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DOE OSTI2022

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.

16 TIDAL AND WAVE POWER↗

DOE OSTI2023

A practical method for modeling temporally-averaged ocean wave frequency-directional spectra for characterizing wave energy climates

Wave energy resource characterization investigations have been hindered because frequency-directional wave spectra are not broadly available for many coastal regions due to the insufficient spatial coverage of buoy observation networks and spectral wave model hindcast outputs. We address this problem by developing and validating a practical method for approximating temporally-averaged frequency-directional wave spectra averaged over periods of months or years from bulk wave parameters, which are available at a much greater coverage and resolution than frequency-directional wave spectra. While the temporally averaged frequency-directional wave spectrum over these periods cannot be used for analyzing a single sea state, it aggregates multiple sea states, identifies dominant wave energy systems representing wave climate, and resolves their spectral characteristics. Therefore, modelling temporally averaged frequency-directional wave spectra is of great value for planning and designing wave energy projects, e.g., resource characterization, site assessment, and conceptual design of wave energy converters. Temporally-averaged frequency-directional wave spectra and related important wave energy parameters approximated using this method are found to be more accurate than commonly used parametric wave spectrum models. This method can be applied to a wide range of wave climates given its universality and high accuracy. Also, the availability of bulk wave parameters from multi-decade high-resolution wave model hindcasts is increasing.

16 TIDAL AND WAVE POWER↗

DOE OSTI2020

Characterization of Extreme Wave Conditions for Wave Energy Converter Design and Project Risk Assessment

Best practices and international standards for determining n-year return period extreme wave (sea states) conditions allow wave energy converter designers and project developers the option to apply simple univariate or more complex bivariate extreme value analysis methods. The present study compares extreme sea state estimates derived from univariate and bivariate methods and investigates the performance of spectral wave models for predicting extreme sea states at buoy locations within several regional wave climates along the US East and West Coasts. Two common third-generation spectral wave models are evaluated, a WAVEWATCH III® model with a grid resolution of 4 arc-minutes (6–7 km), and a Simulating WAves Nearshore model, with a coastal resolution of 200–300 m. Both models are used to generate multi-year hindcasts, from which extreme sea state statistics used for wave conditions characterization can be derived and compared to those based on in-situ observations at National Data Buoy Center stations. Comparison of results using different univariate and bivariate methods from the same data source indicates reasonable agreement on average. Discrepancies are predominantly random. Large discrepancies are common and increase with return period. There is a systematic underbias for extreme significant wave heights derived from model hindcasts compared to those derived from buoy measurements. This underbias is dependent on model spatial resolution. However, simple linear corrections can effectively compensate for this bias. A similar approach is not possible for correcting model-derived environmental contours, but other methods, e.g., machine learning, should be explored.

16 TIDAL AND WAVE POWER↗

DOE OSTI2020

Umbilical Fatigue Analysis for a Wave Energy Converter

Unique umbilical designs for wave energy converters (WECs), including the ability to handle significantly larger motions and loads over long deployments, are often required when conventional marine umbilical designs for offshore oil and gas and offshore wind may not meet the design and cost needs of wave energy technologies. This study details a fatigue analysis of a dynamic power umbilical attached to a two-body floating point absorber WEC system, using the sea states provided for the PacWave testing facilities. The 6 degrees of freedom motion time history for the WEC was simulated, and the motions of the attachment point for the umbilical on the WEC and respective sea states were used to analyze the dynamic motions and fatigue of the connected power umbilical to predict the fatigue life. The results show that the fatigue damage observed is more significant in shallow water, and extensive fatigue damage may occur because of the larger curvature response of the umbilical. The umbilical configurations departing at 90 deg off incoming waves were found to have the highest fatigue life attributed to less extension or compression of the umbilical. However, additional bend stiffener/limiter features may need to be incorporated into the buoyancy section and touchdown regions to minimize curvature-induced fatigue.

