Publications

This article describes the theory, analysis, and initial bench-top testing of a minimally invasive, rotational resonator designed to produce small amounts of electrical energy for use in oceanic observation buoys. This work details the systems of equations that govern such a resonator, its potential power production, and its predicted effects on the modified motion of the buoy. Finally, a bench-top test apparatus is designed and experimented upon to identify the system and verify the system of equations empirically.

Researchers are exploring adding wave energy converters to existing oceanographic buoys to provide a predictable source of renewable power. A ”pitch resonator” power take-off system has been developed that generates power using a geared flywheel system designed to match resonance with the pitching motion of the buoy. However, the novelty of the concept leaves researchers uncertain about various design aspects of the system. This work presents a novel design study of a pitch resonator to inform design decisions for an upcoming deployment of the system. The assessment uses control co-design via WecOptTool to optimize control trajectories for maximal electrical power production while varying five design parameters of the pitch resonator. Given the large search space of the problem, the control trajectories are optimized within a Monte Carlo analysis to identify optimal designs, followed by parameter sweeps around the optimum to identify trends between the design parameters. The gear ratio between the pitch resonator spring and flywheel are found to be the most sensitive design variables to power performance. The assessment also finds similar power generation for various sizes of resonator components, suggesting that correctly designing for optimal control trajectories at resonance is more critical to the design than component sizing.

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This article describes the implementation of a new numerical model of the power take-off system installed in the Monterey Bay Aquarium Research Institute wave energy converter, a device developed to provide power to various oceanic research missions. The simultaneous presence of hydraulic, pneumatic, and electrical subsystems in the power take-off system represents a significant challenge in forging an accurate model able to replicate the main dynamic characteristics of the system. The validation of the new numerical model is addressed by comparing simulations with the measurements obtained during a series of bench tests. Data from the bench tests show good agreement with the numerical model. The validated model provides deeper insights into the complex nonlinear dynamics of the power take-off system and will support further performance improvements in the future.

Wave energy converters (WECs) are designed to produce useful work from ocean waves. This useful work can take the form of electrical power or even pressurized water for, e.g., desalination. This report details the findings from a wave tank test focused on that production of useful work. To that end, the experimental system and test were specifically designed to validate models for power transmission throughout the WEC system. Additionally, the validity of co-design informed changes to the power take-off (PTO) were assessed and shown to provide the expected improvements in system performance.

The “Pioneer WEC” project is targeted at developing a wave energy generator for the Coastal Surface Mooring (CSM) system within the Ocean Observatories Initiative (OOI) Pioneer Array. The CSM utilizes solar photovoltaic and wind generation systems, along with rechargeable batteries, to power multiple sensors on the buoy and along the mooring line. This approach provides continuous power for essential controller functions and a subset of instruments, and meets the full power demand roughly 70% of the time. Sandia has been tasked with designing a wave energy system to provide additional electrical power and bring the CSM up-time for satisfying the full-power demand to 100%. This project is a collaboration between Sandia and Woods Hole Oceanographic Institution (WHOI), along with Evergreen Innovations, Monterey Bay Aquarium Research Institute (MBARI), Eastern Carolina University (ECU), Johns Hopkins University (JHU), and the National Renewable Energy Laboratory (NREL). This report captures Phase I of an expected two phase project and presents project scoping and concept design results. phase project and presents project scoping and concept design results.

Improved power take-off (PTO) controller design for wave energy converters is considered a critical component for reducing the cost of energy production. However, the device and control design process often remains sequential, with the space of possible final designs largely reduced before the controller has been considered. Control co-design, whereby the device and control design are considered concurrently, has resulted in improved designs in many industries, but remains rare in the wave energy community. In this paper we demonstrate the use of a new open-source code, WecOptTool, for control co-design of wave energy converters, with the aim to make the co-design approach more accessible and accelerate its adoption. Additionally, we highlight the importance of designing a wave energy converter to maximize electrical power, rather than mechanical power, and demonstrate the co-design process while modeling the PTO's components (i.e., drive-train and generator, and their dynamics). We also consider the design and optimization of causal fixed-structure controllers. The demonstration presented here considers the PTO design problem and finds the optimal PTO drive-train that maximizes annual electrical power production. The results show a 22% improvement in the optimal controller and drive-train co-design over the optimal controller for the nominal, as built, device design.

