Control Of Wave Energy Converters Research Articles

Approximate Dynamic Programming for Control of Wave Energy Converters With Implementation and Validation on a Point Absorber Prototype

It is recognized that the application of constrained optimal control for wave energy converters (WECs), represented by model predictive control (MPC), is hindered by its computation burden resulting from online optimization, especially when the model contains nonlinearities. In this article, a novel control solution based on approximate dynamic programming (ADP) is proposed, in which an explicit controller is solved by model sampling and neural network training. In this way, the major computation load is moved offline to enable fast online execution, and the need for wave prediction is eliminated. The effectiveness of ADP is verified by a simulation case study based on a nonlinear WEC system. Using nonlinear MPC as the performance benchmark, over 90% energy efficiency is achieved by ADP under various sea states with constraint satisfaction and dramatically faster computation. The ADP controller is further experimentally validated on a newly constructed WEC prototype through wave tank testing, where successful implementation and satisfactory performance are demonstrated.

Environmental-Sensing and adaptive optimization of wave energy converter based on deep reinforcement learning and computational fluid dynamics

This paper introduces a novel coupled model for real-time control of the point absorber wave energy converter (WEC) using parallelized deep reinforcement learning (DRL), where the WEC is situated within a numerical wave tank (NWT) built with the method of computational fluid dynamics (CFD). An in-house solver is developed to couple with the DRL and CFD to solve the interaction between WEC and the fluid environment. Validations on wave generation, wave-floater interaction, and power take-off (PTO) unit are carried out. Then, neglecting the detailed model for the PTO technologies, the DRL-based strategy dynamically adjusts the PTO force as a function of the wave features and floater motion. Based on the interaction data, the model-free DRL is outstanding in adaptability and robustness. Simulation results reveal that DRL control improves the wave energy absorption in irregular wave environments, resulting in improvement of 107.5 % compared to the resistive control, with better device protection performance than the model predictive control (MPC). An additional analysis of model-free characteristics of DRL demonstrates the optimization ability independent of floater modeling. This work is the first in-depth study of DRL control of WECs in CFD simulation, providing a more accurate simulation and an optimization process closer to the reality.

Adaptive PI Control of Wave Energy Converters With Force and Motion Constraints

Adaptive PI Control of Wave Energy Converters With Force and Motion Constraints

Performance characterization and modeling of an oscillating surge wave energy converter

Testing wave energy converters in the ocean could be expensive and complex, which necessitates the use of numerical modeling. However, accurately modeling the response of wave energy converters with high-fidelity simulations can be computationally intensive in the design stage where different configurations must be considered. Reduced-order models based on simplified equations of motion can be very useful in the design, optimization, or control of wave energy converters. Given the complex dynamics of wave energy converters, accurate representation, and evaluation of relative contributions by different forces are required. This effort is concerned with a performance characterization of the hydrodynamic response of an oscillating surge wave energy converter that is based on a reduced-order model. A state-space model is used to represent the radiation damping term. Morison’s representation of unsteady forces is used to account for the nonlinear damping. Wave tank tests are performed to validate simulations. A free response simulation is used to determine the coefficients of the state-space model. Torque-forced simulations are used to identify the coefficients of the nonlinear damping term for different amplitudes and wave frequencies. The impact of varying these coefficients on the response is investigated. An assessment of the capability of the model in predicting the hydrodynamic response under irregular forcing is performed. The results show that the maximum error is 3% when compared with high-fidelity simulations. It is determined that the nonlinear damping is proportional to the torque amplitude and its effects are more pronounced as the amplitude of the flap oscillations increases.