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

DOE OSTI2020

Numerical Model Development of a Variable-Geometry Attenuator Wave Energy Converter

Because the wave energy industry is still in its infancy, an optimal design for wave energy converters (WECs) has yet to be established; more work is needed to explore various cost-reduction pathways. The primary cost-reduction pathway considered for this work is the optimization of the geometric profile on an attenuator WEC to maximize power production while, at the same time, minimizing capital expenditures through the use of variable-geometry modules. In this investigation, the variable-geometry modules consist of inflatable bags placed on either side of a base central steel cylinder that would be inflated in low-moderate sea states to maximize power capture and then deflated in moderate-extreme sea states to minimize wave loading. The numerical model and simulation of the attenuator WEC were developed and completed using WEC-Sim, which is an open-source code that is appropriate for use in evaluating the dynamic response of the different WEC models in operational seas. The power production estimates were obtained from the Wave Energy Prize (WEP) sea states, which are representative of U. S. deployment sites, to calculate the average climate capture width that is used in the WEP ACE calculation. Preliminary capital expenditure costs were obtained assuming the base central steel cylinder mass was equal to the fluid displaced mass, minus the mass of the variable-geometry bags. The additional weight required to offset the additional buoyancy from the variable-geometry bags was assumed to come from the addition of seawater ballast. The variable-geometry attenuator model was found to have a similar power capture efficiency as a fixed-body model, but is expected to have a lower characteristic capital expenditure given its more streamlined profile, which demonstrates that variable-geometry modules may provide a realistic cost-reduction pathway to help design a more cost-competitive WEC.

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

DOE OSTI2020

Numerical Model Development of a Variable-Geometry Attenuator Wave Energy Converter: Preprint

Because the wave energy industry is still in its infancy, an optimal design for wave energy converters (WECs) has yet to be established; more work is needed to explore various cost reduction pathways. The primary cost-reduction pathway considered for this work is the optimization of the geometric profile on an attenuator WEC to maximize power production while, at the same time, minimizing capital expenditures through the use of variable-geometry modules. In this investigation, the variable geometry modules consist of inflatable bags placed on either side of a base central steel cylinder that would be inflated in low moderate sea states to maximize power capture and then deflated in moderate-extreme sea states to minimize wave loading. The numerical model and simulation of the attenuator WEC were developed and completed using WEC-Sim, which is an open-source code that is appropriate for use in evaluating the dynamic response of the different WEC models in operational seas. The power production estimates were obtained from the Wave Energy Prize (WEP) sea states, which are representative of U. S. deployment sites, to calculate the average climate capture width that is used in the WEP ACE calculation. Preliminary capital expenditure costs were obtained assuming the base central steel cylinder mass was equal to the fluid displaced mass, minus the mass of the variable-geometry bags. The additional weight required to offset the additional buoyancy from the variable-geometry bags was assumed to come from the addition of seawater ballast. The variable-geometry attenuator model was found to have a similar power capture efficiency as a fixed-body model, but is expected to have a lower characteristic capital expenditure given its more streamlined profile, which demonstrates that variable-geometry modules may provide a realistic cost-reduction pathway to help design a more cost-competitive WEC.

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

DOE OSTI2021

Open-Loop Control of Adjustable Tuned Mass Dampers for Floating Wind Turbine Platforms: Preprint

