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DOE OSTI2025

Benchmark of numerical modeling approaches on the systematic performance evaluation of wave energy converters

Different numerical modeling methods have been developed and applied to evaluate a variety of performance indicators of wave energy converters (WECs), including the power performance, structural loads, levelized cost of energy, etc. Based on the modeling fidelity, the commonly used numerical modeling approaches can be classified as linear modeling, weakly nonlinear modeling and fully nonlinear modeling approaches. Each method differs in accuracy and computational efficiency, making them suitable for different stages of WEC design. However, the selection of modeling approach could significantly impact evaluation outcomes. For instance, simplified linear models may underestimate structural loads or overestimate energy production in some operational conditions, potentially leading to less cost-effective designs. Given the widespread utilization of these models, it is essential to understand the uncertainties brought by them in performance evaluations. This work is dedicated to benchmarking different linear-potential-flow-based numerical models for evaluating the systematic performance of WECs. Three representative numerical modeling approaches are considered in this work, including linear frequency-domain modeling, statistically linearized spectral-domain modeling and Cummins equation-based nonlinear time-domain modeling. A generic point absorber WEC is considered as the research reference in this work, and different sea sites are taken into account. The numerical models are utilized to predict critical performance indicators, including power performance, the annual energy production, the capacity factor, the levelized cost of energy and the PTO fatigue loads. By comparing the results, this work identifies the uncertainties associated with different modeling approaches in evaluating WEC performance.

Fatigue↗

DOE OSTI2024

Wave-powered water pump for upwelling in aquaculture: Numerical model and ocean test

Wave-powered upwelling can increase the productivity and survivability of several aquaculture species. This enhancement is due to transporting cold, nutrient-rich ocean water, typically found lower in the water column, to the surface. Macroalgaes, like kelp, exhibit increased growth from these altered conditions. The University of New Hampshire’s (UNH) wave-powered water pump (wave pump) is a point absorber wave energy converter (WEC) that uses ocean waves to create relative motion between a spar buoy and a concentric float which drives an internal pump. A numerical model of the wave pump was developed using WEC-Sim to predict device performance in the ocean. Wave pump performance was evaluated during a five day ocean test near Appledore Island in Maine in March 2023, where volumetric flow rate, relative distance between spar and float, and wave conditions were measured. These data were then used for numerical model validation. The ocean deployment recorded the device’s performance in a variety of sea states, with average significant wave heights up to 0.7 m. The ocean test data were compared to the WEC-Sim numerical model of the device with favorable results. Average values of device stroke period, stroke height, and flow rate agreed between the ocean test and model data to within approximately 16 to 22%. Furthermore, the validated numerical model provides a valuable tool for improving the design and developing a commercial-scale, wave-powered water pump for use in aquaculture.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

A cryogenic white light absorption spectroscopy setup with in situ gamma irradiation and thermo-optical annealing for optical fiber radiation-induced attenuation characterization

Silica optical fiber sensors offer a fast, distributed measurement solution in various cryogenic and radiation environments, such as magnets for fusion power. Under these conditions, light-absorbing point defects limit lifetime via radiation-induced attenuation (RIA). To support RIA kinetics prediction, we present an in situ, broadband absorption spectroscopy setup combining gamma irradiation with liquid nitrogen cooling. The apparatus enables continuous monitoring of narrowband RIA levels and the use of secondary optical annealing light sources, alongside broadband spectrum measurements to characterize RIA defects through spectrum decomposition. Initial results confirm the inevitable photobleaching effect of the probe light source, which must be accounted for. In addition, we report RIA kinetics during cycles of gamma irradiation at 77 K and isochronal thermal annealing steps from liquid nitrogen to room temperature, showcasing the setup’s ability to replicate real fiber operation scenarios. These instruments form an ideal platform to further study the kinetics of RIA coupled with thermal and optical annealing.