Robust Learning-based Model Predictive Control for Wave Energy Converters

Robust Learning-based Model Predictive Control for Wave Energy Converters

Deep Reinforcement Learning with Immersion- and Invariance-based State Observer Control of Wave Energy Converters

Deep Reinforcement Learning with Immersion- and Invariance-based State Observer Control of Wave Energy Converters

On the Ratio of Reactive to Active Power in Wave Energy Converter Control

On the Ratio of Reactive to Active Power in Wave Energy Converter Control

Hardware in the Loop Wave Energy Converter Control Under Control Faults and Model Mismatch

Ocean wave energy conversion is operated in a challenging environment featuring massive and impulsive stresses and is subjected to large amounts of biofouling and marine growth. As most wave energy converter technologies are off-shore, operation, maintenance, and repair costs may be significant. Therefore, any cost-effective control and operation of Wave Energy Converters (WECs) must be robust to faults and changes in the operational environment. This paper presents a Bayesian policy gradient-based WEC control approach that is responsive and adaptive to faults in controller feedback, controller actuation, and changes in the plant model. The controller is tested via Hardware in the Loop real-time testbed. The results show that the proposed control is capable of adapting its policy to the loss of information from one or two sensors and recovering nearly full power operation. In the case where sensor loss occurs, after the loss of plate excitation force estimation and displacement sensors, the power decreases to 215.2 kW from 252.7 kW before recovering to 238.4 kW mean power over 20 minutes. Moreover, the Bayesian RL-based control model proves its adaptability by compensating a large portion of power loss due to PTO failures and rapid changes to the dynamic system because of non-destructive damage to the float structure.

Incorporating Mooring Dynamics into the Control Design of a Two-Body Wave Energy Converter

Mooring systems are a critical component of all floating wave energy converter (WEC) systems, yet the impact of amooring system on the WEC dynamics is often neglected during the initial assessment of candidate designs. The purpose of this study was to investigate how the inclusion of mooring dynamics in the early stages of the WEC design process influences decisions regarding hydrodynamic features and control strategies. The study was executed within a mechanical circuit framework to represent the WEC response in the frequency domain. Thevenin’s theorem was applied within this framework to transform a multi-body WEC into a single-body canonical form. This work specifically focused on self-reacting point absorbers and examined how four realistic mooring designs impact WEC intrinsic mechanical impedance across a range of common wave frequencies. We show how the mooring can easily be included in this framework, and a simple approach to identifying the mooring model parameters is described. It was observed that if mooring dynamics are considered within the WEC control design process, a 40% reduction in the required range of the controller physical variable can be achieved while yielding up to 16% more useful power. These results suggest that considering the mooring system early can enhance WEC design.

What a Wave Buoy Actually Measures in 3D: Analysis of a Mild Sea State

Abstract Measurements of surface waves from oceanographic buoys have been regarded as the “ground truth” for validation of sea-state prediction models, providing the basis for input to the design of offshore structures. The engineering practice is to produce wave statistics of vertical surface displacements over periods of years. However, a wave buoy can provide simultaneous time histories of its motion, one vertically and the other two horizontally, giving the complete vector displacement field in time. We investigate the measured time histories of a wave buoy in three orthogonal directions and explore the relationship between them, for a relatively benign, so typical, sea state. We adopt a NewWave-type analysis to investigate the average shape of the large events across the measured time histories. In combination with a conditioning analysis, we give a reciprocity relationship between the vertical displacement of the wave buoy and those in the horizontal plane. The relationship is of value, as it allows for the prediction of wave kinematics in the horizontal plane based on the vertical measurement only. We observe significant second-order components in the measured data in the horizontal directions and smaller contributions vertically. This data-driven analysis paves the way for wave-by-wave prediction and the active control of wave energy converters and personnel transfers offshore.

On the influence of mooring systems in optimal predictive control for wave energy converters

On the influence of mooring systems in optimal predictive control for wave energy converters

Simple and Low-Model-Dependent Strategy for the Economic and Safe Control of Direct-Drive Wave Energy Converters

For engineering application and commercialization, a wave energy converter (WEC) should harness as much wave energy as possible to improve its economy and maintain each component works within their physical constraints for safe operation. Model predictive control (MPC) can maximize wave energy extraction under constraints for the direct-drive WEC. MPC requires accurate modelling parameters, wave prediction and complex computation, while these can hardly be guaranteed in real application. Besides, researchers generally take position and force constraints into consideration, while power constraint is neglected. In this work, we analyze the power extraction characteristics under constraints and propose a strategy to realize economic and safe control of WECs by decoupling it into different control modes of a permanent magnet synchronous generator (PMSG). In this way, the control is simple and low-model-dependent and power constraint can be also maintained. The strategy is put through comprehensive simulation tests with MPC as the benchmark, and it is proven to be effective under various wave conditions and constraint settings. Furthermore, experimental tests are carried out for a prototype device in a wave tank laboratory and these tests validate the applicability, effectiveness, and robustness of our strategy.

