Dynamics Of Wave Energy Converter Research Articles

Oblique wave interaction with dual submerged oscillating buoy as WEC near a partially reflecting wall

The hydrodynamic performance of a submerged dual cylindrical wave energy converter (WEC) in front of a partially reflecting vertical wall is investigated within the framework of linear wave theory. The double cylinders are fully submerged and are constrained only in heave motion. The conversion of wave action into usable power occurs by the coordinated motion of two buoy systems viz. a power take-off mechanism (PTO). The numerical solution for the boundary value problem comprising of wave diffraction and radiation by submerged dual cylinders is obtained using the Boundary Element Method (BEM). The study is devoted to investigating the influence of various factors, the effect of cylinder dimensions, cylinder-cylinder spacing, partially reflecting wall-cylinder distance, angle of wave attack, and its submergence. The compelling results are presented by examining the heave force, surge force, response amplitude operator (RAO), damping factor, and particular interest in the WEC energy capture efficiency under distinct seawall reflections. The study reveals that there is an increase in the WEC efficiency by ≈12% in the case of a dual cylinder compared to a single cylinder. Besides, the amplification of the WEC efficiency is ≈78% for the case of a fully reflecting wall compared to the WEC in the open fluid domain. The present study will further help to understand the dynamics of WECs integrated into protecting shore structures such as breakwaters, groins, and seawalls.

Neural network survivability approach of a wave energy converter considering uncertainties in the prediction of future knowledge

To tune the wave energy converter (WEC) controller parameters such as damping to reduce the line force during extreme wave conditions, future knowledge of the line force is required. To achieve this, the incoming wave and system state should be predicted for a few seconds in the future. It is rather an arduous task to predict the future knowledge of waves and the system’s dynamic when dealing with breaking and steep waves, and the system is subject to various nonlinear forces. The classical model-based control strategies often rely on linear assumptions to estimate the WEC dynamics for the sake of simplicity. Unlike the model-based, the data-driven approaches are free from modeling errors and the algorithms are trained over the true and noisy data to predict non-linear system behaviors. Using data-driven approaches, we are able to model nonlinear dynamics. However, new questions emerge on the accuracy of the future wave and system state predictions, and how this uncertainty propagates into the final prediction of the line force. As incorrect damping may lead to excessive line force and detrimental damage to the system, these are the knowledge gaps that need to be addressed. The main purpose of this paper is to answer these questions through a survivability strategy for wave energy converters by providing a realistic perspective on the implementation of the neural network approaches by accounting for the errors in the input data. For this purpose, a series of neural networks is designed that first predicts the surface elevation for 0.36 s ahead, i.e. corresponding to 2 s in the full-scale WEC. This future knowledge of the wave elevation is then used to predict the system state (i.e. power take-off (PTO) translator position) for the same prediction horizon based on the PTO damping. This information is then fed to a convolutional neural network (CNN) that predicts the peak line force 0.36 s ahead. This paper also evaluates the predictive capabilities of neural network (NN) models, comparing them to classical autoregressive (AR) and Kalman filter methods. While the AR model exhibits slightly higher accuracy in fixed PTO system configurations, it falters in providing real-time predictions when system parameters undergo variations. In contrast, the NN prediction model excels by establishing a robust relationship between system configuration and output signals. Especially noteworthy is its ability to outperform classical methods with minimal training on a selective set of system configurations. Then, the sensitivity of the peak line force prediction to the uncertainties in the input data from NN models and the prediction horizon is analyzed. The neural network models are trained over the experimental data subjected to extreme sea states for a point absorber wave energy converter. The results suggest that the accuracy of the surface elevation prediction has an insignificant direct effect on the peak force prediction model. However, these uncertainties are reflected in the PTO translator position prediction, and the model is considerably sensitive to the accuracy of this prediction. This sensitivity nonetheless is less notable for higher PTO damping values.

