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Within the wave energy community, hydrodynamic coefficients obtained from boundary element methods (BEMs) are commonly used to predict the behaviour of wave energy converters (WECs) in response to incident waves. A number of commercially-available BEM solvers exist, with a number of open-source alternatives also available. While open-source solvers have an obvious cost advantage compared to their commercial counterparts, the results from such solvers are often susceptible to so-called ‘irregular frequencies’, which arise from ill-conditioning in boundary integral problems, and result in large under- or over-estimation of hydrodynamic parameters at certain excitation frequencies. Furthermore, while commercial solvers may employ techniques to suppress the effects of irregular frequencies, such solvers may, under certain circumstances, exhibit other problems in the hydrodynamic results produced. For example, the results obtained for the added mass at high frequencies, and the infinite frequency added mass for a water column, may be incorrect. The current work first focusses on an approach to remove the effects of irregular frequencies from the results obtained for the radiation damping of a particular WEC geometry. The use of radiation damping results to obtain values for the added mass, through the use of the Ogilvie relations, is then considered.The technique described herein has been implemented in BEMRosetta, an open-source tool which allows a user to view the results from various BEM solvers, as well as converting input files between solvers. The results presented in this paper have been obtained using the BEMRosetta implementation.

In recent years, a framework for control of wave energy converters (WECs), termed moment-based control, has been developed within the wave energy conversion literature, exhibiting a remarkable performance in terms of energy absorption, while retaining real-time computational capabilities. Nonetheless, to date, practical results regarding moment-based control for WEC systems have been exclusively provided in numerical simulation, i.e. there is currently a lack of ‘real-world’ assessment of this promising control framework. Motivated by this, we present, in this paper, an experimental assessment and validation of moment-based WEC control for a prototype Wavestar wave energy converter, at the tank-testing facilities of Aalborg University, Denmark. In particular, we address the control design and synthesis procedure in an integrated fashion, covering experimental (physically consistent) system identification, unknown-input estimation and forecasting of wave excitation force, and subsequent control law implementation. We demonstrate that the moment-based controller is able to effectively maximise energy absorption from the wave resource in real-time, with a significant and consistent improvement with respect to the defined benchmark case. The results presented and discussed in this paper demonstrate the feasibility of moment-based WEC control, filling the gap between the attractive theoretical aspects associated with such a strategy, and the practical WEC energy conversion application. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreements No 101024372 and 101034297. This material has also been supported by Science Foundation Ireland (SFI) through the MaREI Centre for Energy, Climate, and Marine, under grant No. 12/RC/2303_P2.

This study addresses the experimental validation of a linear time-invariant (LTI) energy-maximizing control strategy for wave energy converters (WECs), applied to a 1/20 scale Wavestar WEC. To fulfill this objective, system identification routines are utilized to compute a mathematical (parametric) model of the input-output dynamics of the device, suitable for control design and implementation. With this parametric model, the so-called LiTe-Con energy-maximizing strategy, recently published in the literature, is designed, synthesized, and tested under irregular wave excitation in the wave basin at Aalborg University. Given that the LiTe-Con requires instantaneous knowledge of the wave excitation effects, estimates are provided by means of an unknown-input Kalman filter, designed in close synergy with the so-called internal model principle. For the experimental assessment, both controller and estimator are directly implemented in a real-time architecture. The performance of the LiTe-Con is evaluated in terms of energy-absorption, showing consistent results with respect to those obtained in numerical simulation, hence validating the LiTe-Con controller in a realistic real-time scenario.

In this study, we address the issue of real-time energy-maximising control for wave energy converters (WECs), by proposing a receding-horizon optimal control framework based on the concept of a moment . This approach is achieved by extending the so-called moment-based framework, recently published in the WEC literature, to effectively solve the associated optimal control problem within a finite time-horizon, allowing for real-time performance, and a straightforward inclusion of the wave excitation force $\mathcal {F}_e$ estimation and forecasting requirements, which are intrinsic to the wave energy control application. We present a case study, based on a CorPower-like device, subject to both state and input constraints. We show that the proposed strategy can perform almost identically to the ideal performance case, where full knowledge of $\mathcal {F}_e$ over the time-horizon is assumed available. Moreover, a sensitivity analysis is provided, addressing the impact of wave excitation force estimation and forecasting errors in the computation of the moment-based control input. Two main conclusions can be drawn from this analysis: Forecasting mismatch has a negligible impact on the overall performance of the strategy, while potential differences arising from estimating $\mathcal {F}_e$ , in particular, phase errors, can substantially impact total energy absorption.

