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TEAMER: Numerical Modeling and Optimization of the iProTech Pitching Inertial Pump (PIP) Wave Energy Converter (WEC)

This project focused on developing an automated workflow to evaluate and optimize the iProTech Pitching Inertial Pump (PIP) wave energy converter (WEC) using open-source Python packages and the MATLAB/Simulink tool, WEC-Sim. The process involved parameterizing key design variables, running time-domain simulations, and performing sensitivity analyses to determine their impact on power output. The workflow, designed for the PIP device, is generalized and can be extended to optimize other WECs that can be simulated in WEC-Sim. This work establishes a foundation for future time-domain-based WEC design optimizations. Included in this submission are all figures from the final report and the model inputs required to generate them. This includes Python scripts with inputs that produce the meshes, boundary element method (BEM) models, hydrodynamic coefficients, and the WEC-Sim models used for time-domain analyses. Although data for every single run is not included to save space, all of it can be reproduced using the provided models. Detailed instructions for setting up the environment and running the codes are also included.

16 TIDAL AND WAVE POWER↗

Hydrodynamics and Load Shedding Behavior of a Variable-Geometry Oscillating Surge Wave Energy Converter (OSWEC)

In order to improve their long-term viability, wave energy converters (WECs) need to be able to shed loads when a threshold wave condition is exceeded. As shown by Tom et al. (2016) [1], provision of adjustable flaps within the body of an oscillating surge wave energy converter (OSWEC) allows wave energy to pass through the device. A control system may then be able to open and close the flaps when waves approaching the device exceed preset thresholds. The variable-geometry OSWEC (VG-OSWEC) concept studied in this paper is a bottom-hinged, rectangular wave paddle with five flaps of elliptical cross-section embedded into the face of the paddle. System ID tests were conducted on this VG-OSWEC device at a 1:14 scale in a wave basin. Free decay tests showed that the damping was distinctly nonlinear when the flaps were fully open, and the natural frequency increased by 40% when compared with the flaps in a fully closed configuration. Tests with regular wave conditions were used to develop the response amplitude operator for the rotational motion about the hinge. These response amplitude operator results when compared with numerical simulations run using WEC-Sim/WAMIT and ANSYS AQWA, show strong agreement with the flap open and closed conditions. The regular-wave condition measurements also show that the wave excitation moment about the hinge was reduced by up to 60% when the flaps were fully open. The experiments serve to demonstrate the potential of the variable geometry design to shed loads and survive harsh ocean environments.

load shedding↗

Effect of Mechanical Deformation on the Dielectric Electric Field in Dynamic Umbilical Cables

Wave energy converter (WEC) systems have unique umbilical cable design requirements compared to conventional marine designs. Due to their dynamic nature, WEC umbilical cables are required to handle increased loads and larger motions over longer deployment scenarios. However, the life expectancy of dynamic umbilical cables is predominantly analyzed for mechanical fatigue, with little consideration given to the effect of mechanical stress on the response of the dielectric as it has been previously assumed that the non-polymeric components will fail prior to the polymeric components. In this work, we explore the effects of mechanical bending on the concentration of the electric field in the insulation of a conceptual three-core dynamic umbilical cable to determine the limiting requirements for life expectancy. A conceptual industrial schematic of a medium voltage dynamic umbilical cable was used as the basis for the WEC system under study. Simulations on the dynamic umbilical cable were performed using COMSOL Multiphysics®. Mechanical loads up to the calculated limit (2.64 m minimum bend radius or 388 kN transverse load) were applied to the dynamic umbilical in a step-wise fashion with one end of the umbilical cable fixed. One-way coupling in three-dimensions was conducted by first determining the engineering strains, then using the engineering strains as the initial condition for determination of the Green-Lagrange strains, and lastly calculating the electric field in the deformed dielectric. Based upon the input load, deformation of the dielectric at the minimum bend radius produced an increase in the electric field of more than 12% when compared to the undeformed umbilical cable, which may lead to dielectric breakdown of the insulation prior to mechanical failure of the umbilical cable.