Physical Modelling Of A Centralized Controlled Array Of Five Wecfarm Wave Energy Converters

Point absorber wave energy converters (WECs) closely placed in array hydrodynamically interact through wave radiation and diffraction. The power absorption by these WECs is optimised by altering the WEC dynamics through the control of the Power Take-Off (PTO). As the WEC dynamics are changed, the hydrodynamic interactions change as well. Therefore, the PTO control should be optimized taking all these interactions into account, referred to as centralized control. The ‘WECfarm’ project has been initiated to study WEC arrays, and to address the research gap on available realistic and reliable data on WEC array tests to validate numerical models (Vervaet et al., 2022). This work discusses the experimental design, implementation and testing of a centralized controlled array of five ‘WECfarm’ heaving point absorber WECs, tested at the Coastal and Ocean Basin Ostend.

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.

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.

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).

On data-based control-oriented modelling applications in wave energy systems

The development of effective energy-maximising control strategies has a crucial role in the empowerment of wave energy technology, and in its improvement towards economic viability. Within the state-of-the-art, most of the strategies adopted to maximise the absorbed energy exploit a model of the wave energy converter (WEC) to be controlled, i.e. they are model-based. These models attempt to replicate the WEC dynamics with a sufficient degree of fidelity, trying, at the same time, to minimise their associated computational burden. However, due to the presence of the hydrodynamic effects , which inherently characterise wave energy systems, simultaneously achieving high-fidelity and computational efficiency is not trivial. Oversimplification of the problem through, for example, linearity assumptions, could lead to non-representative models and/or large uncertainty levels. To overcome these issues, in the last decade, several approaches based on data have been proposed in the wave energy field. These approaches, falling under the umbrella of system identification techniques, exploit data coming from experimental tests or high fidelity simulations, and build control -oriented models with a pre-defined level of complexity. In this paper, we analyse the different strategies that have been adopted in the literature to build data-based control-oriented models for WECs, highlighting the characteristics of each approach, together with their opportunities and inherent drawbacks. An analysis of eventual “partial” data-based modelling of WEC subsystems (e.g. moorings, PTO, or hydrodynamics only) is also reported. Moreover, considerations on the choice of inputs and outputs depending on the WEC type are reported, in an attempt to highlight the different issues that characterise the system identification problem depending on the WEC technology. Finally, conclusions are drawn regarding the capabilities that this type of approach has in (at least partially) solving the modelling issues that affect WEC control system design, and the pitfalls that pure adoption of these strategies has when applied on larger scales, or in the operational stage.

Modeling of a hinged-raft wave energy converter via deep operator learning and wave tank experiments

Model identification for a hinged-raft wave energy converter (WEC) is investigated in this paper, based on wave tank experiments and deep operator learning. Different from previous works which all formulated this issue as a function approximation task, this work, for the first time, formulates it as an operator approximation task (which learns the mapping from a function space to another function space). As such, a continuous-time WEC model is identified from data, greatly expanding the horizon of data-based WEC modeling because previous works were limited to discrete-time model identification. The error accumulation for multi-step predictions in the discrete-time formulation is thus also addressed. The model is developed by first carrying out a set of wave tank experiments to generate the training data, and then the deep operator learning model, i.e. the DeepONet, is constructed and trained based on the experimental data. The validation study shows that the model captures the WEC dynamics accurately. A new set of experimental runs are further carried out and the results show that after training, the model can be used as a digital wave tank, an alternative to the expensive numerical and physical wave tanks, for accurate and real-time simulations of the WEC dynamics.

Online maximization of extracted energy in sea wave energy converters using temporal-difference learning

This article presents temporal-difference (TD) learning which is a combination of Monte Carlo and dynamic programing (DP) as a Method for controlling single-body wave energy converters (WECs). Since TD methods are designed to solve the prediction problems, we use this feature to maximize the energy captured from the sea waves. The entered force to the buoy system is addressed implicitly in the state matrix to design the problem into a TD framework. In order to enhance the captured power by the WEC, the control method is built to have an online active control. This will help the device to predict the best controller based on its previous experiences in the same situations. Two methods of TD, Q-Learning and SARSA, are used and the features are analyzed and several testing functions are carried out in simulation part. To perform on-line optimal control, a force control has acted as a controller and TD coefficients are tuned at a proper rate significantly after specific number of episodes. The power of suggested TD methods is compared to PGM, IPOPT and with other learning control strategies. Several computer simulations were carried out to evaluate the controller effectiveness by applying different sea-states and analyzing the resultant WEC dynamics.

