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.
Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE
Mackay, Ed; Haselsteiner, Andreas F.; Coe, Ryan G.; Manuel, Lance
Estimating extreme environmental conditions remains a key challenge in the design of offshore structures. This paper describes an exercise for benchmarking methods for extreme environmental conditions, which follows on from an initial benchmarking exercise introduced at OMAE 2019. In this second exercise, we address the problem of estimating extreme metocean conditions in a variable and changing climate. The study makes use of several very long datasets from a global climate model, including a 165-year historical run, a 700-year pre-industrial control run, which represents a quasi-steady state climate, and several runs under various future emissions scenarios. The availability of the long datasets allows for an in-depth analysis of the uncertainties in the estimated extreme conditions and an attribution of the relative importance of uncertainties resulting from modelling choices, natural climate variability, and potential future changes to the climate. This paper outlines the methodology for the second collaborative benchmarking exercise as well as presenting baseline results for the selected datasets.
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.
The ability to handle data is critical at all stages of marine energy development. The Marine and Hydrokinetic Toolkit (MHKiT) is an open-source marine energy software, which includes modules for ingesting, applying quality control, processing, visualizing, and managing data. MHKiT-Python and MHKiT-MATLAB provide robust and verified functions that are needed by the marine energy community to standardize data processing. Calculations and visualizations adhere to International Electrotechnical Commission technical specifications and other guidelines. A resource assessment of National Data Buoy Center buoy 46050 near PACWAVE is performed using MHKiT and we discuss comparisons to the resource assessment provided performed by Dunkle et al. (2020).
Environmental contours of extreme sea states are often utilized for the purposes of reliability-based offshore design. Many methods have been proposed to estimate environmental contours of extreme sea states, including, but not limited to, the traditional inverse first-order reliability method (I-FORM) and subsequent modifications, copula methods, and Monte Carlo methods. These methods differ in terms of both the methodology selected for defining the joint distribution of sea state parameters and in the method used to construct the environmental contour from the joint distribution. It is often difficult to compare the results of proposed methods to determine which method should be used for a particular application or geographical region. The comparison of the predictions from various contour methods at a single site and across many sites is important to making environmental contours of extreme sea states useful in practice. The goal of this paper is to develop a comparison framework for evaluating methods for developing environmental contours of extreme sea states. This paper develops generalized metrics for comparing the performance of contour methods to one another across a collection of study sites, and applies these metrics and methods to develop conclusions about trends in the wave resource across geographic locations, as demonstrated for a pilot dataset. These proposed metrics and methods are intended to judge the environmental contours themselves relative to other contour methods, and are thus agnostic to a specific device, structure, or field of application. The metrics developed and applied in this paper include measures of predictive accuracy, physical validity, and aggregated temporal performance that can be used to both assess contour methods and provide recommendations for the use of certain methods in various geographical regions. The application and aggregation of the metrics proposed in this paper outline a comparison framework for environmental contour methods that can be applied to support design analysis workflows for offshore structures. This comparison framework could be extended in future work to include additional metrics of interest, potentially including those to address issues pertinent to a specific application area or analysis discipline, such as metrics related to structural response across contour methods or additional physics-based metrics based on wave dynamics.
The aim of this study is to determine the threshold wave energy converter (WEC) type and size to charge a fleet of U.S. Navy autonomous underwater vehicles (AUVs) in various geographic locations of interest. The U.S. Navy deploys AUVs in locations around the world that must be charged manually, decreasing their operational endurance and creating operational limitations. Ocean waves are a potential power source that can be converted into electricity using a WEC and stored using a battery. It would be beneficial to develop a WEC that could autonomously charge AUVs offshore. Numerous locations were analyzed to determine the minimum size of a WEC capable of providing sufficient charging power and offering a strategic advantage. By predicting the WEC efficiency (based on empirical equations) and wave resource (based on available data), electrical power generation across numerous WEC types and locations was compared in MATLAB. The generalized process developed here could be used to determine the required size and type of WECs to charge a fleet of AUVs in different locations around the world.
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.
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.
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.