is tethered directly to the subsurface body through tether lines each connected to a separate PTO. Adjusting the geometry of both the surface and subsurface bodies along with the PTO coefficients can be shown to maximize power in design sea states while reducing motion response and PTO forces when transitioning to sea states where rated power is reached and load shedding is prioritized in hopes of increasing the sea state operational map.

geometry control↗

DOE OSTI2021

Optimizing Power Generation of a Bottomraised Oscillating Surge Wave Energy Converter Using a Theoretical Model

Preliminary sizing of an oscillating surge wave energy converter (OSWEC) is an iterative process that relies on knowledge of the relevant hydrodynamic coefficients for a given geometry. Often, the complex definition of the device geometry requires coefficients to be obtained through experiments or numerical boundary element solvers such as WAMIT. These techniques demand significant user and computational effort, therefore inhibiting the fine scale parametrization of object dimensions. In this study, a theoretical model, originally presented in Michele et al. (2016), is developed and demonstrated to efficiently optimize the power production for an OSWEC device (subjected to certain environmental conditions) with variations in device widths, heights, and distances from the seabed. Assuming negligible device thickness, the OSWEC motions are modelled as a bottom-raised two-dimensional flap in regular waves using potential flow theory formulated in elliptical coordinates. The solutions to this diffraction-radiation problem are obtained using Mathieu functions with appropriate boundary conditions. The resulting potentials are then used to derive frequency-dependent expressions for the added mass and radiation damping coefficients, along with wave excitation magnitude in surge, pitch, and coupled surge-pitch motions. Good agreement in hydrodynamic coefficient curves is shown between the theoretical model and the numerical results obtained from the boundary element-based program WAMIT. The theoretical model is then employed to maximize the time-averaged output power while maintaining or reducing the hinge reaction force, with variations in device dimensions, wave frequency and amplitude.

ACE↗

DOE OSTI2022

Influence on Structural Loading of a Wave Energy Converter by Controlling Variable-Geometry Components and the Power Take-Off

Oceans are harsh environments and can impose significant loads on deployed structures. The deployment of wave energy converters (WECs) faces a design challenge with apparently contradictory goals. A WEC should be designed to maximize the energy absorbed while ensuring the operating wave condition does not exceed the failure limits of the device itself. Therefore, the loads endured by the support structure are a design constraint for the system. Adaptability to different sea states is, therefore, highly desirable. This work uses a WEC-Sim model of a variable-geometry oscillating wave energy converter (VGOSWEC) mounted on a support structure simulated under different wave scenarios. A VGOSWEC resembles a paddle pitching about a fixed hinge perpendicular to the incoming wave fronts. Therefore, the hinge experiences loads perpendicular to its axis as it maintains its position. The geometry of the VGOSWEC is varied by opening a series of controllable flaps on the pitching paddle when the structure experiences threshold loads. Because opening the flaps lets the waves transmit through the paddle, it is hypothesized that opening the flaps should result in load shedding at the base of the support structure. The load shedding is achieved by reducing the moments about the hinge axis. This work compares the hydrodynamic coefficients, natural periods, and response amplitude operators from completely closed to completely open configurations of the controllable flaps. The comparisons quantify the effects of letting the waves transmit through the VGOSWEC. This work shows that the completely open configuration can reduce the pitch and surge loads on the base of the support structure by as much as 80%. It was observed that at the paddle's resonance frequency, the loads on the structure increased substantially. This increase in loads can be mitigated by a rotational power take-off damping about the hinge axis. Changing the rotational power take-off damping was identified as an additional design parameter that can be used to control the loads experienced by the WEC's support structure.

fixed and floating structures↗

DOE OSTI2022

Influence on Structural Loading of a Wave Energy Converter by Controlling Variable-Geometry Components and the Power Take-Off: Preprint