Weakly nonlinear surface wave prediction using a data-driven method with the help of physical understanding

Abstract Accurate surface wave prediction can potentially improve the safety and efficiency of various offshore operations, such as heavy lifts and active control of wave energy converters and floating wind turbines. Prediction of surface waves, even if only for a few periods in advance, is of value for decision-making. This study aims on predicting weakly nonlinear surface waves (up to the 2nd-order) in real-time using a data-driven model based on Artificial Neural Networks (ANN), where the application of physics is investigated to aid the development of a data-driven model. Based on numerically synthesized nonlinear wave records calculated using exact 2nd-order theory, ANN models were trained to separate the nonlinear bound components at an up-wave location, propagate the linear waves and reintroduce the nonlinear components as a correction to the prediction at a down-wave location. Our findings indicate that the optimal approach is to predict each stage separately following the basic physical structure of weakly nonlinear water waves using a series of ANN rather than direct prediction in a single step using ANN. Further, we examined the generalization of the models across different sea states and investigated the impact of the 2nd-order bound waves on prediction accuracy.

A Control Framework for Ocean Wave Energy Conversion Systems: The Potential of Moments

The control of wave energy converters (WECs) to maximize power capture is a challenging problem. In particular, the nature of the wave excitation, which is in general panchromatic (or multi-sinusoidal), presents a reciprocating energy source that needs to be rectified through some means. In addition, the development of suitable control-oriented models is also challenging, requiring correct representation of system hydrodynamics and power take-off (PTO) components, while also lending themselves to control synthesis and real-time computational performance, along with a challenging optimal control problem. This article presents a moment-based mathematical framework for the formulation and solution of WEC control. It shows that moments are ideally suited to WEC control in terms of their ability to accurately characterize the nature of the wave excitation force (and the consequent evolutions in the system variables) while also gracefully including hydrodynamic and PTO nonlinearities as well as a natural extension to WEC arrays. Model reduction, to mold the system model into a control-friendly form, is also a feature of this framework. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 7 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Comparison of Advanced Control Strategies Applied to a Multiple-Degrees-of-Freedom Wave Energy Converter: Nonlinear Model Predictive Controller versus Reinforcement Learning

Achieving energy maximizing control of a Wave Energy Converter (WEC) not only needs a comprehensive dynamic model of the system—including nonlinear hydrodynamic effects and nonlinear characteristics of Power Take-Off (PTO)—but to treat the entire system using an integrated approach, i.e., as a cyber–physical system considering the WEC dynamics, control strategy, and communication interface. The resulting energy-maximizing optimization formulation leads to a non-quadratic and nonstandard cost function. This article compares the (1) Nonlinear Model Predictive Controller (NMPC) and (2) Reinforcement Learning (RL) techniques as applied to a class of multiple-degrees-of-freedom nonlinear WEC–PTO systems subjected to linear as well as nonlinear hydrodynamic conditions in simulation, using the WEC-Sim™ toolbox. The results show that with an optimal choice of RL agent and hyperparameters, as well as suitable training conditions, the RL algorithm is more robust under more stringent operating requirements, for which the NMPC algorithm fails to converge. Further, RL agents are computationally efficient on real-time target machines with a significantly reduced Task Execution Time (TET).