Floating offshore wind turbines have several advantages over their land-based counterparts, including access to stronger, more consistent winds and proximity to population centers. However, increased costs from the platform have been a challenge inhibiting their widespread adoption. New damping technologies with tunable target frequencies and damping ratios promise a greater degree of control over platform motions, allowing hulls to be designed smaller and reducing the overall cost of the turbines. In this work, a control strategy is proposed for these adjustable tuned mass dampers (TMDs). A frequency-domain model of the system is developed, from which response amplitude operators (RAOs) for the platform's rigid-body modes can be obtained for different natural frequencies and damping ratios of the dampers. Using these RAOs, and JONSWAP spectrums of operational and extreme sea states, the performance of the various damper settings are compared by evaluating the standard deviation of a rigid-body motion of interest (platform pitch or heave). By finding the optimal damper setting for a range of representative design load cases (DLCs), a lookup function is made to return the damper target frequency given the peak period of the sea state. To determine the current sea state, we propose a simple estimator that uses wave measurements (e.g., from a measurement buoy) to determine the peak period and significant wave height. The significant wave height is determined using the statistics of the past 100 seconds of wave elevation information and the peak period is computed using a frequency locked loop. Initial results show that we can use these estimated values to control the TMD natural frequency with an open loop controller. The controlled system is tested in a range of environmental conditions determined by the International Electrotechnical Commission design load cases (DLCs), which include normal and extreme wind and wave models. In these tests, we compare the performance of 4 cases: (1) no TMD, (2) a constant TMD based on the worst case DLC, (3) a controlled TMD based on known wind and wave environments, and (4) a real-time controlled TMD using estimated wind and wave environments. The effect of hull-based TMD control is also compared to changes in traditional wind turbine control via blade pitch.

control↗

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 OSTI2021

Open-Loop Control of Adjustable Tuned Mass Dampers for Floating Wind Turbine Platforms

In this study, we demonstrate the ability of adjustable tuned mass dampers (TMDs) to reduce the platform motion of floating offshore wind turbines (FOWTs). The TMDs are located in the hull and provide control authority by varying the amount of water ballast and compressed air in a reservoir over time. The optimal TMD settings depend on the wind and wave conditions of the FOWT. We present an open-loop control scheme that changes the TMD natural frequency based on sea state and a simple method for estimating the peak wave period and significant wave height. The performance of this open-loop control is compared to ideal control of the TMDs (set knowing the exact sea state), a TMD with a constant natural frequency targeting the design load case with the greatest platform motion, and a baseline set of simulations of the platform without TMDs. The constant natural frequency case performs nearly as effectively as the actively controlled case, suggesting that the TMDs can be simply designed for extreme load conditions and provide consistent control over a range of environments; however, the methods used to find the optimal TMD parameters and estimate sea state statistics could be used in other aspects of FOWT control and design.

artificial intelligence↗

DOE OSTI2023

A Comparison of Power Take-Off Architectures for Wave-Powered Reverse Osmosis Desalination of Seawater with Co-Production of Electricity

Several power take-off (PTO) architectures for wave-powered reverse osmosis (RO) desalination of seawater are introduced and compared based on the annual average freshwater production and the size of the components, which strongly relate to the costs of the system. The set of architectures compared includes a novel series-type PTO architecture not previously considered. These seawater hydraulic PTO architectures are composed of a WEC-driven pump, an RO module, an intake charge pump driven by an electric motor, and a hydraulic motor driving an electric generator for electric power production. This study is performed using an efficient two-way coupled steady-state model for the average performance of the system in a given sea state, including freshwater permeate production, electric power production, and electric power consumption. A multi-objective design problem is formulated for the purposes of this comparative study, with the objectives of maximizing annual freshwater production, minimizing the displacement of the WEC-driven pump, and minimizing the installed RO membrane area. This establishes a framework for comparison in the absence of a mature techno-economic model. The requirement that the system produces enough electric power to meet its consumption is applied as a constraint on the operation of the system. The oscillating wave surge converter Oyster 1 is assumed as the WEC. Weights on performance of the system in a given sea state are based on historical data from Humboldt Bay, CA. This study finds that (1) architectures in a series configuration allow for a reduction in the WEC-driven pump size of 59–92% compared to prior work, (2) varying the displacement of the WEC-driven pump between sea conditions does not provide any significant advantage in performance, and (3) varying the active RO membrane area between sea condition offers improvements between 7% and 41% in each design objective.