A Linear Time Invariant (LTI) energy-maximising control strategy for Wave Energy Converters (WECs) is proposed in this paper. Using the fundamental requirement of impedance-matching, the controller is tuned to maximise the energy obtained under polychromatic wave excitation. Given the LTI nature of the proposed controller, the design and implementation procedure is significantly simpler than well-established energy-maximising controllers, including state-of-the-art numerical optimisation routines, which are predominant in this field. Additionally, a LTI constraint handling mechanism is provided. The effectiveness of both the LTI control strategy and the constraint handling mechanism are assessed using regular and irregular waves in unconstrained and constrained cases. The resulting performance is compared to those obtained using existing WEC optimal control strategies. Finally, the benefits, in terms of power production, for both the controller and the constraint handling mechanism are explicitly highlighted by means of an application case.

For wave energy converter control applications, autoregressive (AR) models have been proposed as a simple wave forecasting method, solely based on measured or estimated values of the past wave elevation (or excitation force) signal. Using offline-filtered wave time series, AR models can achieve accurate forecasts several wave periods into the future. In this paper, the AR method is examined from the broader perspective of linear, Gaussian processes. In particular, assuming Gaussian waves and perfect knowledge of the wave spectrum, it is possible to derive a theoretically-optimal wave elevation predictor. It is shown that, in realistic situations, AR models can achieve a performance comparable to the theoretically optimal, spectrum-based predictor, both in simulated wave time series and using actual wave elevation records.

Considering the Wave Star wave energy converter (WEC), which is a standard point absorber prototype, this study addresses the complete energy maximising control design procedure. The WEC model is obtained using system identification routines. Then, using the identified model, a LTI energy maximising control strategy, recently presented in the literature, is designed. Additionally, for the wave excitation force estimation, a standard Kalman filter with a harmonic oscillator is considered. Finally, for the assessment of the performance of the complete system, the controller and estimator are implemented in the numerical WEC simulation environment WEC-Sim. The system is tested under realistic conditions and satisfying performance of the LTI controller is shown. Thus, through a non-conventional approach, and considering a realistic software environment, a novel energy maximising controller is implemented, obtaining results which indicate the feasibility of the approach.

Wave energy converters (WECs) need to be optimally controlled to be commercially viable. These controllers often require an estimate of the (unmeasurable) wave excitation force. To date, observers for WECs are often based upon ‘complex’ techniques, which are counter-intuitive in their design, additionally requiring an explicit model to describe the excitation as part of an (augmented) system. The latter imposes strong assumptions on the design of each observer, while also implying an additional computational burden associated with the necessity of augmenting the WEC model to include the dynamics of the input. We propose a simple and effective excitation force estimator based on linear time-invariant (LTI) theory, without the need for an explicit model of the input. In particular, we re-formulate the unknown-input estimation problem as a tracking control-loop, so that a wide-variety of LTI design techniques (arising from either classical or modern control theory) can be used to compute an estimate of the excitation force}. We demonstrate performance, simplicity, and intuitive appeal of the proposed observer, by means of a case study based on a realistic computational fluid dynamics simulation, comparing the technique against a large set of WEC observers, showing that the approach is able to outperform available estimators.

Due to the inherent relevance of passive (physically representative) models for control, state‐estimation, and motion simulation in the field of marine systems, in this paper, an optimisation‐based approach to passivation of linear time‐invariant (LTI) systems is proposed with application to physically consistent dynamical modelling of marine structures. In particular, the presented strategy is based upon the introduction of a suitably designed perturbation, computed via minimisation of a linear objective subject to a specific set of linear matrix inequalities (LMIs). The performance of the passivation technique is showcased in terms of two case studies: An offshore platform, with a frequency‐domain response computed by means of hydrodynamic codes, and a 1:20 scale wave energy converter (WEC), is characterised in terms of real experimental data.