Robust Tube-Based Model Predictive Control for Wave Energy Converters

This paper proposes an efficient robust tube-based model predictive control (RTMPC) strategy for energy-maximization control of wave energy converters (WECs) subject to constraints due to safety considerations. Compared with the existing MPC strategies developed for the WEC control problem, the RTMPC method provides an effective approach to explicitly handle plant-model mismatches with guaranteed constraint satisfaction, contributing to improved energy capture efficiency. The fundamental idea is to integrate disturbance invariant sets into the MPC scheme for energy-maximization control to form a tube-based predictive controller, which enhances the robustness of MPC for a WEC without increasing online computational complexity. The resulting RTMPC controller can bound the WEC plant trajectories in a tube centered around a nominal WEC model trajectory, and uncertainties from un-modeled WEC dynamics and unmeasured disturbances can be mitigated by an error feedback portion. Numerical simulations demonstrate the effectiveness of the proposed control strategy.

Evaluation of the Stiffness Mechanism on the Performance of a Hinged Wave Energy Converter

Abstract This paper presents the numerical and experimental study of a new spring mechanism adapted to a cone-shaped point absorber wave energy converter (WEC). The WEC is intended to be hinged to a floating wind platform with a long arm to create a combined wind and wave harvesting concept. The main objective of the spring mechanism is to improve the platform by restoring moments against the wind thrust forces, generated by the wind turbine. However, the study is presented for the case where the WEC dynamics is investigated outside the platform and attached to a fixed frame, to validate the mathematical model of the WEC concept and study the effects of the spring mechanism on wave energy absorption. In addition, the impact on the power harvesting performance is investigated with and without spring mechanism scenarios and different sea states.

Midfidelity model verification for a point-absorbing wave energy converter with linear power take-off

In the preliminary design stage of a waveenergy converter (WEC), researchers need fast and reliablesimulation tools. High-fidelity numerical models are usu-ally employed to study the wave-structure interaction, butthe computational cost is demanding. As an alternative,midfidelity models can provide simulations in the order ofreal time. In this study, we operate Uppsala University’sWEC in a relatively mild sea state and model it usingWEC-Sim. The model is verified based on OpenFOAMsimulations. To analyze the ability of the midfidelitymodel to capture WEC dynamics, we investigate the systemseparately with 1, 2, and 3 degrees of freedom. We examinethe contribution of viscous phenomena, and study bothlinear and weakly nonlinear solutions provided by WEC-Sim. Our results indicate that the viscous effects can beneglected in heave and surge motion, but not for pitch.We also find that the weakly nonlinear WEC-Sim solutionsuccessfully agrees with the computational fluid dynam-ics, whereas the linear solution could suggest misleadingresults.

Real-Time Nonlinear Model Predictive Controller for Multiple Degrees of Freedom Wave Energy Converters with Non-Ideal Power Take-Off

An increase in wave energy converter (WEC) efficiency requires not only consideration of the nonlinear effects in the WEC dynamics and the power take-off (PTO) mechanisms, but also more integrated treatment of the whole system, i.e., the buoy dynamics, the PTO system, and the control strategy. It results in an optimization formulation that has a nonquadratic and nonstandard cost functional. This article presents the application of real-time nonlinear model predictive controller (NMPC) to two degrees of freedom point absorber type WEC with highly nonlinear PTO characteristics. The nonlinear effects, such as the fluid viscous drag, are also included in the plant dynamics. The controller is implemented on a real-time target machine, and the WEC device is emulated in real-time using the WECSIM toolbox. The results for the successful performance of the design are presented for irregular waves under linear and nonlinear hydrodynamic conditions.