Spencer, Mychal P.↗

Lab Collaboration Project (LCP) for Marine Energy: Nonlinear Ocean Waves and PTO Control Strategy (Task 11)

The objectives for this task was to advance analysis and simulation capabilities for wave-WEC interactions and PTO analysis in nonlinear ocean waves. The improvements involve advancements in the generation of nonlinear wave time series and in nonlinear control strategies resulting in a detailed examination of WEC-wave interaction under scarcely-studied nonlinear conditions.

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Review of WEC-Sim Development and Applications

WEC-Sim (Wave Energy Converter Simulator) is an open-source code for simulating wave energy converters that has been actively developed and applied to simulate a wide variety of device archetypes, and has become a popular tool since its release. This paper reviews the development efforts and usage of WEC-Sim. The publications considered in this study have been broken down into six topic areas, namely, feature development, experimental validation, device modelling, control modelling, powertake-off (PTO) and grid modelling, and novel applications, which includes some non-wave energy applications. This review paper also recognizes the contributions of academic researchers and technology developers from around the world toward the broader WEC-Sim development effort. The growing number of external applications of WEC-Sim demonstrates a broader acceptance of the open-source code, and the ways WEC-Sim has been used in certain topic areas also highlight potential future development needs.

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Mooring System Cost Estimates for Wave Energy Farms in Shared Mooring Arrays

As wave energy converters (WECs) become more advanced and cost-efficient, so too must their mooring systems. A key question in the development plans for WECs is the cost of the mooring system, particularly for large wave farms. WEC devices deployed in a WEC farm array, where each device can be connected by shared mooring lines in various array layouts, have potential to reduce mooring system costs significantly. This paper presents the modeling and designing of mooring systems for large WEC arrays and the calculation of the cost of each mooring system to determine the change in cost as the number of WECs in a farm increases. A baseline mooring system for a single floating oscillating water column (OWC) WEC was developed for this analysis. The mooring system utilizes four anchored mooring lines connected to a square assembly of wire rope mooring lines, supported by four floating buoys, and attached to the floating WEC by four polyester rope mooring lines. This assembly, referred to as a floating cell, can be tiled to form various rectangular WEC arrays. The objective of this analysis is to determine how the mooring system cost changes as more WECs are added to an array layout, each with their own interconnected floating cell. To do this, complete mooring systems need to be designed for each WEC array layout. To narrow down the design space of a WEC array mooring system, a couple assumptions were made. It was assumed that the floating cell parameters of the baseline design were to stay constant across all floating cells in the WEC array. It was also assumed that the anchored mooring lines would be of the baseline configuration, a predominantly chain mooring line with a short section of polyester rope near the fairlead, and a drag-embedment anchor. These anchored lines were assumed to extend from the outer edges of the WEC array, inline with the headings of the wire rope mooring lines of the floating cells, or diagonal if extending from a corner of the WEC array. Full mooring systems were designed for 2xN and NxN WEC array layouts and efficiently simulated in the mooring dynamics simulation tool, MoorDyn, to ensure all dynamic constraints were met. The system costs were calculated and then refined by shortening unnecessary chain line lengths and reducing the chain diameters of the downstream anchored mooring lines. It was found that, in general, mooring system costs per WEC decrease when WECs are installed in an array. Compared to the baseline mooring system for a single WEC, the 2x3 mooring system array had the lowest mooring system cost per WEC, reducing the cost per WEC by 59%. The 3x3 and 4x4 array mooring systems also saw significant reductions in cost per WEC but had negligible cost savings between the two designs, primarily because the larger 4x4 mooring system requires larger chain diameters, which increases cost. These results provide an interesting glimpse into modeling, designing, and calculating the cost of mooring systems for large WEC arrays.

cost↗

Limits on the Range and Rate of Change in Power Take-Off Load in Ocean Wave Energy Conversion: A Study Using Model Predictive Control