The motion of a Wave Energy Converter (WEC) can be described in terms of an integro-differential equation, which involves a convolution operator. This convolution term accounts for the effect of radiation forces acting on the device, and represents a computational and representational drawback both for simulation, and analysis/design of control/estimation strategies. We present herein a moment-based strategy to compute a parametric form of the radiation force subsystem for multiple degree of freedom WECs. The strategy allows for the computation of a model that exactly matches the steady-state behaviour of the target system at a set of user-defined frequencies, while retaining the underlying physical properties of radiation forces. The potential and capabilities of the presented method are illustrated considering a CorPower-like device (heaving point absorber) as an application case

Energy-maximising control of wave energy converters can be separated into two different classes: optimisation and non-optimisation based strategies. While optimisationbased controllers can outperform non-optimisation based strategies, the computational requirements associated with numerical optimisation routines, and the high control forces required under optimal conditions, can render these energymaximising control laws unsuitable for realistic scenarios. Nonoptimisation-based controllers present an alternative solution, where linear time-invariant systems are used to approximate the so-called impedance-matching condition. These strategies are often simple to implement but suffer from performance degradation when motion constraints are considered. This paper aims to present a critical comparison between both families of controllers, highlighting the strengths and weaknesses of each approach. We present simulation results for a state-of-theart CorPower-like device under polychromatic (irregular) wave excitation, for both (motion) unconstrained and constrained scenarios.

When it comes to parameterisation of dynamical models for arrays of Wave Energy Converters (WECs), the most used approach, within the wave energy literature, provides a state-space representation whose order (dimension) increases quadratically with the number of devices composing the WEC array. This represents a major drawback for key WEC design elements, such as motion simulation and unknown input estimation, being the latter essential to effectively maximise energy extraction from ocean waves. We present herein a multi-input, multi-output (MIMO) parameterisation strategy based on a system-theoretic interpretation of moments. The state-space representations computed with this moment-based approach exactly match the steady-state behaviour of the target WEC system at specific (user-selected) interpolation points, providing efficient low dimensional models that can accurately represent the input-output dynamics of WEC arrays. Moreover, we show that there exists an intrinsic connection between wave excitation force estimation strategies and the moment-based parameterisation method proposed in this paper. We exploit this mathematical correlation to provide low order models that deliver the same degree of wave excitation force estimation accuracy to that obtained by implementing the currently-used parameterisation methods, with mild computational requirements. The performance of the strategy is analysed in terms of a case study, considering a WEC array composed of state-of-the-art CorPower-like devices, for both WEC motion simulation and wave excitation force estimation scenarios.

Numerical wave tanks (NWTs) provide efficient test beds for the numerical analysis at various stages during the development of wave energy converters (WECs). To ensure the acquisition of accurate, high-fidelity data sets, validation of NWTs is a crucial step. However, using experimental data as reference during model validation, exact knowledge of all system parameters is required, which may not always be available, thus making an incremental validation inevitable. The present paper documents the numerical model validation of a 1/20 scale Wavestar WEC. The validation is performed considering different test case of increasing complexity: wave-only, wave excitation force, free decay, forced oscillation, and wave-induced motion cases. The results show acceptable agreement between the numerical and experimental data so that, under the well-known modelling constraints for mechanical friction and uncertainties in the physical model properties, the developed numerical model can be declared as validated. Numerical wave tanks (NWTs) provide efficient test beds for the numerical analysis at various stages during the development of wave energy converters (WECs). To ensure the acquisition of accurate, high-fidelity data sets, validation of NWTs is a crucial step. However, using experimental data as reference during model validation, exact knowledge of all system parameters is required, which may not always be available, thus making an incremental validation inevitable. The present paper documents the numerical model validation of a 1/20 scale Wavestar WEC. The validation is performed considering different test case of increasing complexity: wave-only, wave excitation force, free decay, forced oscillation, and wave-induced motion cases. The results show acceptable agreement between the numerical and experimental data so that, under the well-known modelling constraints for mechanical friction and uncertainties in the physical model properties, the developed numerical model can be declared as validated.

To maximize energy conversion, real-time control of a wave energy converter (WEC) requires knowledge of the present and future excitation force ( $F_{\rm{ex}}$ ) acting on the device, which is a nonmeasurable quantity. The problem of estimation and forecasting of $F_{\rm{ex}}$ becomes more challenging when arrays of WECs are considered, due to the hydrodynamic interactions in the array. In this paper, a global $F_{\rm{ex}}$ estimator for a complete WEC array is developed and compared to a set of independent estimators, which utilize information local only to each device. A significant question is whether the array of measurements is sufficient to compensate for the greater complexity of the wave field, compared to the isolated body case. The paper shows that the global estimator is always more accurate than the independent estimator, improving up to $\text{45}\%$ the estimation accuracy of the independent estimator. Regarding prediction, two different $F_{\rm{ex}}$ forecasters for a WEC array are compared: a global forecaster, utilizing $F_{\rm{ex}}$ estimates from the full set of array devices, and an independent forecaster, utilizing only a local $F_{\rm{ex}}$ estimate. We demonstrate that the global forecaster achieves more accurate results, not only compared to the independent forecaster, but also compared to the isolated body case.