The wave energy control competition established a benchmark problem which was offered as an open challenge to the wave energy system control community. The competition had two stages: In the first stage, competitors used a standard wave energy simulation platform (WEC-Sim) to evaluate their controllers while, in the second stage, competitors were invited to test their controllers in a real-time implementation on a prototype system in a wave tank. The performance function used was based on converted energy across a range of standard sea states, but also included aspects related to economic performance, such as peak/average power, peak force, etc. This paper compares simulated and experimental results and, in particular, examines if the results obtained in a linear system simulation are borne out in reality. Overall, within the scope of the device tested, the range of sea states employed, and the performance metric used, the conclusion is that high-performance WEC controllers work well in practice, with good carry-over from simulation to experimentation. However, the availability of a good WEC mathematical model is deemed to be crucial.

This report describes testing conducted related to the development of a “hydrostatic power takeoff” (HPTO) system for a wave energy converter. Tests were conducted with an experimental electric motor rig to provide preliminary results and de-risk future testing. Efficiency mapping tests were conducted as well as hardware-in-the-loop (HIL) testing. The results of the efficiency mapping tests provide good insight into how to systematically perform efficiency mapping tests. The HIL testing indicates good overall performance of the system and provides a stepping stone towards more complete system tests in the future.

The open-source WecOptTool was developed to make wave energy converter (WEC) control co-design accessible. WecOptTool is based on the pseudo-spectral method which is capable of efficiently dealing with any linear or nonlinear constraints and nonlinear dynamics by solving the WEC optimal control problem in the time domain using a gradient based optimization algorithm. This work1 presents a control co-optimization study of the AquaHarmonics Inc. heaving point absorber WEC sized for ocean deployment to solve practical industry design problems. Components such as the specific type of generator, the hull shape, and the displaced volume are pre-determined. We co-optimize the WEC’s mass versus mooring line pretension in conjunction with the controller. The optimization is subject to the power-take-off (PTO) dynamics and the rated constraints of the components. In particular, the continuous torque rating is implemented as an explicit constraint, a novel approach for WEC optimization. The PTO dynamics are incorporated into the optimization algorithm via a combination of first principle methods (linear drivetrain model) and empirical efficiency maps (electrical generator) represented as a power loss map. This is a practical method applicable to a variety of PTO architectures and transferable to other WECs. A discussion between using an efficiency coefficient versus a power loss map and their implication for the optimization method is presented. This application of WecOptTool represents a real world WEC by combining simplified models with empirical efficiency data. The WEC, as a dynamically coupled, oscillatory system, requires consideration of the time trajectory dependent power loss for optimizing the average electrical power. This objective function, the modelling approach, and the realistic loss terms makes the common practice of artificially penalizing the reactive power needless.

As part of the development process, scaled testing of wave energy converter devices are necessary to prove a concept, study hydrodynamics, and validate control system approaches. Creating a low-cost, small, lightweight data acquisition system suitable for scaled testing is often a barrier for wave energy converter developers’ ability to test such devices. This paper outlines an open-source solution to these issues, which can be customized based on specific needs. This will help developers with limited resources along a path toward commercialization.

As part of the development process, scaled testing of wave energy converter devices are necessary to prove a concept, study hydrodynamics, and validate control system approaches. Creating a low-cost, small, lightweight data acquisition system suitable for scaled testing is often a barrier for wave energy converter developers’ ability to test such devices. This paper outlines an open-source solution to these issues, which can be customized based on specific needs. Furthermore, this will help developers with limited resources along a path toward commercialization.