A time domain approach for the optimal control of wave energy converter arrays

Wave energy converters typically use various control methods to extract energy from ocean waves. The objective of the control system is to optimize the energy extraction process, taking into account the dynamics of the system and the wave conditions. The task of deriving the optimal control laws of wave energy converter arrays for regular and irregular waves using the Pontryagin minimum principle was previously investigated in the literature. The result is a combination between the singular arc and bang-bang control laws. For irregular waves, some complexity arises due to the radiation state-space representation, which requires ignoring the hydrodynamic coupling terms related to the added mass and radiation-damping coefficients; this reduces the computational complexity of the control force but adversely affects the solution's accuracy. Also, the derived control laws are specific to a particular wave condition. Recently, the optimal control of a flexible buoy wave energy converter was derived using the convolution representation for the radiation force. In this work, the optimal control laws of flexible buoy wave energy converters are modified to simulate wave energy converter arrays; then, the results are compared to those obtained by dropping the hydrodynamic radiation coupling terms. Although using a convolution representation adds computational complexity to the optimal control problem, it generates an equation that is generic to any wave condition, can be used with any wave spectrum, and provides an expression for the switching condition.

HAPiGYM

The HAPiGYM is a collection of numerical and experimental modelling environments for testing control of wave energy converters (WECs). It has two applications: rapid prototyping of the control policies themselves, and co-design of control and other WEC subsystems. This collection will grow over time. Initially two environments (‘GYM machines’) will be offered. These will be described in this paper.
 The HAPiGYM addresses several technical and resourcing challenges surrounding control prototyping and co-design. Time, money, and cross-disciplinary knowledge are common barriers. Tank time can be prohibitively expensive. Hence many control researchers rely on numerical simulations, and many WEC developers use non-representative control models when designing the hydrodynamic absorbers. The state of the art in hydrodynamic models are not suitable for rapid control prototyping: they are either too slow or insufficiently accurate, leading to a ‘Sim2Tank’ gap, where simulation and tank trial results disagree. Hardware-in-the-Loop removes thosemodelling uncertainties associated with the drive train and control hardware. However, uncertainties associated with the hydrodynamic model remain, and unrepresentative artefacts associated with the rig could be added. Two notable schemes that included tank testing for comparative evaluation were WECCCOMP and the Wave Energy Prize (WEP). WECCCOMP allowed participants to compare the performance of their controllers on the same tank test model. The WEP allowed participants to test their own WECs and controllers.Both had metrics that were proxies for levelised cost of energy. The single metric and prescribed methodology focused the efforts and objectives of participants. As a consequence, simplifications inherent in metrics (e.g., the formula for electrical power) and methodology (e.g., spectral parameters of the sea state available as inputs to the control policy) led to control approaches that could not be replicated in real seas, i.e., certain types of control were able to exploit the ‘Tank2Sea’ gap. The HAPiGYM approach acknowledges theissues surrounding Sim2Tank and Tank2Sea gaps. Rather than attempting to eliminate these, participants will be invited to contribute to a discussion of how testing methodology interacts with control. Participants will be able to suggest methods, metrics, and even future GYM machines. The HAPiGYM will offer a selection of settings for each GYM machine, including the resource (waves), type of PTO, and metrics. Participants will be able to rate their controllers against a suite of metrics and experimental set-ups. This will allow a more nuanced comparison between controllers. It will also facilitate more basic research on co-design, e.g. how PTO operational rangeimpacts control and hydrodynamic performance. 
 Stakeholder engagement identified the need for a simple environment to get started on (a small Sim2Tank gap), and a more challenging environment that reflected the control problems of commercial devices (a small Tank2Sea gap). The first two GYM machines offered will use the same buoy with different constraints: constrained to heave only, and unconstrained (6 DoF). Participants will be able to run Processor-in-the-Loop tests using a tank-calibrated rig simulation running on Open-Hardware controllers. The most promising projectswill be given free remote-access to the HAPiGYM, running in the FloWave tank.

Experimental validation of rollout-based model predictive control for wave energy converters on a two-body, taut-moored point absorber prototype

Model predictive control (MPC) has proven its effectiveness in improving the energy capture efficiency of wave energy converters (WECs) under physical constraints. Further application of MPC requires to speed up its online computation for an industrial controller. To this end, the rollout-based MPC (RMPC) for WECs has been developed. The idea of rollout is to decouple the optimization horizon and the prediction horizon, so as to achieve long-horizon performance with short-horizon optimization. In this paper, the RMPC that has previously only been validated by simulation is further put through wave tank testing. The experimental device is a realistic two-body, taut-moored point absorber prototype. The RMPC is based on a simplified model of the device and implemented in real time with wave force estimation and prediction. Experiment results confirm RMPC’s energy efficiency as well as constraint satisfaction, so its computational advantage against conventional MPC is highlighted.