Absorption spectroscopy↗

DOE OSTI2022

Additional Degree of Freedom for WEC Model

'Additional Degree of Freedom for WEC' - WEC-Sim numerical model from RFTS 1 TEAMER project. An increase in wave energy converter (WEC) efficiency requires not only consideration of the nonlinear effects in the WEC dynamics and the power take-off (PTO) mechanisms, but also more integrated treatment of the whole system, i.e., the buoy dynamics, the PTO system, and the control strategy. It results in an optimization formulation that has a nonquadratic and nonstandard cost functional. This model presents the application of real-time nonlinear model predictive controller (NMPC) to two degrees of freedom point absorber type WEC with highly nonlinear PTO characteristics. The nonlinear effects, such as the fluid viscous drag, are also included in the plant dynamics. The controller may be implemented on a real-time target machine, and the WEC device is emulated in real-time using the WECSIM toolbox. Please see the ‘ReadMe’ within the root directory for an explanation of how to set-up and run the model. An article covering the development of this model is attached as "Real-Time Nonlinear Model Predictive Controller for Multiple Degrees of Freedom Wave Energy Converters with Non-Ideal Power Take-Off"

16 TIDAL AND WAVE POWER↗

DOE OSTI2024

UMass 2-Body WEC Techno-Economic Assessment

The University of Massachusetts (UMass) is developing a 2-body wave energy converter (WEC) device that is converting mechanical power into electricity using a mechanical motion rectifier that allows the system to couple to a flywheel. UMass has completed numerical modeling, wave tank testing, and PTO sub-system testing and needed assistance in developing a techno-economic model to enable optimization of their topology, comparison to a generic heaving point absorber topology, and guide the next steps in their development efforts. The core objective was to develop a techno-economic approach and modeling tool that allows benchmarking of the two topologies across a wide range of scales to evaluate their respective competitiveness in different application spaces. This data includes the final report as well as a supporting spreadsheet containing the data produced for this report.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Lessons Learned: Summary of Insights From the HERO WEC and Waves to Water Deployments Between 2022 and 2024

In 2020, a team from the National Renewable Energy Laboratory (NREL) partnered with the East Carolina University Coastal Studies Institute to develop a small, modular, wave-powered point absorber desalination prototype. That prototype, known as the hydraulic and electric reverse osmosis wave energy converter (HERO WEC), was intended to de-risk the installation activities planned for the Waves to Water Prize sponsored by the Water Power Technologies Office. The NREL team was given approximately 18 months to design, build, bench test, and deploy the HERO WEC prototype. Since the initial HERO WEC development, it has been used for two in-lab test programs and three ocean deployments. The first in-lab test program focused on ensuring that the overall operation of the device occurred as expected and on validating the operation of safety systems such as pressure relief valves or electrical breakers for load mitigation. The second in-lab test program was the first time the NREL team leveraged NREL’s large-amplitude motion platform to characterize the performance of the HERO WEC. Of the three in-water deployments, the first deployment was effectively an installation and recovery practice with no meaningful wave activity during the time that it was installed. The second deployment was a 2-week effort that enabled both the electric and hydraulic configurations of the device to be in the water for approximately 5 days each. This deployment was also the first time that the team had the opportunity to perform a drivetrain swap on the Coastal Studies Institute research vessel. The third deployment had to be split into two separate installations due to minor damage incurred from the WEC spinning during the initial installation. This report summarizes the deployments, the challenges encountered with each deployment, and the lessons learned for future work.

16 TIDAL AND WAVE POWER↗

DOE OSTI2026

Applied Research and Development to Support Open-Water Testing at PacWave

This report presents the findings from Task 7 of the project, which focused on improving the performance and reliability of wave energy converters (WECs) under real-world conditions, particularly in the presence of marine growth (biofouling) and system faults. The work was conducted using the RM3 point absorber WEC model, a marine current turbine based on the SHARKS project model, and the WEC-Sim simulation platform, and it included both modeling and control system development.

16 TIDAL AND WAVE POWER↗

DOE OSTI2024

Analysis on Evaluations of Monterey Bay Aquarium Research Institute’s Wave Energy Converter’s Field Data Using WEC-Sim and Gazebo: A Simulation Tool Comparison

Although many studies have validated wave energy converter (WEC) numerical models against scaled prototype experimental data, there remains a notable lack of validation using data from full-scale deployed WECs. This paper compares two numerical models of Monterey Bay Aquarium Research Institute’s Wave Energy Converter (MBARI-WEC), a two-body point absorber with an electro-hydraulic power take-off system (PTO). The models are implemented in WEC-Sim/Simscape and Gazebo Simulator. A statistical analysis of the models was performed, and field results were obtained to compare the models’ accuracy in predicting the RMS piston velocity, RMS motor speed, and mean electric power compared to field data for 56 observations across varying sea states. The Gazebo model demonstrated a closer agreement across all three parameters for a majority of the observations. When compared to the field data, the Gazebo and WEC-Sim models exhibited average mean electric power overestimations of 13% and 22%, respectively.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Real-Time Wave Energy Converter Control Using Instantaneous Frequency