Previous work comparing power take-off (PTO) architectures for ocean wave-powered reverse osmosis suggests that variable displacement in the wave energy converter (WEC)-driven pump does not offer a significant performance advantage. A limitation of that study is that the WEC was subject to a constant load within a given sea state (“Coulomb damping”) and did not account for controlled, moment-to-moment variation of the PTO load enabled by a variable displacement pump. This study explores the potential performance advantage of a variable PTO load over Coulomb damping. Model predictive control is used to provide optimal load control with constraints on the PTO load. The constraints include minimum and maximum loads and a limit on the rate of load adjustment. Parameter studies on these constraints enable conclusions about PTO design requirements in addition to providing an estimated performance advantage over Coulomb damping. Numerical simulation of the Oyster 1 WEC is carried out with performance weighted by historical sea state data from Humboldt Bay, CA. The results show a performance advantage of up to 20% higher yearly-average power absorption over Coulomb damping. Additionally, the parameter studies suggest that the PTO load should be adjustable down to at least 25% of the maximum load and should be adjustable between the minimum and maximum loads within a few seconds.

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Advanced Laboratory and Field Arrays (ALFA)/Lab Collaboration Project (LCP) for Marine Energy (Final Scientific/Technical Report)

The objective of the Advanced Laboratory and Field Arrays (ALFA) project was to reduce the Levelized Cost of Energy (LCOE) of Marine and Hydrokinetic (MHK) energy by leveraging research, development, and testing capabilities at Oregon State University, University of Washington, and the University of Alaska, Fairbanks. ALFA is a project within the Pacific Marine Energy Center (PMEC; formerly NNMREC), a multi-institution entity with a diverse funding base that focuses on research and development for marine renewables. The ALFA project aimed to accelerate the development of next-generation arrays of wave energy conversion (WEC) and tidal energy conversion (TEC) devices through a suite of field-focused R&D activities spanning a broad range of strategic opportunity areas identified in the Funding Opportunity Announcement: • Device and/or array operation and maintenance (O&M) logistics development; • High-fidelity resource characterization and/or modeling technique development and validation; • Array-specific component technology development (e.g. moorings and foundations, transmission, and other offshore grid components); • Array performance testing and evaluation; and • Novel cost-effective environmental monitoring techniques and instrumentation testing and evaluation. The objective of the Lab Collaboration Project (LCP) was to accelerate the development of next-generation marine energy conversion systems. The LCP aimed to achieve these project objectives in collaboration with the national laboratories by: • Developing concept generation and assessment tools; • Improving access to existing testing resources; • Validating collision risk models between fish and turbines; and • Advancing analysis and simulation capabilities for wave-WEC interactions and PTO analysis in nonlinear ocean waves. The ALFA portion of the project was comprised of six overarching technical tasks: • Task 1: Debris Modeling, Detection and Mitigation; • Task 2: Autonomous Monitoring & Intervention; • Task 3: Resource Characterization for Extreme Conditions; • Task 4: Robust Models for Design of Offshore Anchoring and Mooring Systems; • Task 5: Performance Enhancement for Marine Energy Converter (MEC) Arrays; and • Task 6: Evaluating Sampling Techniques for MHK Biological Monitoring. The LCP was divided into four overarching technical tasks: • Task 7: Project Management and Reporting • Task 8: Novel Design and Assessment Methodologies for Wave Energy Converter Design (Wave- SPARC) • Task 9: Testing Access for Commercial Marine Renewable Energy Technology Developers • Task 10: Quantifying Collision Risk for Fish and Turbines • Task 11: Nonlinear Ocean Waves and PTO Control Strategy Each ALFA/LCP task listed above functioned as a separate and discreet project. A final Technical Report was written for each individual task and these reports were uploaded to OSTI, after receiving DOE approval. The following document is a compilation of each of these final, approved reports arranged as individual chapters.

