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.
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.
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.
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.
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 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.
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.
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.
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.
An increasing number of experiments are being conducted to study the design and performance of wave energy converters. Often in these tests, a real-time realization of prospective control algorithms is applied in order to assess and optimize energy absorption as well as other factors. This paper details the design and execution of an experiment for evaluating the capability of a model-scale WEC to execute basic control algorithms. Model-scale hardware, system, and experimental design are considered, with a focus on providing an experimental setup capable of meeting the dynamic requirements of a control system. To more efficiently execute such tests, a dry bench testing method is proposed and utilized to allow for controller tuning and to give an initial assessment of controller performance; this is followed by wave tank testing. The trends from the dry bench test and wave tank test results show good agreement with theory and confirm the ability of a relatively simple feedback controller to substantially improve energy absorption. Additionally, the dry bench testing approach is shown to be an effective and efficient means of designing and testing both controllers and actuator systems for wave energy converters.
Through the use of advanced control techniques, wave energy converters have significantly improved energy absorption. The motion of the WEC device is a significant contribution to the energy absorbed by the device. Reactive control (complex conjugate control) maximizes the energy absorption due to the impedance matching. The issue with complex conjugate control is that the controller is non-causal, which requires prediction into the oncoming waves to the device. This paper explores the potential of using system identification (SID) techniques to build a causal transfer function that approximates the complex conjugate controller over a specific frequency band of interest. The resulting controller is stable, and the average efficiency of the power captured by the causal controller is 99%, when compared to the non-causal complex conjugate.
The purpose of this paper is to investigate Wave Energy Converter (WEC) technologies that are required to transform power from the waves to the electrical grid. WEC system components are reviewed that reveal the performance, stability, and efficiency. These WEC system individual components consists of; control methods, electro-mechanical drive-train, generator machines, power electronic converters, energy storage systems, and electrical grid integration. Initially, the transformation of energy from the wave to the electric grid is explored in detail for an individual WEC system. A control design methodology is then presented that addresses high penetration of Renewable Energy Sources (RES) and loads for networked AC/DC microgrid islanded subsystems. Both static and dynamic stability conditions are identified for the networked AC/DC microgrid system. Detailed numerical simulations were conducted for the electro-mechanical drivetrain system which includes; the dynamic responses, power generation for multiple wave conditions, and total efficiency of the energy/power conversion process. As a renewable energy scenario, the AC/DC microgrid islanded subsystem is employed to integrate an array of WECs. Preliminary Energy Storage System (ESS) power requirements are determined for the renewable energy scenario.
This paper presents a solution to the optimal control problem of a three degrees-of-freedom (3DOF) wave energy converter (WEC). The three modes are the heave, pitch, and surge. The dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. This paper uses Fourier series (FS) as basis functions to approximate the states and the control. A simplified model is first used where the parametric excitation term is neglected and a closed-form solution for the optimal control is developed. For the parametrically excited case, a sequential quadratic programming approach is implemented to solve for the optimal control numerically. Numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.
In this study, we employ a numerical model to compare the performance of a number of wave energy converter control strategies. The controllers selected for evaluation span a wide range in their requirements for implementation. Each control strategy is evaluated using a single numerical model with a set of sea states to represent a deployment site off the coast of Newport, OR. A number of metrics, ranging from power absorption to kinematics, are employed to provide a comparison of each control strategy's performance that accounts for both relative benefits and costs. The results show a wide range of performances from the different controllers and highlight the need for a holistic design approach which considers control design as a parallel component within the larger process WEC design.
For a three-degree-of-freedom wave energy converter (heave, pitch, and surge), the equations of motion could be coupled depending on the buoy shape. This paper presents a multiresonant feedback control, in a general framework, for this type of a wave energy converter that is modeled by linear time invariant dynamic systems. The proposed control strategy finds the optimal control in the sense that it computes the control based on the complex conjugate criteria. This control strategy is relatively easy to implement since it is a feedback control in the time domain that requires only measurements of the buoy motion. Numerical tests are presented for two different buoy shapes: a sphere and a cylinder. Regular, Bretschnieder, and Ochi-Hubble waves are tested. Simulation results show that the proposed controller harvests energy in the pitch-surge-heave modes that is about three times the energy that can be harvested using a heave-only device. This multiresonant control can also be used to shift the energy harvesting between the coupled modes, which can be exploited to eliminate one of the actuators while maintaining about the same level of energy harvesting.