Wave Energy Converters (WECs) rely on effective Power Take-Off (PTO) control strategies to maximize energy absorption under dynamic sea conditions. Traditional hydrodynamic modeling techniques may require computationally intensive convolution calculations, making real-time control implementation challenging. This paper presents an alternative approach by leveraging instantaneous frequency estimation to dynamically adjust PTO damping in response to varying wave frequencies. Two real-time frequency estimation methods are explored: the Hilbert Transform (HT) and Phase-Locked Loop (PLL). The Hilbert Transform method provides accurate frequency tracking but introduces a delayed response due to its dependence on causal data. Conversely, the PLL approach demonstrates strong potential in frequency tracking but requires careful gain tuning, particularly in complex sea states. Comparative evaluations across multiple test cases—including sinusoidal variations, amplitude steps, frequency step changes, and real-world JONSWAP spectrum waves—highlight the strengths and limitations of each method. The two different PTO control techniques across the various frequency estimation methods were tested under real-sea states using a state-space model of a point-absorbing Wave Energy Converter. The Capture Width Ratio (CWR) is used as a performance metric, with results showing that the HT achieves a 10.6% improvement, while the PLL estimation yields a 0.9% improvement relative to the fixed parameter control baseline. These results highlight the effectiveness of real-time frequency estimation in improving energy absorption compared to static control parameters.

WEC control↗

DOE OSTI2025

Real-Time Sea State Estimation for Wave Energy Converter Control via Machine Learning

Wave energy converters (WECs) harness the untapped power of ocean waves to generate renewable energy, offering a promising solution to sustainable energy. An optimal WEC control strategy is essential to maximize power capture that dynamically adjusts system parameters in response to rapidly changing sea states. This study presents a novel control approach that leverages neural networks to estimate sea states from onboard WEC measurements such as position, velocity, and force. Using a point absorber WEC device as a test platform, our proposed approach estimates sea states in real-time and subsequently adjusts PID controller gains to maximize energy extraction. Simulation results across diverse sea conditions demonstrate that our strategy eliminates the need for external wave monitoring equipment while maintaining power capture efficiency. The results show that our neural network-based control technique can improve power capture by 25.6% while significantly reducing system complexity. This approach offers a practical alternative for WEC deployments where direct wave measurements are either infeasible or cost prohibitive.

PIDcontrol↗

DOE OSTI2026

Biconjugate Impedance Matching Control of the HERO WEC: Preprint

Effective control strategies are essential for maximizing the power output of wave energy converters (WECs). In this study, we explore the methodology of port-based modelling which can be used for bi-conjugate impedance matching, a type of reactive control that involves maximizing power transfer by setting the load (PTO) impedance to be the complex conjugate of the source impedance (WEC). Despite its foundational role in electrical engineering, this method has seen limited application in wave energy and has not yet been demonstrated in wave-powered desalination systems. We represent our complex multidisciplinary system as an equivalent circuit to explore frequency-based relations. The HERO WEC, a small-scale, modular point absorber (PA) designed for reverse osmosis desalination is used as a case study to demonstrate port-based modelling for control applications. Improving the performance of wave-powered water desalination systems could play a critical role in addressing freshwater scarcity for coastal communities, especially those in remote or disaster-prone regions.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Absorbing boundary conditions in material point method adopting perfectly matched layer theory

This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work integrates the Perfectly Matched Layer (PML) theory into the implicit MPM framework. The proposed approach introduces absorbing particles surrounding the computational domain that efficiently absorb outgoing waves and reduce reflections, allowing for accurate modeling of wave propagation and its further impact on geotechnical slope stability analysis. The study also includes several benchmark tests to validate the effectiveness of the proposed method, such as several types of impulse loading and symmetric and asymmetric base shaking. The conducted numerical tests also demonstrate the ability to handle large deformation problems, including the failure of elasto-plastic soils under gravity and dynamic excitations. The findings extend the capability of MPM in simulating continuous analysis of earthquake-induced landslides, from shaking to failure.