Energy & Fuels↗

DOE OSTI2020

Performance evaluation of surface riding wave energy converter with linear electric generator

In this work, we devised a new WEC (wave energy converter) called SR-WEC (Surface Riding WEC). The SR-WEC consists of two bodies: the outer cylinder with an armature assembly (body #1) and a magnet assembly (body #2) sliding inside the armature. For the SR-WEC, the relative sliding displacement and velocity are caused by gravity acceleration and the outer cylinder's motions, and they lead to electrical power generation. To evaluate its performance, a numerical simulation tool was developed, which solves the fully-coupled floater-mooring-generator dynamics. During the developing stage, the appropriate hydrodynamics model, sliding mechanics model, mooring dynamics model, and LEG (linear electric generator) electro-magnetic model were independently developed and then fully coupled in time domain to account for the cross-coupling interactions among them. Then, the developed simulation tool was verified component by component against various laboratory tests. Subsequently, systematic parametric studies were conducted with several important design parameters under various wave conditions to enhance power generation. After that, the average output power was evaluated in enlarged operational wave conditions. The present SR-WEC is particularly designed to be efficient at low sea states, which is good since they cover the majority of typical annual sea states.

42 ENGINEERING↗

DOE OSTI2023

An Efficient Three-Dimensional CFD-Based Numerical Wave Tank for a Wave Energy Converter in Extreme Irregular Waves

A numerical wave tank approach for computational fluid dynamics (CFD) modelling of an extreme irregular seastate is presented. The technique couples a potential flow solution with a CFD solver for more efficient numerical predictions. This method has recently become attractive both for the research community and the industry working with offshore structures. The model is used to determine the response of a submerged pressure differential wave energy converter (WEC) in a fully nonlinear irregular wave condition using the high-fidelity CFD code, STAR-CCM+. Potential flow based numerical models are commonly used to predict motions and performance of wave energy converters. Wave kinematics can deviate from potential flow predictions for extreme wave conditions; the excitation loads on an absorber can also be increasingly influenced by viscous effects, not predicted by potential flow engineering level models. In these extreme conditions, a Reynolds-averaged Navier-Stokes CFD model can better predict motions and loads for a WEC. Long time series with varying random seed numbers can be used to identify singular extreme wave events from a stochastic irregular sea state. This approach simulates a more realistic wave series for a given sea state than a regular wave or a focused wave. However, it is computationally infeasible to run these long time series for three-dimensional (3D) CFD simulations. In this work, two-dimensional (2D) CFD simulations with a long domain allow the full development of an extreme nonlinear wave condition. The results are used to identify extreme events from a 50-year storm condition for the PacWave site off the coast of Oregon. A relatively short time window including this extreme event is then mapped to a 3D simulation using a user defined wave methodology. Convergence studies for domain length, wave forcing lengths, and time before the extreme event were conducted.

CFD↗

DOE OSTI2023

An Efficient Three-Dimensional CFD-Based Numerical Wave Tank for a Wave Energy Converter in Extreme Irregular Waves: Preprint

A numerical wave tank approach for computational fluid dynamics (CFD) modelling of an extreme irregular seastate is presented. The technique couples a potential flow solution with a CFD solver for more efficient numerical predictions. This method has recently become attractive both for the research community and the industry working with offshore structures. The model is used to determine the response of a submerged pressure differential wave energy converter (WEC) in a fully nonlinear irregular wave condition using the high fidelity CFD code, STAR-CCM+. Potential flow based numerical models are commonly used to predict motions and performance of wave energy converters. Wave kinematics can deviate from potential flow predictions for extreme wave conditions; the excitation loads on an absorber can also be increasingly influenced by viscous effects, not captured in engineering level models. In these extreme conditions, a Reynolds-averaged Navier-Stokes CFD model can better predict motions and loads for a WEC. Long time series with varying random seed numbers can be used to identify singular extreme wave events from a stochastic irregular sea state. This approach simulates a more realistic wave series for a given sea state than a regular wave or a focused wave. However, it is computationally infeasible to run these long time series for three-dimensional (3D) CFD simulations. In this work, two-dimensional (2D) CFD simulations with a long domain allow the full development of an extreme nonlinear wave condition. The results are used to identify extreme events from a 50-year storm condition for the PacWave site off the coast of Oregon. A relatively short time window including this extreme event is then mapped to a 3D simulation using a user defined wave methodology. Convergence studies for domain length, wave forcing lengths, and time before the extreme event were conducted.