Oceans are a harsh environment and can impose significant loads on deployed structures. Deployment of wave energy converters (WECs) faces a design challenge with apparently contradictory goals. A WEC should be designed to maximize the energy absorbed while ensuring the operating wave condition does not exceed the failure limits of the device itself. Therefore, the loads endured by the support structure are a design constraint for the system. Adaptability to different sea states is, therefore, highly desirable. This work uses a WEC-Sim model of a Variable Geometry Oscillating Wave Energy Converter (VGOSWEC) mounted on a support structure simulated under different wave scenarios. A VGOSWEC resembles a paddle pitching about a fixed hinge perpendicular to the incoming waves-fronts. Therefore, the hinge experiences loads perpendicular to its axis as it maintains its position. The geometry of the VGOSWEC was varied by opening a series of controllable flaps on the pitching paddle when the structure experiences threshold loads. Since opening the flaps lets the waves transmit through the paddle, it is hypothesized that opening the flaps should result in load shedding at the base of the support structure. This load shedding is achieved by reducing the moments about the hinge axis. This work compares the hydrodynamic coefficients, natural periods, and Response Amplitude Operators (RAOs) from completely closed to completely open configurations of the controllable flaps. These comparisons quantify the effects of letting the waves transmit through the VGOSWEC. This work shows that the completely open configuration can reduce the pitch and surge loads on the base of the support structure by as much as 80%. It was observed that at the paddle's resonance frequency, the loads on the structure increased substantially. This increase in loads can be mitigated by a rotational Power Take-off (PTO) damping about the hinge axis. Changing the rotational PTO damping was identified as an additional design parameter that can be used to control the loads experienced by the WEC's support structure.

fixed and floating structures↗

DOE OSTI2021

Optimizing Power Generation of a Bottom-Raised Oscillating Surge Wave Energy Converter Using a Theoretical Model: Preprint

ACE↗

DOE OSTI2026

Report on Coastal Structure Integrated Wave Energy Converters (CSI-WECs)

This report investigates a largely underexplored, and underexploited, application for wave energy: coastal structure integrated wave energy converters (CSI-WECs). These WEC types have significant potential to rapidly advance the wave energy industry while addressing the challenges of coastal community resiliency and marine energy integration and application, and the urgent need for increased coastal protection. To further support the value proposition investigation of this work, three wave energy developers agreed to conduct an energy production analysis of their technology for the four sites identified. Additionally, a geographic information system-based tool was developed that supports efficient and comprehensive site assessment for optimal and high-value deployments.

16 TIDAL AND WAVE POWER↗

DOE OSTI2026

New Report Highlights LAMP's Role as a Robust and Reliable System for Wave Energy Converter Testing

Harnessing the power of waves requires more than just putting devices in the ocean - it takes tools that can refine and accelerate innovation before the first deployment. That's where NLR's largeamplitude motion platform, or LAMP, comes in. LAMP is a six-degree-of-freedom motion system designed to replicate the response of a wave energy converter (WEC) device in realistic ocean conditions. By letting researchers evaluate WEC performance in a safe, controlled lab environment before moving offshore, LAMP helps accelerate innovation while reducing risk. An NLR report, titled Initial Characterization of the NLR LargeAmplitude Motion Platform (https://www.nrel.gov/docs/fy26osti/93733.pdf), provides a deeper understanding of LAMP's capabilities and also lays the groundwork for future advancements in WEC testing methodologies. Researchers studied LAMP's amplitude and frequency limits across different payloads and collected data from 16 test profiles. Testing demonstrated that platform accuracy remained consistent across all payloads evaluated; researchers expect similar accuracy up to LAMP's 10,000-kilogram capacity limit. The measured position limits for single degrees of freedom experienced by WECs, including surge, sway, heave, roll, pitch, and yaw, also exceeded the original manufacturer specifications, providing new insight into the true boundaries of the system.

16 TIDAL AND WAVE POWER↗

DOE OSTI2026

Wave energy converter buoy for Arctic observations

Ocean observation buoys are currently powered-constrained by battery storage capacity or available solar power. Power constraints limit the number of measurements that can be made and the lifetime of the buoys. Ocean surface wave energy could be used for power production, but wave energy converters are not yet commercially available for ocean observation buoys. Here we present the design and testing of a drifting wave energy converter buoy using a pendulum transmission system (PTS). The wave energy converter buoy was designed to operate in Arctic temperatures and wave conditions, but it could be used in areas with warmer temperatures and larger waves. Field tests measured a maximum power production of 5 watts in waves with a significant wave height of 0.42 meters and a ten minute average power production of 37 milliwatts. Power production increased with the energy period and significant wave height. The energy harvesting capabilities of the PTS showed the utility of adding a wave energy conversion device to a drifting ocean observation buoy.