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With a wide variety of wave energy device archetypes currently under consideration, it is a major challenge to ensure that research findings and methods are broadly applicable. In particular, the design and testing of wave energy control systems, a process which includes experimental design, empirical modeling, control design, and performance evaluation, is of interest. This goal motivated the redesign and testing of a floating dual flap wave energy converter. As summarized in this paper, the steps taken in the design, testing, and analysis of the device mirrored those previously demonstrated on a three-degree of freedom point absorber device. The method proposed does not require locking WEC degrees of freedom to develop an excitation model, and presents a more attainable system identification procedure for at-sea deployments. The results show that the methods employed work well for this dual flap device, lending additional support for the broad applicability of the design and testing methods applied here. The aim of this paper is to demonstrate that these models are particularly useful for deducing areas of device design or controller implementation that can be reasonably improved to increase device power capture.

This paper compares four different formulations of model predictive control that attempt to maximise electrical power generated by a wave energy converter (WEC). Control laws include (1) pure maximisation of mechanical power, (2) maximisation of mechanical power with a control penalty factor, (3) maximisation of electrical power using power conversion efficiency, and (4) maximisation of electrical power using the full electro-mechanical model of a system. For this study, a wave-to-wire model is developed for a floating spherical buoy connected to a permanent magnet synchronous generator. The performance of the controllers, including the mechanical and electrical power outputs, is compared in irregular wave conditions for the unconstrained and force-constrained scenarios. The results demonstrate that the controller designed to maximise mechanical power is not suitable for practical applications and may lead to negative electrical power output due to the non-ideal power take-off efficiency. Moreover, the replacement of the power take-off dynamics by the efficiency coefficient does not guarantee the maximum electrical power production.

Wave energy converters have yet to reach broad market viability. Traditionally, levelized cost of energy has been considered the ultimate stage gate through which wave energy developers must pass in order to find success (i.e., the levelized cost of wave energy must be less than that of solar and wind). However, real world energy decisions are not based solely on levelized cost of energy. In this study, we consider the energy mix in California in the year 2045, upon which the state plans to achieve zero carbon energy production. By considering temporal electricity production and consumption, we are able to perform a more informed analysis of the decision process to address this challenge. The results show that, due to high level of ocean wave energy in the winter months, wave energy provides a valuable complement to solar and wind, which have higher production in the summer. Thus, based on this complementary temporal aspect, wave energy appears cost-effective, even when the cost of installation and maintenance is twice that of solar and wind.

Wave energy converters have yet to reach broad market viability. Traditionally, levelized cost of energy has been considered the ultimate stage gate through which wave energy developers must pass in order to find success (i.e., the levelized cost of wave energy must be less than that of solar and wind). However, real world energy decisions are not based solely on levelized cost of energy. In this study, we consider the energy mix in California in the year 2045, upon which the state plans to achieve zero carbon energy production. By considering temporal electricity production and consumption, we are able to perform a more informed analysis of the decision process to address this challenge. The results show that, due to high level of ocean wave energy in the winter months, wave energy provides a valuable complement to solar and wind, which have higher production in the summer. Thus, based on this complementary temporal aspect, wave energy appears cost-effective, even when the cost of installation and maintenance is twice that of solar and wind.

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While a great deal of research has been performed to quantify and characterize the wave energy resource, there are still open questions about how a wave energy developer should use this wave resource information to design a wave energy converter device to suit a specific environment or, alternatively, to assess potential deployment locations. It is natural to focus first on the impressive magnitudes of power available from ocean waves, and to be drawn to locations where mean power levels are highest. However, a number of additional factors such as intermittency and capacity factor may be influential in determining economic viability of a wave energy converter, and should therefore be considered at the resource level, so that these factors can influence device design decisions. This study examines a set of wave resource metrics aimed towards this end of bettering accounting for variability in wave energy converter design. The results show distinct regional trends that may factor into project siting and wave energy converter design. Although a definitive solution for the optimal size of a wave energy converter is beyond the reaches of this study, the evidence presented does support the idea that smaller devices with lower power ratings may merit closer consideration.