13 HYDRO ENERGY↗

Theoretical modeling of a bottom-raised oscillating surge wave energy converter structural loadings and power performances

Here, this study presents theoretical formulations to evaluate the fundamental parameters and performance characteristics of a bottom-raised oscillating surge wave energy converter (OSWEC) device. Employing a flat plate assumption and potential flow formulation in elliptical coordinates, closed-form equations for the added mass, radiation damping, and excitation forces/torques in the relevant pitch-pitch and surge-pitch directions of motion are developed and used to calculate the system's response amplitude operator and the forces and moments acting on the foundation. The model is benchmarked against numerical simulations using WAMIT and WEC-Sim, showcasing excellent agreement. The sensitivity of plate thickness on the analytical hydrodynamic solutions is investigated over several thickness-to-width ratios ranging from 1:80 to 1:10. The results show that as the thickness of the benchmark OSWEC increases, the deviation of the analytical hydrodynamic coefficients from the numerical solutions grows from 3% to 25%. Differences in the excitation forces and torques, however, are contained within 12%. While the flat plate assumption is a limitation of the proposed analytical model, the error is within a reasonable margin for use in the design space exploration phase before a higher-fidelity (and thus more computationally expensive) model is employed. A parametric study demonstrates the ability of the analytical model to quickly sweep over a domain of OSWEC dimensions, illustrating the analytical model's utility in the early phases of design.

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Numerical Model of IProTech PIP WEC Device

iProTech PIP wave energy converter (WEC) is a slack moored, single hull device with no moving parts in the water, joints or bearings. This submission includes data of the simulation, reports, and code for the iProTech PIP (WEC) project. The organization of the data included in the provided archive is detailed below and in the data description of the archive. The data teamer-iprotech-nrel folder includes and explains matlab and python code developed to hydrodynamically model the PIP WEC device in WEC-Sim. The subfolders cover the following steps: 1) report: explanatory information on device geometry 2) pip_mesher: python code to generate mesh panels from device profile data 3) wec-sim_models: matlab code to run WEC-Sim The data uploaded is a snapshot as of 11/02/2121 of code residing in a Github repository administered by David Ogden of NREL.

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Load Mitigating Feedback Control of WECs

This report outlines the development of load-mitigating feedback control for wave energy converters. A simple, self-tuning multi-objective controller is demonstrated in simulation for a 3-DOF (surge, heave, pitch) point absorber. In previous work, the proposed control architecture has been shown to be effective in experiment for a variety of device archetypes for the single objective of the maximization of electrical power capture: here this architecture is extended to reduce device loading as well. In particular, PTO actuation forces and the minimization of fatigue damage (determined from the sum of wave-exerted and PTO forces) are considered as additional objectives for the self-tuning controller. This controller is demonstrated for two similar, but distinct systems: one described by the identified linear models from physical testing of the WaveBot device, and another based upon a WEC-Sim simulation that expands upon boundary element method data from the WaveBot device. In both cases, because the power surface is consistently fairly flat in the vicinity of control parameters that maximize power capture in contrasting sea-states, it is found to be generally possible to mitigate either fatigue damage or PTO load. However, PTO load is found to conflict with fatigue damage in some sea-states, limiting the efficacy of control objectives that attempt to mitigate both simultaneously. Additionally, coupling between the surge and pitch DOFs also limits the extent to which fatigue damage can be mitigated for both DOFs in some sea-states. Because control objectives can be considered a function of the sea-state (e.g., load mitigation may not be a concern until the sea is sufficiently large) a simple transition strategy is proposed and demonstrated. This transition strategy is found to be effective with some caveats: firstly, it cannot circumvent the aforementioned objective contradictions. Secondly, this objective transition is too slow to act as a system constraint, and objective thresholds must thus be considered quite conservatively. Improvement of the adjustment strategy is demonstrated through the addition of an integral term. Selection of well-performing transition parameters can be a function of sea-state. While a simple selection procedure is proposed, it is non-optimal, and a more robust selection procedure is suggested for future work.

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Performance Modeling of a Variable-Geometry Oscillating Surge Wave Energy Converter on a Raised Foundation