cfd↗

DOE OSTI2019

High-Resolution Regional Wave Hindcast for the U.S. Alaska Coast

Regional long-term wave hindcast with state-of-art third-generation models is essential for characterization of regional wave resources. This report summarizes modeling efforts for the simulation of the wave climate along southern Alaska, which used an unstructured, nested-grid modeling approach that incorporates a global-regional nested grid using WAVEWATCH III ® and the high-resolution SWAN (Simulating Waves Nearshore) model. Wave resource and wave bulk parameters were simulated for a 32-year period from 1979 to 2010 and were subsequently validated with wave buoy data in the model domain. Error statistics of model skills were calculated at all buoy stations. Overall, model results, both resource and bulk parameters, match observations well. The model hindcast was able to reproduce the seasonal variation of the sea state with large waves that occur in the winter and early spring months when wind forcing is strong and the calm sea state during the summer when wind forcing is weak. The hindcast also considers the effect of sea ice on wave growth, which affects the southern Bering Sea. The hindcast results, including resource and bulk parameters, were archived at every model grid point for the entire model domain at three-hour intervals. In addition, spectral results were saved at National Data Buoy Center buoy stations and selected virtual buoy locations at hourly intervals. The nested-grid modeling framework employed in this study provides a powerful and efficient modeling approach for accurately simulating wave climate at regional and long-term temporal scales with sufficiently fine resolutions in the nearshore region.

54 ENVIRONMENTAL SCIENCES↗

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 OSTI2023

The wave energy converter control competition (WECCCOMP): Wave energy control algorithms compared in both simulation and tank testing

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.

16 TIDAL AND WAVE POWER↗

DOE OSTI2023

Coupled wave-current modeling for hydrodynamic load analysis of macroalgae cultivation farms

Large-scale cultivation of macroalgae is one of the most promising biofuel sources that could reduce our consumption of fossil fuels and would be particularly economically competitive when grown for the co-production of additional goods such as food and textiles. Current production of biofuel from algal biomass is limited by labor costs and lack of data on potential impacts of cultivation and harvesting on marine and coastal environments as well as a comprehensive characterization of the impact of environmental conditions on macroalgal feedstock and their bioproduct and biofuel yield and quality. Awarded by the United States (U.S.) Department of Energy Advanced Research Projects Agency-Energy (ARPA-E) Macroalgae Research Inspiring Novel Energy Resources (MARINER) program, which seeks to enable the U.S. as a global leader in the production of marine biomass, the Marine Biological Laboratory (MBL) has been developing a test system for tropical seaweed cultivation in the Gulf of Mexico and the Caribbean. An integral step in designing macroalgae cultivation farms is to adequately characterize the hydrodynamic climate at potential growth sites. In regions like the Gulf of Mexico and the Caribbean, which are highly exposed to tropical cyclones, it is critical to not only consider the day-to-day hydrodynamic conditions but to also assess the risk of extreme sea states to ensure the survivability of future macroalgae farms. Under these considerations, the Pacific Northwest National Laboratory (PNNL) is providing modeling support for MBL to inform the design and siting of the farm systems that have been proposed for their ARPA-E MARINER project. This report describes the development of a high-resolution coupled storm surge and wave model to simulate the hydrodynamics and wave climate at proposed macroalgae cultivation sites selected by MBL in Florida and Puerto Rico. Model results, including model validation, water level, current distributions, and sea states, are discussed for both selected sites in Florida and Puerto Rico coast. These simulations provide an accurate insight into the hydrodynamic conditions that a macroalgae farm is likely to experience during its operational lifetime, including current information to support fine-scale hydrodynamic load modeling, risk analysis and system design.

09 BIOMASS FUELS↗

DOE OSTI2023

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.

16 TIDAL AND WAVE POWER↗