Effect of a model predictive control on the design of a power take-off system for wave energy converters

In this study, a model predictive control (MPC) strategy is developed for a wave energy converter (WEC) to investigate how the controller settings affect the design of the power take-off machinery. The WEC chosen for this analysis is a submerged multi-degree-of-freedom WEC inspired by the multi-moored CETO system. A nonlinear numerical model of the WEC dynamics is built and tested for a potential deployment site off the coast of Albany, Western Australia. Tuning parameters of the MPC include the prediction horizon and control force penalties. In addition, the effect of a mechanical spring on the controller performance is investigated. The results show the significance of the penalty terms on the power production and control forces dynamics if the power take-off efficiency is not ideal.

Power maximising control of a heaving point absorber wave energy converter

Control systems play a critical role in improving the economic viability of wave energy converters (WEC). This paper presents a framework for a causal power-maximising feedback controller inspired by Phi method. Quadratic damper control and PID control are combined to collectively achieve the optimal power absorption conditions for the peak wave periods, which results in a nonlinear controller being suboptimal in irregular waves. The proposed controller is tested on a fully submerged heaving spherical point absorber in regular and irregular wave conditions in time domain. The tuning of the PID gains are investigated in frequency-domain from a stability and control bandwidth perspective. The modelled WEC dynamics includes linear hydrodynamic forces (excitation and radiation) and the nonlinear viscous drag force. The main benefits of the proposed controller are (i) it does not require any time-consuming optimisation either online or offline; (ii) has a wider bandwidth and better power absorption performance as compared to the conventional spring-damper (PI) controller; and (iii) easy to implement in practice like standard PID control.

Comparison and Validation of Hydrodynamic Theories for Wave Energy Converter Modelling

Dynamic Wave Energy Converter (WEC) models utilize a wide variety of fundamental hydrodynamic theories. When incorporating novel hydrodynamic theories into numerical models, there are distinct impacts on WEC rigid body motions, cable dynamics, and final power production. This paper focuses on developing an understanding of the influence several refined hydrodynamic theories have on WEC dynamics, including weakly nonlinear Froude-Krylov and hydrostatic forces, body-to-body interactions, and dynamic cable modelling. All theories have evolved from simpler approaches and are of importance to a wide array of WEC archetypes. This study quantifies the impact these theories have on modelling accuracy through a WEC case study. Theoretical differences are first explored in a regular sea state. Subsequently, numerical validation efforts are performed against field data following wave reconstruction techniques. Comparisons of significance are WEC motion and cable tension. It is shown that weakly nonlinear Froude-Krylov and hydrostatic force calculations and dynamic cable modelling both significantly improve simulated WEC dynamics. However, body-to-body interactions are not found to impact simulated WEC dynamics.

Damping Studies on PMLG-Based Wave Energy Converter under Oceanic Wave Climates

Wave energy converters (WECs), which are designed to harvest ocean wave energy, have recently been improved by the installation of numerous conversion mechanisms; however, it is still difficult to find an appropriate method that can compromise between strong environmental impact and robust performance by transforming irregular wave energy into stable electrical power. To solve this problem, an investigation into the impact of varied wave conditions on the dynamics of WECs and to determine an optimal factor for WECs to comply with long-term impacts was performed. In this work, we researched the performance of WECs influenced by wave climates. We used a permanent magnet linear generator (PMLG)-based WEC that was invented at Uppsala University. The damping effect was first studied with a PMLG-type WEC. Then, a group of sea states was selected to investigate their impact on the power production of the WEC. Two research sites were chosen to investigate the WEC’s annual energy production as well as a study on the optimal damping coefficient impact. In addition, we compared the WEC’s energy production between optimal damping and constant damping under a full range of sea states at both sites. Our results show that there is an optimal damping coefficient that can achieve the WEC’s maximum power output. For the chosen research sites, only a few optimal damping coefficients were able to contribute over 90% of the WEC’s annual energy production. In light of the comparison between optimal and constant damping, we conclude that, for specific regions, constant damping might be a better choice for WECs to optimize long-term energy production.

