The idea of acausality for control of a wave energy converter (WEC) is a concept that has been popular since the birth of modern wave energy research in the 1970s. This concept has led to considerable research into wave prediction and feedforward WEC control algorithms. However, the findings in this report mostly negate the need for wave prediction to improve WEC energy absorption, and favor instead feedback driven control strategies. Feedback control is shown to provide performance that rivals a prediction-based controller, which has been unrealistically assumed to have perfect prediction.
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.
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.
The idea of acausality for control of a wave energy converter (WEC) is a concept that has been popular since the birth of modern wave energy research in the 1970s. This concept has led to considerable research into wave prediction and feedforward WEC control algorithms. However, the findings in this report mostly negate the need for wave prediction to improve WEC energy absorption, and favor instead feedback driven control strategies. Feedback control is shown to provide performance that rivals a prediction-based controller, which has been unrealistically assumed to have perfect prediction. It is well known in classical control engineering that perfect knowledge of past and future events will always lead to higher performing systems. However, it is also well known that the underlying system must be well-designed; control cannot fix a bad design. Additionally, one must consider the practical application of a control design, which relies on measurements and actuation systems. There are major implications to cost and reliability when relying on remote sensors requiring real-time data-streaming (e.g., remote wave buoys). This report shows that for a well-designed WEC, in which closed loop dynamics is considered since early stages of design, a suboptimal controller using no prediction can achieve more than 90% of the theoretical maximum. A predictionless feedback resonating (FBR) controller performs within 0.1% percent of a controller with perfect future knowledge (something which is not practically attainable). Given the major challenges with accurate and robust wave prediction, this result provides a major argument and incentive for utilizing feedback for WEC control. Implementation of these feedback strategies is readily attainable, while the strategy requiring perfect wave prediction will demand an unknown number of additional years to research and develop, all in the service of a marginal 1% benefit.
Efficient design of wave energy converters requires an accurate understanding of expected loads and responses during the deployment lifetime of a device. A study has been conducted to better understand best-practices for prediction of design responses in a wave energy converter. A case-study was performed in which a simplified wave energy converter was analyzed to predict several important device design responses. The application and performance of a full long-term analysis, in which numerical simulations were used to predict the device response for a large number of distinct sea states, was studied. Environmental characterization and selection of sea states for this analysis at the intended deployment site were performed using principle-components analysis. The full long-term analysis applied here was shown to be stable when implemented with a relatively low number of sea states and convergent with an increasing number of sea states. As the number of sea states utilized in the analysis was increased, predicted response levels did not change appreciably. However, uncertainty in the response levels was reduced as more sea states were utilized.
This study demonstrates a systematic methodology for establishing the design loads of a wave energy converter. The proposed design load methodology incorporates existing design guidelines, where they exist, and follows a typical design progression; namely, advancing from many, quick, order-ofmagnitude accurate, conceptual stage design computations to a few, computationally intensive, high-fidelity, design validation simulations. The goal of the study is to streamline and document this process based on quantitative evaluations of the design loads' accuracy at each design step and consideration for the computational efficiency of the entire design process. For the wave energy converter, loads, and site conditions considered, this study demonstrates an efficient and accurate methodology of evaluating the design loads.
A wave energy converter must be designed to survive and function efficiently, often in highly energetic ocean environments. This represents a challenging engineering problem, comprising systematic failure mode analysis, environmental characterization, modeling, experimental testing, fatigue and extreme response analysis. While, when compared with other ocean systems such as ships and offshore platforms, there is relatively little experience in wave energy converter design, a great deal of recent work has been done within these various areas. Here, this article summarizes the general stages and workflow for wave energy converter design, relying on supporting articles to provide insight. By surveying published work on wave energy converter survival and design response analyses, this paper seeks to provide the reader with an understanding of the different components of this process and the range of methodologies that can be brought to bear. In this way, the reader is provided with a large set of tools to perform design response analyses on wave energy converters.
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.
This report contains work completed by a group of student interns during the summer of 2017. Under the guidance of Ryan Coe, Aubrey Eckert-Gallup, and Nevin Martin, a series of interrelated projects were completed on topics relating to extreme response and survival analysis of wave energy converters (WECs). Jarred Canning studied long-term design response analysis methods for WECs. Sam Edwards studied how variation in the selection of an environmental contour affects the characterization of WEC response in extreme conditions. Sam also led the integration of various components of this report and overall editing. Tyler Esterly produced a catalog of analyses for different ocean sites. Bibiana Seng studied clustering analyses for comparing the wave environments of different ocean sites. Lori Smith performed a comparison between analyses conducted using spectral wave data and analyses using deterministic time-domain wave data. William ("Zach") Stuart studied the sensitivity and convergence of environmental contour methods.
