A fundamental coupling methodology for modeling near-field and far-field wave effects of floating structures and wave energy devices

This research focuses on the numerical modelling of wave fields around (oscillating) structures such as wave energy converters (WECs), to study both near and far field WEC effects. As a result of the interaction between oscillating WECs and the incident wave field, additional wave fields are generated: the radiated and the diffracted wave field around each WEC. These additional wave fields, together with the incident wave field, make up the perturbed wave field. Several numerical methods are employed to analyse these wave fields around WECs. For example, for investigating wave-structure (wave-WEC) interactions, wave energy absorption and near field effects, the commonly used and most suitable models are based on Boundary Element Methods for solving the potential flow formulation, or models based on the Navier-Stokes equations. These models are here referred to as 'wave-structure interaction solvers'. On the other hand, for investigating far field effects of WEC farms in large areas, wave propagation models are most suitable and commonly employed. However, all these models suffer from a common problem; they cannot be used to model simultaneously both near and far field effects due to limitations. In this paper, a generic coupling methodology is presented, developed to combine the advantages of the above two approaches; (a) the approach of wave-structure interaction solvers, which are used to investigate near field effects because they can more correctly model wave energy absorption and the resulting wave fields induced by oscillating WECs or WEC farms. These solvers suffer from high computational cost and thus are mainly used for limited: (i) areas around WECs; (ii) number of WECs, and (b) the approach of wave propagation models, which are used for predicting far field effects and which can model the effect of WEC farms on the wave field and the shoreline in a cost-effective manner, but usually cannot deliver high-fidelity results on wave energy absorption by the WECs. In addition, a novel wave generation technique is presented, for generating the perturbed wave field induced by an oscillating WEC, in a wave propagation model. The results obtained from the proposed coupling methodology and wave generation technique along a circle are validated and show very good agreement. Finally, the benefits of the proposed coupling methodology to model floating bodies in a phase resolving wave propagation model are discussed. (C) 2019 Elsevier Ltd. All rights reserved

Control of a Realistic Wave Energy Converter Model using Least-Squares Policy Iteration

PublishedThis is the author accepted manuscript. The final version is available from Institute of Electrical and Electronics Engineers via the DOI in this record.An algorithm has been developed for the resistive control of a non-linear model of a wave energy converter using least-squares policy iteration, which incorporates function approximation, with tabular and radial basis functions being used as features. With this method, the controller learns the optimal PTO damping coefficient in each sea state for the maximization of the mean generated power. The performance of the algorithm is assessed against two on-line reinforcement learning schemes: Q-learning and SARSA. In both regular and irregular waves, least-squares policy iteration outperforms the other strategies, especially when starting from unfavourable conditions for learning. Similar performance is observed for both basis functions, with a smaller number of radial basis functions underfitting the Q-function. The shorter learning time is fundamental for a practical application on a real wave energy converter. Furthermore, this work shows that least-squares policy iteration is able to maximize the energy absorption of a wave energy converter despite strongly non-linear effects due to its model-free nature, which removes the influence of modelling errors. Additionally, the floater geometry has been changed during a simulation to show that reinforcement learning control is able to adapt to variations in the system dynamics.This work was supported partly by the Energy Technologies Institute and the Research Councils Energy Programme (grant EP/J500847/), partly by the Engineering and Physical Sciences Research Council (grant EP/J500847/1), and partly by Wave Energy Scotland

Numerical modelling of a 1.5 MW tidal turbine in realistic coupled wave–current sea states for the assessment of turbine hub-depth impacts on mechanical loads

This paper considers hub-depth impacts on mechanical loads for a tidal turbine operating in realistic coupled wave–current sea states. A novel medium-fidelity actuator-line CFD model for simulating tidal turbine non-steady hydrodynamic rotor load responses in the presence of turbulence, shear, and surface waves is developed. The model is validated using tank testing data from a lab-scale turbine. The validated model is then upscaled, to a power rating of 1.5 MW, and simulated in realistic wave–current conditions consistent with those of the MeyGen site. Mean torque and thrust are found to increase with turbine hub height, and the presence of waves is shown to increase mean torque and thrust values by up to 22% and 11%, respectively. The effect on standard deviations and maximum values for these variables is more pronounced, with increases of up to 2500% and 1700% in signal standard deviations, and up to 80% and 30% in maximum values for torque and thrust, respectively. The presence of longer period waves is also shown to reduce mean torque levels, while the corresponding standard deviations and maximum values remained relatively unchanged. In such circumstances, the turbine is operating with an undesirable combination of low-power and high-fatigue. Tidal turbine hub loading characteristics and sensitivities, in the context of the operational loads which subsequently enter the drivetrain and turbine support structure, are also analysed. The magnitude of out-of-plane rotor moments are found to increase with the hub height and wave height. Complex flow interactions are shown to play an important role in this context, leading to what is termed “wave-driven moment-type dominance” effects. Overall, both the rotor location and wave composition are found to significantly impact the turbine’s rotor mechanical load response

Radiation Force Modeling for a Wave Energy Converter Array

The motivation and focus of this work is to generate passive transfer function matrices that model the radiation forces for an array of WECs. Multivariable control design is often based on linear time-invariant (LTI) systems such as state-space or transfer function matrix models. The intended use is for designing real-time control strategies where knowledge of the model’s poles and zeros is helpful. This work presents a passivity-based approach to estimate radiation force transfer functions that accurately replace the convolution operation in the Cummins equation while preserving the physical properties of the radiation function. A two-stage numerical optimization approach is used, the first stage uses readily available algorithms for fitting a radiation damping transfer function matrix to the system’s radiation frequency response. The second stage enforces additional constraints on the form of the transfer function matrix to increase its passivity index. After introducing the passivity-based algorithm to estimate radiation force transfer functions for a single WEC, the algorithm was extended to a WEC array. The proposed approach ensures a high degree of match with the radiation function without degrading its passivity characteristics. The figures of merit that will be assessed are (i) the accuracy of the LTI systems in approximating the radiation function, as measured by the normalized root mean squared error (NRMSE), and (ii) the stability of the overall system, quantified by the input passivity index, , of the radiation force transfer function matrix

Control of a Point Absorber using Reinforcement Learning

This work presents the application of reinforcement learning for the optimal resistive control of a point absorber. The model-free Q-learning algorithm is selected in order to maximise energy absorption in each sea state. Step changes are made to the controller damping, observing the associated penalty, for excessive motions, or reward, i.e. gain in associated power. Due to the general periodicity of gravity waves, the absorbed power is averaged over a time horizon lasting several wave periods. The performance of the algorithm is assessed through the numerical simulation of a point absorber subject to motions in heave in both regular and irregular waves. The algorithm is found to converge towards the optimal controller damping in each sea state. Additionally, the model-free approach ensures the algorithm can adapt to changes to the device hydrodynamics over time and is unbiased by modelling errors.The authors would like to thank the Energy Technology Institute and the Research Council Energy Programme for funding this research as part of the IDCORE programme (grant EP/J500847) as well as the Engineering and Physical Sciences Research Council (grant EP/J500847/1). In addition, Mr. Anderlini would like to thank Wave Energy Scotland for sponsoring his Eng.D. research project