Control of multiple PTOs in single OWC air chambers

The paper presents the study of multi-PTO interaction in single-air chamber oscillating-water-column (OWC) wave energy converters (WECs). This strategy seeks: i) tunning system's performance to sea states, ii) increasing reliability through modular designs that are easier to install and replace, and iii) increasing conversion efficiency through better matching between available power and electric conversion equipment. The strategy was assessed through a novel non-linear time-domain model for OWC WECs implemented in the multi-physics object-oriented language Modelica. The model considers multiple degrees of freedom associated with the various PTOs. Different case studies are presented to show the proposed approach's versatility, some of the constraints expected in real implementations, and potential pathways to overcome them. The wave-to-wire model considers air compressibility and non-linear power take-off systems, which is fundamental to assessing the damping level variation required for each sea state considered. The cases presented are for a fixed-structure coaxial-duct OWC WEC, but the results are generalisable for floating structures. Results show a significant increase in mean annual power, and control strategies are proposed for power maximisation. Furthermore, some critical points are shown in the operational conditions' envelop for the system under a selected Portuguese wave climate. The identification of these critical values is important for the control of the OWC WECs. This study represents an advance in the control strategies considering multiple PTOs for a single OWC air chamber to foster innovation actions.

Quantification of uncertainty in linear wave energy hydrodynamic models from experimental data

Considerable testing and modeling are required in order to fully realise, efficiently develop, and successfully industrialise the wave energy converters (WECs). Numerical modeling, full-scale measurements, and scaled prototype testing are the various methodologies that can be applied to model WECs and predict the dynamic response. Mathematical WEC models form the basis of model-based energy maximising control and directly affect the ability of model-based controllers to maximise energy capture. Linear WEC models are attractive in leading to simpler control designs, but may not cover the complete operational space. One solution is to identify a range of linear models at different operating points, which give a measure of the underlying nonlinear behaviour [1], [2]. This model set can then be used to extract a nominal model, and an associated uncertainty region, which can be used as a basis for a robust WEC controller synthesis process, such as articulated in [3].
 Recently, such an approach has been adopted using data generated from a high-fidelity numerical computational fluid dynamics (CFD) model [4]. However, numerical wave tanks (NWTs) and physical wave tanks differ significantly in terms of the range of tests which can be performed, and the contamination which can affect the measurements used to determine the data-based models e.g. measurement noise, numerical effects, wave reflections, etc [5]. As a result, the determination of nominal models and uncertainty regions in a physical wave tank may provide some advantages (and disadvantages) which need to be examined carefully. In addition, the range of post-processing techniques which could, or should, be applied to the different experimental/numerical domains, to improve the fidelity of the identified models, may differ between domains.
 In this paper, experimental testing of a WEC, by recreating a wave field similar to real-life conditions and a small-scale version of the device, is used to understand the hydrodynamic behaviour and to obtain an accurate dynamic model for WECs, which are considered to be essential towards optimal WEC design. Physical wave tank experiments, even though having their own disadvantages, overcome some difficulties of CFD-based NWT experiments, most notably huge computation time, problems in accurate representation of viscous fluids, uncertainty in the specification of an appropriate turbulence model, and propagation of incident waves [6]. 
 In this study, representative linear models of a point-absorber type WEC from a physical wave tank in the wave basin at Aalborg University are determined which give insight into the system dynamics and provide a basis for robust control of WECs. Among different stimulation techniques to excite the system dynamics in physical wave tank tests, the particular types of excitation signals covering the complete range of frequencies and amplitudes of the system dynamics, while considering limitations on the range of excitation signals or the wave tank reflections, are adopted for the determination of representative linear models. Moreover, a full investigation is carried out to ascertain the appropriate post-processing needed to optimise the signals as the basis for model identification. The model identification includes the non-parametric frequency response by means of empirical transfer function estimate (ETFE).