Arctic observations↗

DOE OSTI2022

Techno-Economic Implications of Electrical Machine Scaling for Wave Energy Converters

The sizing of an electrical machine for a Wave Energy Converter (WEC) can have a substantial impact on the overall sizing, cost, and rating of the device. An electrical generator is typically part of the power take-off system, which is the mechanism by which the energy absorbed by the prime mover is transformed into usable electrical energy. For practically all WECs, the rate of change of actuation is predominantly determined by the wave resource (i.e., the wave height and frequency), and devices will see a sinusoidal varying velocity according to the wave conditions. The same can then be said for both directly and indirectly coupled power take-offs with electrical generators. This techno-economic study investigates electrical machine scaling and associated cost implications through core machine design theory, manufacturer data, supporting literature, and the Reference Model Project sponsored by the U.S. Department of Energy. The Reference Model Project was a partnered effort to develop open-source marine energy point designs as reference models to benchmark marine energy technology performance and costs, methods for design and analysis of marine energy technologies, estimations for capital costs, operational costs, and levelized cost of energy. The results from this study show torque is directly related to (1) the physical size of the machine required to increase the air-gap sheer stresses, (2)the amount of active material, (3) the support structure, (4) bearing size and rating, and (5) offshore cable rating, all of which have a significant effect on overall system costs in terms of both capital and operational expenditures. This paper aims to be a critical benchmark in helping determine an "optimal" nameplate rating for wave energy devices and their associated power take-offs. With an optimized rating and sizing process, WEC costs can be reduced and overall performance can be improved.

cables↗

DOE OSTI2022

Techno-Economic Implications of Electrical Machine Scaling for Wave Energy Converters

The sizing of an electrical machine for a Wave Energy Converter (WEC) can have a substantial impact on the overall sizing, cost, and rating of the device. An electrical generator is typically part of the power take-off (PTO) system, which is the mechanism by which the energy absorbed by the prime mover is transformed into useable electrical. For practically all WECs, the rate of change of actuation is predominantly determined by the wave resource (i.e., the wave height and frequency) and devices will see a sinusoidally varying velocity according to the wave conditions. The same can then be said for both directly and indirectly coupled PTOs with electrical generators. This techno-economic study investigates electrical machine scaling and associated cost implications through core machine design theory, manufacturer data, supporting literature, and the DOE sponsored Reference Model Project (RMP). The RMP was a partnered effort to develop open-source marine energy (ME) point designs as reference models (RMs) to benchmark ME technology performance and costs, methods for design and analysis of ME technologies, estimations for capital costs, operational costs, and levelized costs of energy (LCOE). The results from this study show torque is directly related to (1) the physical size of the machine required to increase the airgap sheer stresses, (2) the amount of active material, (3) the support structure, (4) bearing size and rating, and (5) offshore cable rating, all of which have a significant effect on overall system costs in terms of both CAPEX and OPEX. This paper aims to be a critical benchmark in helping determine an “optimal” nameplate rating for wave energy devices and their associated PTO. With an optimized rating and sizing process, WEC costs can be reduced, and overall performance can be improved.

cables↗

DOE OSTI2023

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.

16 TIDAL AND WAVE POWER↗

DOE OSTI2024

Impedance Emulation Control of Wave Energy Converters

Modeling and control of wave energy conversion (WEC) systems for maximum power extraction is challenging due to complex multiphysics that include fluids, mechanics, and machine drives. To uncover an intuitive model that clearly depicts WEC system operation, we utilize a force-current equivalent circuit framework which then enables us to design an impedance emulation control strategy. To provide context for our framework, we focus on a standard reference model-3 (RM3) point absorber device coupled to a permanent magnet synchronous generator. After the proposed extremum seeking controller is computed, we experimentally validate its performance on a platform that consists of two back-to-back connected inverters that emulate the WEC system.

wave energy conversion, impedance emulation, machi↗

DOE OSTI2022

Effect of Heave Plate Hydrodynamic Force Parameterization on a Two-Body Wave Energy Converter