Real-Time Wave Excitation Forces Estimation: An Application on the ISWEC Device

Optimal control strategies represent a widespread solution to increase the extracted energy of a Wave Energy Converter (WEC). The aim is to bring the WEC into resonance enhancing the produced power without compromising its reliability and durability. Most of the control algorithms proposed in literature require for the knowledge of the Wave Excitation Force (WEF) generated from the incoming wave field. In practice, WEFs are unknown, and an estimate must be used. This paper investigates the WEF estimation of a non-linear WEC. A model-based and a model-free approach are proposed. First, a Kalman Filter (KF) is implemented considering the WEC linear model and the WEF modelled as an unknown state to be estimated. Second, a feedforward Neural Network (NN) is applied to map the WEC dynamics to the WEF by training the network through a supervised learning algorithm. Both methods are tested for a wide range of irregular sea-states showing promising results in terms of estimation accuracy. Sensitivity and robustness analyses are performed to investigate the estimation error in presence of un-modelled phenomena, model errors and measurement noise.

A Real-Time Detection System for the Onset of Parametric Resonance in Wave Energy Converters

Parametric resonance is a dynamic instability due to the internal transfer of energy between degrees of freedom. Parametric resonance is known to cause large unstable pitch and/or roll motions in floating bodies, and has been observed in wave energy converters (WECs). The occurrence of parametric resonance can be highly detrimental to the performance of a WEC, since the energy in the primary mode of motion is parasitically transferred into other modes, reducing the available energy for conversion. In addition, the large unstable oscillations produce increased loading on the WEC structure and mooring system, accelerating fatigue and damage to the system. To remedy the negative effects of parametric resonance on WECs, control systems can be designed to mitigate the onset of parametric resonance. A key element of such a control system is a real-time detection system, which can provide an early warning of the likely occurrence of parametric resonance, enabling the control system sufficient time to respond and take action to avert the impending exponential increase in oscillation amplitude. This paper presents the first application of a real-time detection system for the onset of parametric resonance in WECs. The method is based on periodically assessing the stability of a mathematical model for the WEC dynamics, whose parameters are adapted online, via a recursive least squares algorithm, based on online measurements of the WEC motion. The performance of the detection system is demonstrated through a case study, considering a generic cylinder type spar-buoy, a representative of a heaving point absorber WEC, in both monochromatic and polychromatic sea states. The detection system achieved 95% accuracy across nearly 7000 sea states, producing 0.4% false negatives and 4.6% false positives. For the monochromatic waves more than 99% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude, whereas for the polychromatic waves 63% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude and 91% while it was less than 1/3 of its maximum amplitude.

Experimental Investigation of the Mooring System of a Wave Energy Converter in Operating and Extreme Wave Conditions

A proper design of the mooring systems for Wave Energy Converters (WECs) requires an accurate investigation of both operating and extreme wave conditions. A careful analysis of these systems is required to design a mooring configuration that ensures station keeping, reliability, maintainability, and low costs, without affecting the WEC dynamics. In this context, an experimental campaign on a 1:20 scaled prototype of the ISWEC (Inertial Sea Wave Energy Converter), focusing on the influence of the mooring layout on loads in extreme wave conditions, is presented and discussed. Two mooring configurations composed of multiple slack catenaries with sub-surface buoys, with or without clump-weights, have been designed and investigated experimentally. Tests in regular, irregular, and extreme waves for a moored model of the ISWEC device have been performed at the University of Naples Federico II. The aim is to identify a mooring solution that could guarantee both correct operation of the device and load carrying in extreme sea conditions. Pitch motion and loads in the rotational joint have been considered as indicators of the device hydrodynamic behavior and mooring configuration impact on the WEC.