This paper analyzes the power capture potential, structural loadings, and costs associated with an oscillating surge wave energy converter (OSWEC) operating on a raised foundation. The raised OSWEC offers opportunities for reduced installation costs, improved energy production, and greater flexibility of deployment when compared with fixed-bottom models. In this investigation, we simulated several different foundation geometries using WEC-Sim to estimate power capture and structural loads. In an effort to maximize power capture, several cases in which flat plates of varying size were attached to the top of the foundation, under and parallel with the OSWEC, were also simulated. These plates were found to enhance power capture by preventing the wave-induced pressure from passing underneath the OSWEC, diverting this pressure toward the OSWEC instead. The OSWEC was simulated in the six Wave Energy Prize sea states, which were chosen as a representative sample of U.S. deployment sites. A first-order estimate of structural costs was calculated using the Wave Energy Prize ACE metric, with the foundation comprised predominantly of steel-reinforced concrete and the OSWEC comprised of A36 steel. Influence of foundation geometry on power capture, structural loadings, and ACE are topics of particular interest. This work has been inspired by advances in large-scale additive manufacturing techniques that have the potential to dramatically reduce the cost of subsea foundations. These advancements may enable cost-effective WEC systems to be deployed on raised foundations.

cost↗

Multibody for Everybody (M4E) - A Linearization Approach to Enable Frequency Domain Analysis, Time Integration and Control Co-Design

1.1 Background/Objectives: Marine energy represents a promising yet underexploited source of power. To increase the harvested power, significant efforts have been made to improve wave energy converter (WEC) modeling capabilities and optimize power take-off (PTO) performance; however, these efforts have often treated WEC dynamics, PTO design, and controller development sequentially. In contrast, control co-design (CCD) is emerging as a promising strategy to address these issues directly, creating a growing need for fast analysis tools suitable for repeated simulation and parametric studies [1]. To support this need, this work presents the Multibody for Everybody (M4E) [2] linearization module, which employs a symbolic toolbox to provide deeper insight of WEC design parameters. The objective is to demonstrate that a minimal-coordinate linearization of articulated WEC dynamics can provide accurate wave response predictions and substantial computational savings relative to nonlinear time-domain simulation, while preserving compatibility with broader wave-energy analysis workflows, enabling CCD. 1.2 Approach/Activities: The proposed approach linearizes the equations of motion, generated by M4E, in minimal coordinates about a selected operating point and combines the resulting system with frequencydomain hydrodynamic terms to incorporate the reduced mass, damping, stiffness, and forcing operators. The linearized model is used for both impedance-based response amplitude operator (RAO) prediction and rapid regular-wave time integration. The methodology is demonstrated on a single-flap device and a FOSWEC configuration, with linearized M4E responses compared against the corresponding nonlinear M4E simulations and WEC-Sim results. Regular-wave time histories, RAO trends, and runtime differences are assessed. The framework is also compatible with broader wave-energy workflows, including coupling to WecOptTool, although that capability is not the focus of this work [3]. 1.3 Results/Lessons: The linearized M4E model reproduces key regularwave response characteristics such as integration and Response Amplitude over multiple frequencies. This module matches nonlinear M4E and WEC-Sim results while substantially reducing integration cost. Thus, the proposed framework can serve as a rapid analysis layer for articulated WEC design, parameter studies, and controls-oriented workflows. The analysis is most appropriate in the near-equilibrium regime, about the linearization point.

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DOE WPTO FY2021 Seedling End Report: Coupling Soil-Foundation Models to MHK Device Dynamic Models to Tighten the Design Envelope

The purpose of this Seedling project is to couple a marine renewable energy (MRE) dynamics simulation software with the soil-foundation models in the OC6 Phase II project [Bergua et al., 2021] and evaluate the software’s performance. This is a first step to accurately evaluating soil-foundation impacts on other types of MRE, like wave or current energy converters (WECs, CECs). OC6 Phase II compares offshore wind turbine (OWT) simulations using several different soil-foundation models to identify and fill key gaps in soil-foundation analyses. WEC-Sim was chosen to model the OC6 Phase II offshore wind turbine and various load cases because of its adaptability, accuracy of hydrodynamic loads, and ability to apply an arbitrary wind loading. Of the four methods used in OC6, the apparent fixity soil-foundation method was coupled with WEC-Sim. Technical challenges with flexible hydrodynamic bodies, added mass and external function libraries inhibited the ability to compare the WEC-Sim results to other OC6 participants. These challenges required that the WEC-Sim model of the OC6 OWT use a combination of rigid and flexible bodies to ensure a numerically stable solution. The rigid monopile creates a more stiff system and causes smaller amplitude motion under hydrodynamic loading and higher dominant frequency of motion under wind loading. These discrepancies are expected based on the increased stiffness of the WEC-Sim case.