58 GEOSCIENCES↗

DOE OSTI2023

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. So our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

42 ENGINEERING↗

DOE OSTI2022

HERO WEC V1.0 - WEC-Sim Detailed Simulation Runs and Summary Data

Data sets from simulation runs include 144 wave cases that were run based on the WEC-Sim model (https://mhkdr.openei.org/submissions/483). The 144 wave cases represent waves with the following wave height and wave period ranges: - Significant Wave Height: 0.25 - 4.0m in 0.25m increments - Wave Period: 5 - 13 sec in 1 sec increments Each run was simulated using a Pierson-Moskowitz irregular wave spectrum with a 200 second ramp time and a total simulation time of 2,200 seconds. Summary data set includes a spreadsheet and image files with matrices that are associated with data from simulation runs. All matrices cover the same significant wave height and wave periods from the sim runs, in the same increments. The following matrices are included: - Mechanical Power Input: Absorbed power calculated using linear input velocity at PTO (power take-off) multiplied by winch tension. - Mechanical Power Output: The hydraulic power calculated at the pump output prior to the pressure relief valve dump. - Feed Pressure: Average pressure at RO (reverse osmosis) input prior to pre-filters - RO Power Input: The hydraulic power calculated at the RO system inlet, accounts for flow loss due to pressure relief valve - Water Production: Average clean water flow at RO output

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Hydrodynamic characterization of the coastal pioneer array ocean observing system

Ocean observation buoys require relatively small amounts of power, yet traditionally necessitate costly resupply trips for battery replacement. With the offshore location of the buoys and small power requirements, wave energy may be an effective solution for providing consistent and reliable power to support the buoy instrumentation. The US National Science Foundation Ocean Observatories Initiative (OOI) includes arrays of point absorber-like buoy systems used for ocean observation that have been deployed at multiple locations including the Southern Mid-Atlantic Bight. A study is currently underway to design a pitch resonator wave energy converter to supplement existing renewable energy generation for powering observation instrumentation. This paper details field measurements from surface moorings of the OOI Coastal Pioneer Array, which informs the subsequent development of a numerical model for the moored observation system. The model is developed in Wave Energy Converter Simulator (WEC-Sim), which leverages the Simscape multibody solver within the MATLAB/Simulink framework and linear potential flow theory to simulate the hydrodynamic interactions and multibody dynamics in 6 degrees of freedom. Multiple tuning variables are considered to produce a model for the system that matches well with empirical data (about 8% error). In conclusion, the WEC-Sim model will serve as a platform for integrating the pitch resonator wave energy converter concept and deployment preparation (detailed design including power take-off and control systems, response evaluation, etc.).

hydrodynamic modeling↗

DOE OSTI2022

HERO WEC V1.0 - WEC-Sim Model

This zip file contains the files that are needed to simulate NREL's HERO WEC (hydraulic and electric reverse osmosis wave energy converter). This requires the user to have already installed WEC-Sim. In addition to the standard toolboxes that are required to run WEC-Sim the user will also need the Simscape Fluids and Simscape Driveline packages. In the zip file you will find the following: - HEROV1_HPTO.slx: Simulink-based WEC Sim model of the first gen (V1.0) Hydraulic PTO (power take-off) that was designed for the HERO WEC - wecSimInputFile.m: Input file needed to run the model - userDefinedFunctionsMCR.m: MCR (multi condition run) script that is needed if a use wants to simulate multiple wave conditions. - geometry (folder): Includes the geometry file that is needed for visualization - hydroData (folder): Includes the required WAMIT data to run WEC-Sim

16 TIDAL AND WAVE POWER↗

DOE OSTI2022

HERO WEC V1.0 - SolidWorks Model

The attached zip file includes a SolidWorks pack-and-go assembly of NREL's HERO WEC (hydraulic and electric reverse osmosis wave energy converter) V1.0. This model does not include all aspects of the design (i.e. RO (reverse osmosis) system, electrical enclosure, hose, cable) it only includes the WEC and PTO (power take-off) design.

16 TIDAL AND WAVE POWER↗

DOE OSTI2022

HERO WEC V1.0 - Electrical PTO Deployment Data and Analysis

This submission includes the processed and raw field electrical data from NREL's August 2022 HERO WEC (hydraulic and electric reverse osmosis wave energy converter) deployment at Jennette's Pier for the electrical PTO (power take-off).

16 TIDAL AND WAVE POWER↗