Interest in wave energy converters to provide autonomous power to various ocean-bound systems, such as autonomous underwater vehicles, sensor systems, and even aquaculture farms, has grown in recent years. The Monterey Bay Aquarium Research Institute has developed and deployed a small two-body point absorber wave energy device suitable to such needs. This paper provides a description of the system to support future open-source access to the device and further the general development of similar wave energy systems. Additionally, to support future control design and system modification efforts, a set of hydrodynamic models are presented and cross-compared. To test the viability of using a linear frequency-domain admittance model for controller tuning, the linear model is compared against four WEC-Sim models of increasing complexity. The linear frequency-domain model is found to be generally adequate for capturing system dynamics, as the model agreement is good and the degree of nonlinearity introduced in the WEC-Sim models is generally less than 2.5%.

The potential for control design to dramatically improve the economic viability of wave energy has generated a great deal of interest and excitement. However, for a number of reasons, the promised benefits from better control designs have yet to be widely realized by wave energy devices and wave energy remains a relatively nascent technology. This brief paper summarizes a simple, yet powerful approach to wave energy dynamics modeling, and subsequent control design based on impedance matching. Our approach leverages the same concepts that are exploited by a simple FM radio to achieve a feedback controller for wave energy devices that approaches optimal power absorption. If fully utilized, this approach can deliver immediate and consequential reductions to the cost of wave energy. Additionally, this approach provides the necessary framework for control co-design of a wave energy converter, in which an understanding of the control logic allows for synchronous design of the device control system and hardware.

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The present work addresses the need for an efficient, versatile, accurate and open-source numerical tool to be used during the design stage of wave energy converters (WECs). The device considered here is the heaving point-absorber developed and tested by Sandia National Laboratories. The smoothed particle hydrodynamics (SPH) method, as implemented in DualSPHysics, is proposed since its meshless approach presents some important advantages when simulating floating devices. The dynamics of the power take-off system are also modelled by coupling DualSPHysics with the multi-physics library Project Chrono. A satisfactory matching between experimental and numerical results is obtained for: (i) the heave response of the device when forced via its actuator; (ii) the vertical forces acting on the fixed device under regular waves and; (iii) the heave response of the WEC under the action of both regular waves and the actuator force. This proves the ability of the numerical approach proposed to simulate accurately the fluid–structure interaction along with the WEC’s closed-loop control system. In addition, radiation models built from the experimental and WAMIT results are compared with DualSPHysics by plotting the intrinsic impedance in the frequency domain, showing that the SPH method can be also employed for system identification.

This paper reports results from an ongoing investigation on potential ways to utilize small wave energy devices that can be transported in, and deployed from, torpedo tubes. The devices are designed to perform designated ocean measurement operations and thus need to convert enough energy to power onboard sensors, while storing any excess energy to support vehicle recharging operations. Examined in this paper is a traditional tubular oscillating water column device, and particular interest here is in designs that lead to optimization of power converted from shorter wind sea waves. A two step design procedure is investigated here, wherein a more approximate two-degree-of-freedom model is first used to identify relative dimensions (of device elements) that optimize power conversion from relative oscillations between the device elements. A more rigorous mathematical model based on the hydrodynamics of oscillating pressure distributions within solid oscillators is then used to provide the hydrodynamic coefficients, forces, and flow rates for the device. These results provide a quick but rigorous way to estimate the energy conversion performance of the device in various wave climates, while enabling more accurate design of the power takeoff and energy storage systems.

The main objective of this letter is to consolidate the knowledge about the dynamics and control of oscillating-body wave energy converters (WECs). A number of studies have shown that control systems strongly affect power absorption; however, there remains a need for a concise and integrated explanation of the theoretical and practical implications that control can have on both performance and the broader WEC design process. This short letter attempts to fill this gap by presenting a discussion on the key practical aspects concerning the dynamics and control of oscillating-body WEC. In particular, the focus is on the choice of control models and a simple causal control scheme suitable for real-time implementation. Finally, consideration is given to the effect of the power takeoff (PTO) on the maximization of electrical power, thus leading to the derivation of useful conditions for the control co-design of the PTO system.