For a heave-pitch-surge three-degrees-of-freedom wave energy converter, the heave mode is usually decoupled from the pitch-surge modes for small motions. The pitch-surge modes are usually coupled and are parametrically excited by the heave mode, depending on the buoy geometry. In this paper, a Model Predictive Control is applied to the parametric excited pitch-surge motion, while the heave motion is optimized independently. The optimality conditions are derived, and a gradient-based numerical optimization algorithm is used to search for the optimal control. Numerical tests are conducted for regular and Bretschneider waves. The results demonstrate that the proposed control can be implemented to harvest more than three times the energy that can be harvested using a heave-only wave energy converter. The energy harvested using a parametrically excited model is higher than that is harvested when using a linear model.
Optimal control theory is applied to compute control for a single-degree-of-freedom heave wave energy converter. The goal is to maximize the energy extraction per cycle. Both constrained and unconstrained optimal control problems are presented. Both periodic and non-periodic excitation forces are considered. In contrast to prior work, it is shown that for this non-autonomous system, the optimal control, in general, includes both singular arc and bang-bang modes. Conditions that determine the switching times to/from the singular arc are derived. Simulation results show that the proposed optimal control solution matches the solution obtained using the complex conjugate control. A generic linear dynamic model is used in the simulations. The main advantage of the proposed control is that it finds the optimal control without the need for wave prediction; it only requires the knowledge of the excitation force and its derivatives at the current time.
This report gives a brief discussion and examples on the topic of state estimation for wave energy converters (WECs). These methods are intended for use to enable real-time closed loop control of WECs.
A linear dynamic model for a wave energy converter (WEC) has been developed based on the results of experimental wave tank testing. Based on this model, a model predictive control (MPC) strategy has been designed and implemented. To assess the performance of this control strategy, a deployment environment off the coast of Newport, OR has been selected and the controller has been used to simulate the WEC response in a set of irregular sea states. To better understand the influence of model accuracy on control performance, an uncertainty analysis has been performed by varying the parameters of the model used for the design of the controller (i.e. the control model), while keeping the WEC dynamic model employed in these simulations (i.e. the plant model) unaltered. The results of this study indicate a relative low sensitivity of the MPC control strategy to uncertainties in the controller model for the specific case studied here.
A study was performed to optimize the geometry of a point absorber style wave energy converter (WEC). An axisymmetric single-body device, moving in heave only, was considered. Design geometries, generated using a parametric definition, were optimized using genetic algorithms. Each geometry was analyzed using a boundary element model (BEM) tool to obtain corresponding frequency domain models. Based on these models, a pseudo-spectral method was applied to develop a control methodology for each geometry. The performance of each design was assessed using a Bretschneider sea state. The objective of optimization is to maximize harvested energy. In this preliminary investigation, a constraint is imposed on the the geometry to guarantee a linear dynamic model would be valid for all geometries generated by the optimization tool. Numerical results are presented for axisymmetric buoy shapes.
Many of the control strategies for wave energy converters (WECs) that have been studied in the literature rely on the availability of estimates for either the wave elevation or the exciting force caused by the incoming wave; with the objective of addressing this issue, this paper presents the design of a state estimator for a WEC. In particular, the work described in this paper is based on an extended Kalman filter that uses measurements from pressure sensors located on the hull of the WEC to estimate the wave exciting force. Simulation results conducted on a heaving point absorber WEC shows that the extended Kalman filter provides a good estimation of the exciting force in the presence of measurement noise combined with a simplified model of the system, thus making it a suitable candidate for the implementation in an experimental set-up.