The motion of a Wave Energy Converter (WEC) can be described in terms of an integro-differential equation, which involves a convolution product. The convolution term, which accounts for the radiation forces, represents a computational and representational drawback both for simulation, and analysis/design of control strategies. Several studies attempt to find a suitable finite parametric form that approximates the radiation impulse response, to express the equation of motion in the time-domain by a state-space representation. Ideally, this approximated parametric model should behave as closely as possible to the system under analysis, particularly at key frequencies, such as the resonant frequency of the device. This study presents a method to obtain a parametric model of both the force-to-motion dynamics and/or the radiation force convolution term, based on moment-matching. Recent advances in moment-matching, allow the computation of a model that exactly matches the frequency response of the original system at the chosen frequencies, while enforcing specific physical properties of the device, depicting a robust and efficient method to compute a state-space representation for the dynamics of a WEC. The potential of the algorithm is illustrated by numerical examples, and the approximation error is shown to be monotonically decreasing with increasing model order.

The motion of a Wave Energy Converter (WEC) can be described in terms of a particular integro-differential equation, which involves a convolution product accounting for the radiation forces. This convolution term has a computational and a representational drawback both for simulation, and for analysis/design of control strategies. This study presents an application case of a method to obtain a parametric model of the force-to-motion dynamics and/or the radiation force convolution term, based on recent advances in moment-matching. This allows the computation of a model that exactly matches the frequency response of the original system at a chosen set of frequencies, while enforcing specific physical properties of the device.

Within the ocean engineering literature, and, particularly, within the wave energy research and hydrodynamic fields, different methods can be found that aim to identify a finite-order parametric model to represent the radiation force convolution term of the well-known Cummins’ equation. Such an approximation process is required for several reasons: firstly, to obtain a mathematical representation that requires low computational effort and, secondly, to ease the model-based control/estimation design procedures. Recently, a new Matlab toolbox has been released to obtain a parametric approximation of such a convolution term based on moment-matching. This paper aims to compare this new moment-matching-based application, with other well-established software. This comparison is based not only on the quality of the approximation, but also on the preservation of the intrinsic physical properties of radiation forces. Three different case studies are used as a basis for the comparison.

Several methods have been developed to identify a parametric model thatrepresents the radiation force convolution term in Cummins’ equation.The reason behind such an approximation is twofold: obtaining a modelwith less computational (effort) requirements, and easing model-basedcontrol design procedures. In this paper, a case study on the paramet-ric approximation of such a convolution term using frequency-domaindata is considered, based on recent advances in model order reductionby moment-matching. Both the force-to-motion and radiation impulseresponse dynamics are considered. The advantages of a moment-basedstrategy are discussed, while providing a comparison with well-knownexisting methods.

The motion of a Wave Energy Converter (WEC) can be described in terms of an integro-differential equation, which includes a convolution term accounting for the radiation forces. Since such a convolution term represents a drawback for both simulation and model-based control, it is usually approximated by a parametric form to be later embedded into the WEC dynamical equation. When an array of WECs is considered, a separate convolution term is required for each cross-coupling component (arising from device interactions), which increases the complexity of the problem. In this paper, a framework to compute a parametric model for array of WEC devices based on moment-matching is presented. The proposed method shows a significant simulation computational saving, compared to other parametric identification methods, which is illustrated by the means of a numerical example.

The motion of a Wave Energy Converter (WEC) can be described in terms of an integro-differential equation, which involves a convolution operator. This convolution term accounts for the effect of radiation forces acting on the device, and represents a computational and representational drawback both for simulation, and analysis/design of control/estimation strategies. We present herein a moment-based strategy to compute a parametric form of the radiation force subsystem for multiple degree of freedom WECs. The strategy allows for the computation of a model that exactly matches the steady-state behaviour of the target system at a set of user-defined frequencies, while retaining the underlying physical properties of radiation forces. The potential and capabilities of the presented method are illustrated considering a CorPower-like device (heaving point absorber) as an application case