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TEAMER Technical Support of Ramboll's for Numerical Modeling of WECs to Support OES Task 10: Cooperative Research and Development (Final Report)

National Technology & Engineering Solutions of Sandia, LLC (NTESS) in collaboration with the National Renewable Energy Laboratory (NREL), and with guidance from Ramboll, will perform fluid dynamics simulations to support of The Ocean Energy Systems (OES) Energy Technology Collaboration Program Task 10 Wave Energy Converters (WEC) Modelling Verification and Validation effort. Specific numerical simulations include the fixed device wave impingement studies to benchmark the performance of simulation techniques against physical testing results.

16 TIDAL AND WAVE POWER↗

Numerical Modeling & Optimization of the iProTech Pitching Inertial Pump (PIP) Wave Energy Converter (WEC) (CRADA Final Report)

This project represents a continuation of the collaboration between iProTech and NLR to simulate, optimize and design the iProTech Pitching Inertial Pump (PIP) device. The objectives of this TEAMER project are twofold: 1. Refining the physical characteristics of the existing iProTech PIP WEC-Sim model to enhance the model’s fidelity and include controllable components. Key model enhancements target the inclusion of Coulomb friction, the introduction of a controllable bypass valve, and the replacement of traditional check valves with advanced motorized ones. 2. Exploring traditional and advanced control algorithms. From traditional methods like latching control to cutting-edge reinforcement learning (RL) algorithms, the goal is to ensure the PIP device's adaptability and optimal performance across a range of ocean conditions. NLR is tasked with augmenting the WEC-Sim model and implementing the control algorithms, culminating in performance comparison analyses. iProTech will update their existing 3D models, advise on model improvements, and determine crucial system metrics. WEC-Sim, developed in MATLAB/SIMULINK with Simscape Multibody, is the main piece of software that will be used in this project. Coupled with the MATLAB RL Toolbox, it offers a robust platform for in-depth simulation and optimization of the iProTech PIP device. Building on previous work to explore the PIP design space and optimize its geometry, mass distribution, center of gravity and other key parameters, this project aims to refine iProTech’s existing numerical models and develop effective control algorithms that can seamlessly integrate into their future hardware testing campaigns.

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Initial Characterization of the NREL Large-Amplitude Motion Platform

The Large Amplitude Motion Platform (LAMP) at NREL represents a significant advancement in the controlled testing of Wave Energy Converters (WECs) under laboratory conditions. Originally designed by E2M as a six-degree-of-freedom (DOF) Stewart platform for flight simulation, LAMP has been adapted by NREL to facilitate the mounting and evaluation of WECs. This adaptation enables dry testing of WECs using motion profiles similar to the ocean, facilitating the iterative design, testing, and validation of WEC performance prior to ocean deployments. This report presents the initial work completed to characterize LAMP, with particular emphasis on its stability and operational capabilities across various single and multi-degree-of-freedom (DOF) motion profiles. The report includes planned comparisons at three distinct mass payloads, aimed at assessing the platform's positional accuracy, frequency response, and endurance over extended runtime periods. These experimental tests are critical for establishing the platform's limitations and ensuring that the data generated during WEC validation is both accurate and reproducible. The outcomes of this study not only contribute to a deeper understanding of LAMP's capabilities but also lay the groundwork for future advancements in WEC testing methodologies. By providing robust and reliable performance data within a controlled laboratory setting, the findings are expected to significantly enhance the development and commercialization of marine energy technologies. This report presents the initial findings of the LAMP Characterization work and proposed steps to further understand and characterize LAMP. Data collected during this work can be found on MHKDR at: https://mhkdr.openei.org/submissions/602 Note that this report shares the measured/found instantaneous maximum operating range of LAMP. For most applications the maximum operating range cannot be used for system health and longevity. The operating range and capabilities of LAMP will be evaluated on a case-by-case basis, single-DOF position, velocity, and acceleration values presented in Table 4a-c, and Table 5 should be taken as instantaneous absolute maximum values. Future use of LAMP will likely be limited to smaller values.

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