A model-scale wave tank test was conducted in the interest of improving control systems design of wave energy converters (WECs). The success of most control strategies is based directly upon the availability of a reduced-order model with the ability to capture the dynamics of the system with sufficient accuracy. For this reason, the test described in this report, which is the first in a series of planned tests on WEC controls, focused on system identification (system ID) and model validation.
The addition of a compressible degree of freedom (CDOF) to a wave energy converter (WEC)-which results in a compressible WEC-has been shown to significantly increase power absorption compared to a rigid WEC of the same shape and mass for a variety of architectures. This study demonstrates that a compressible point absorber, with a passive power-take-off (PTO) and optimized damping, can also achieve equal or better performance levels than an optimally controlled rigid point absorber (with the same shape and mass) using reactive power from the PTO. Wave energy is converted to mechanical energy in both cases using a linear damper PTO, with the PTO coefficient optimized for each resonance frequency and compressible volume. The large compressible volume required to tune the compressible point absorber to the desired frequency is a practical limitation that needs to be addressed with further research, especially for low frequencies. While realistic, these auxiliary units would increase the CapEx and OpEx costs, potentially reducing the aforementioned benefits gained by CDOF. However, alternative approaches can be developed to implement CDOF without the large compressible volume requirements, including the development of flexible surface panels tuned with mechanical springs.
The operation of Wave Energy Converter (WEC) devices can pose many challenging problems to the Water Power Community. A key research question is how to significantly improve the performance of these WEC devices through improving the control system design. This report summarizes an effort to analyze and improve the performance of WEC through the design and implementation of control systems. Controllers were selected to span the WEC control design space with the aim of building a more comprehensive understanding of different controller capabilities and requirements. To design and evaluate these control strategies, a model scale test-bed WEC was designed for both numerical and experimental testing (see Section 1.1). Seven control strategies have been developed and applied on a numerical model of the selected WEC. This model is capable of performing at a range of levels, spanning from a fully-linear realization to varying levels of nonlinearity. The details of this model and its ongoing development are described in Section 1.2.
The addition of a compressible degree of freedom (CDOF) has been shown to significantly increase the power absorption compared to a traditional rigid WEC of the same shape and mass for a variety of architectures. The present study demonstrates that a compressible point absorber, with a passive power-take-off (PTO) and optimized damping, can also achieve at the same performance levels or better than an optimally controlled rigid point absorber using reactive power from the PTO. Eliminating the need for a reactive PTO would sub- stantially reduce costs by reducing PTO design complexity. In addition, it would negate the documented problems of reactive PTO efficiencies on absorbed power. Improvements to per- formance were quantified in the present study by comparing a compressible point absorber to a conventional rigid one with the same shape and mass. Wave energy is converted to mechan- ical energy in both cases using a linear damper PTO, with the PTO coefficient optimized for each resonance frequency and compressible volume. The large compressible volumes required to tune the compressible point absorber to the desired frequency are a practical limitation that needs to be addressed with further research; especially for low frequencies. If fact, all compressible volumes exceed the submerged volume of the point absorber by significant amounts; requiring auxiliary compressible volume storage units that are connected to the air chamber in the submerged portion of the point absorber. While realistic, these auxiliary units would increase the Cap Ex and Op Ex costs, potentially reducing the aforementioned benefits gained by CDOF. However, alternative approaches can be developed to implement CDOF without the large compressible volume requirements, including the development of flexible surface panels tuned with mechanical springs.
A new multi-year effort has been launched by the Department of Energy to validate the extent to which control strategies can increase the power produced by resonant wave energy conversion (WEC) devices. This paper describes the design of a WEC device to be employed by this program in the development and assessment of WEC control strategies. The operational principle of the device was selected to provide a test-bed for control strategies, in which a specific control strategies effectiveness and the parameters on which its effectiveness depends can be empirically determined. Numerical design studies were employed to determine the device geometry, so as to maximize testing opportunities in the Maneuvering and Seakeeping (MASK) Basin at the Naval Surface Warfare Centers David Taylor Model Basin. Details on the physical model including specific components and model fabrication methodologies are presented. Finally the quantities to be measured and the mechanisms of measurement are listed.