Heave plates are one approach to generating the reaction force necessary to harvest energy from ocean waves. In a Morison equation description of the hydrodynamic force, the components of drag and added mass depend primarily on the heave plate oscillation. These terms may be parameterized in three ways: (1) as a single coefficient invariant across sea state, most accurate at the reference sea state, (2) coefficients dependent on the oscillation amplitude, but invariant in phase, that are most accurate for relatively small amplitude motions, and (3) coefficients dependent on both oscillation amplitude and phase, which are accurate for all oscillation amplitudes. We validate a MATLAB model for a two-body point absorber wave energy converter against field data and a dynamical model constructed in ProteusDS. We then use the MATLAB model to evaluate the effect of these parameterizations on estimates of heave plate motion, tension between the float and heave plate, and wave energy converter electrical power output. We find that power predictions using amplitude-dependent coefficients differ by up to 30% from models using invariant coefficients for regular waves ranging in height from 0.5 to 1.9 m. Amplitude- and phase-dependent coefficients, however, yield less than a 5% change when compared with coefficients dependent on amplitude only. This suggests that amplitude-dependent coefficients can be important for accurate wave energy converter modeling, but the added complexity of phase-dependent coefficients yields little further benefit. We show similar, though less pronounced, trends in maximum tether tension, but note that heave plate motion has only a weak dependence on coefficient fidelity. Finally, we emphasize the importance of using experimentally derived added mass over that calculated from boundary element methods, which can lead to substantial under-prediction of power output and peak tether tension.

dynamical model↗

DOE OSTI2025

Design Principles for Resonant Wave Energy Converters: Benchmarking Power Capture and Flow

Control co-design (CCD) in Wave Energy Converters (WECs) integrates the controller, power take-off (PTO), and buoy models during system design to optimize power output. Using the bi-conjugate impedance matching principle, this study models the PTO as a two-port network, revealing impedance matching conditions at the input and output ports as a function of the buoy, PTO, and controller. Here, this study examines the pairing of a flywheel-type pitch resonator PTO within a given buoy constrained by limited space and ballast capacity. The results show that physical constraints imposed by the buoy affect PTO performance. While controller tuning achieves optimal output impedance matching and flywheel inertia is maximized within the buoy's limitations, the PTO's input impedance remains smaller than the complex conjugate of the buoy's intrinsic impedance. This mismatch limits the PTO's ability to generate sufficient reaction torque, particularly outside the resonance frequency, resulting in narrow-band power transfer. The findings emphasize the need for PTO design modifications to improve input power transfer. Pendulum-based PTO mechanisms are proposed as alternatives to couple with multiple buoy motion modes and improve wave-to-wire efficiency while respecting system constraints.

Control Co-Design↗

DOE OSTI2024

GIS Supported Optimal Site Selection for Coastal Structure Integrated Wave Energy Converters: Preprint

There is an urgent need for adaptative engineering towards more resilient coastal communities, and Coastal Structure Integrated Wave Energy Converters (CSI-WECs) are a promising solution. CSI-WECs are wave energy converters (WECs) that are built into coastal protection structures, such as breakwaters. These devices provide the dual benefits of coastal protection and local energy production, and unlike other WECs, maximizing energy production is not always the main objective. CSI-WECs are located near the shore, where the wave resource is lower, thus site selection for these devices differs from the typical offshore WECs. Other attributes of a site that may be more important than wave power include existing coastal structures, port proximity, electric transmission line proximity, and location of disadvantaged communities. Geospatial information systems (GIS) interfaces can be used to easily visualize geospatial data that represents these difference kinds of criteria important for the determination of optimal marine energy sites. Multi-Criteria Decision Analysis (MCDA) is a geospatial analysis method that allows for the evaluation of multiple, usually overlapping, criteria. This project applies GIS-based MCDA methods to two distinct case studies in Puerto Rico and California for CSI-WEC site selection. The two study sites contrast in terms of wave resource, coastal hazards, and local energy needs. This research demonstrates the utility of applying an MCDA framework within GIS to facilitate efficient site selection for devices with unique characteristics in different use cases.

coastal protection↗