This study presents a numerical model of a WEC array. The model will be used in subsequent work to study the ability of data assimilation to support power prediction from WEC arrays and WEC array design. In this study, we focus on design, modeling, and control of the WEC array. A case study is performed for a small remote Alaskan town. Using an efficient method for modeling the linear interactions within a homogeneous array, we produce a model and predictionless feedback controllers for the devices within the array. The model is applied to study the effects of spectral wave forecast errors on power output. The results of this analysis show that the power performance of the WEC array will be most strongly affected by errors in prediction of the spectral period, but that reductions in performance can realistically be limited to less than 10% based on typical data assimilation based spectral forecasting accuracy levels.

Potential performance gains from optimal (non-causal) impedance-matching control of wave energy devices in irregular ocean waves are dependent on deterministic wave elevation prediction techniques that work well in practical applications. Although a number of devices are designed for operation in intermediate water depths, little work has been reported on deterministic wave prediction in such depths. Investigated in this paper is a deterministic wave-prediction technique based on an approximate propagation model that leads to an analytical formulation, which may be convenient to implement in practice. To improve accuracy, an approach to combine predictions based on multiple up-wave measurement points is evaluated. The overall method is tested using experimental time-series measurements recorded in the U.S. Navy MASK basin in Carderock, MD, USA. For comparison, an alternative prediction approach based on Fourier coefficients is also tested with the same data. Comparison of prediction approaches with direct measurements suggest room for improvement. Possible sources of error including tank reflections are estimated, and potential mitigation approaches are discussed.

While some engineering fields have benefited from systematic design optimization studies, wave energy converters have yet to successfully incorporate such analyses into practical engineering workflows. The current iterative approach to wave energy converter design leads to sub-optimal solutions. This short paper presents an open-source MATLAB toolbox for performing design optimization studies on wave energy converters where power take-off behavior and realistic constraints can be easily included. This tool incorporates an adaptable control co-design approach, in that a constrained optimal controller is used to simulate device dynamics and populate an arbitrary objective function of the user’s choosing. A brief explanation of the tool’s structure and underlying theory is presented. To demonstrate the capabilities of the tool, verify its functionality, and begin to explore some basic wave energy converter design relationships, three conceptual case studies are presented. In particular, the importance of considering (and constraining) the magnitudes of device motion and forces in design optimization is shown.

This report describes the testing of a model scale wave energy converter. This device, which uses two aps that pivot about a central platform when excited by waves, has a natural frequency within the range of the waves by which it is excited. The primary goal of this test was to assess the degree to which previously developed modeling, experimentation, and control design methods could be applied to a broad range of wave energy converter designs. Testing was conducted to identify a dynamic model for the impedance and excitation behavior of the device. Using these models, a series of closed loop tests were conducted using a causal impedance matching controller. This report provides a brief description of the results, as well as a summary of the device and ex- perimental design. The results show that the methods applied to this experimental device perform well and should be broadly applicable.

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A self-tuning proportional-integral control law prescribing motor torques was tested in experiment on a three degree-of-freedom wave energy converter. The control objective was to maximize electrical power. The control law relied upon an identified model of device intrinsic impedance to generate a frequency-domain estimate of the wave-induced excitation force and measurements of device velocities. The control law was tested in irregular sea-states that evolved over hours (a rapid, but realistic time-scale) and that changed instantly (an unrealistic scenario to evaluate controller response). For both cases, the controller converges to gains that closely approximate the post-calculated optimal gains for all degrees of freedom. Convergence to near-optimal gains occurred reliably over a sufficiently short time for realistic sea states. In addition, electrical power was found to be relatively insensitive to gain tuning over a broad range of gains, implying that an imperfectly tuned controller does not result in a large penalty to electrical power capture. An extension of this control law that allows for adaptation to a changing device impedance model over time is proposed for long-term deployments, as well as an approach to explicitly handle constraints within this architecture.

Through the use of advanced control techniques, wave energy converters (WECs) can achieve substantial increases in energy absorption. The motion of the WEC device is a significant contribution to the energy absorbed by the device. Reactive (complex conjugate) control maximizes the energy absorption due to the impedance matching. The issue with complex conjugate control is that, in general, the controller is noncausal, which requires prediction of the incoming waves. This article explores the potential of employing system identification techniques to build a causal transfer function that approximates the complex conjugate controller over a finite frequency band of interest. This approach is quite viable given the band-limited nature of ocean waves. The resulting controller is stable, and the average efficiency of the power captured by the causal controller in realistic ocean waves is 99%, when compared to the noncausal complex conjugate.

Sandia National Laboratories and the Department of Energy (DOE) have completed on a multi-year program to examine the effects of control theory on increasing power produced by resonant wave energy conversion (WEC) devices. The tank tests have been conducted at the Naval Surface Warfare Center Carderock Division (NSWCCD) Maneuvering and Sea Keeping Basin (MASK) in West Bethesda, MD. This report outlines the "MASK₃" wave tank test within the Advanced WEC Dynamics and Controls (AWDC) project. This test represents the final test in the AWDC project. The focus of the MASK₃ test was to consider coordinated ₃-degree-of-freedom (₃DOF) control of a WEC in a realistic ocean environment. A key aspect of this test was the inclusion of a "self-tunine mechanism which uses an optimization algorithm to update controller gains based on a changing sea state. The successful implementation of the self-tuning mechanism is the last crucial step required for such a controller to be implemented in real ocean environments.

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This report serves as a comprehensive summary of the work completed by the "Advanced WEC Dynamics and Controls projecr during the period of 2013-2019. This project was first envisioned to simply consider the question of designing a controller for wave energy converters (WECs), without a complete recognition of the broader considerations that such a task must necessarily examine. This document describes both the evolution of the project scope and the key findings produced. The basic goal of the project has been to deliver tractable methodologies and work flows that WEC designers can use to improve the performance of their machines. Engineering solutions, which may offer 80% of the impact, but require 20% of the effort compared to a perfect result (which may be many years of development down the road) were preferred. With this doctrine, the work of the project often involved translating existing methods that have been successfully developed and applied for other fields, into the application area of wave energy.

This paper presents a nonlinear geometric buoy design for Wave Energy Converters (WECs). A nonlinear dynamic model is presented for an hour glass (HG) configured WEC. The HG buoy operates in heave motion or as a single Degree-of-Freedom (DOF). The unique formulation of the interaction between the buoy and the waves produces a nonlinear stiffening effect that provides the actual energy storage or reactive power during operation. A Complex Conjugate Control (C3) with a practical Proportional-Derivative (PD) controller is employed to optimize power absorption for off-resonance conditions and applied to a linear right circular cylinder (RCC) WEC. For a single frequency the PDC3 RCC buoy is compared with the HG buoy design. A Bretschneider spectrum of wave excitation input conditions are reviewed and evaluated for the HG buoy. Numerical simulations demonstrate power and energy capture for the HG geometric buoy design which incorporates and capitalizes on the nonlinear geometry to provide reactive power for the single DOF WEC. By exploiting the nonlinear physics in the HG design simplified operational performance is observed when compared to an optimized linear cylindrical WEC. The HG steepness angle α with respect to the wave is varied and initially optimized for improved energy capture.

Wave Energy Converter (WEC) technologies transform power from the waves to the electrical grid. WEC system components are investigated that support the performance, stability, and efficiency as part of a WEC array. To this end, Aquaharmonics Inc took home the 1.5 million grand prize in the 2016 U.S. Department of Energy Wave Energy Prize, an 18-month design-build-test competition to increase the energy capture potential of wave energy devices. Aquaharmonics intends to develop, build, and perform open ocean testing on a 1: 7 scale device. Preliminary wave tank testing on the mechanical system of the 1: 20 scale device has yielded a data-set of operational conditions and performance. In this paper, the Hamiltonian surface shaping and power flow control (HSSPFC) method is used in conjunction with scaled wave tank test data to explore the design space for the electrical transmission of energy to the shore-side power grid. Of primary interest is the energy storage system (ESS) that will electrically link the WEC to the shore. Initial analysis results contained in this paper provide a trade-off in storage device performance and design selection.

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This report details the background, design, and initial results for wave energy converter design optimization tool. This tool is intended to provide researchers and developers with a means of optimizing existing wave energy converter designs by including realistic dynamics and control algorithms early in the design cycle.