Moment-Matching-Based Input-Output Parametric Approximation for a Multi-DoF WEC Including Hydrodynamic Nonlinearities

We present in this paper a moment-matching method to compute a parametric approximation of the inputoutput (force-to-motion) response of a multiple Degree of Freedom (DoF) Wave Energy Converter (WEC), based on the algorithm presented in [1]. This method allows the user to select a set of interpolation frequencies where the approximating model exactly matches the steady-state response of the target WEC under analysis, while being able to retain key underlying physical properties of the device. Furthermore, we show how to systematically accommodate nonlinear effects using this approximation method, depicting an efficient and versatile approach to compute a parametric representation for WEC design, control and estimation procedures. We illustrate the capabilities and characteristics of this method by means of a study case, using a CorPower-like (heaving point absorber) device. Our numerical analysis shows that, when compared to the currently most-used methodology to parameterise the dynamics of a multi-DoF WEC, the proposed approach can compute mathematical models with the same degree of accuracy and up to ≈ 50 % of improvement in terms of computational time

Wave energy control: status and perspectives 2020

Wave energy has a significant part to play in providing a carbon-free solution to the world’s increasing appetite for energy. In many countries, there is sufficient wave energy to cater for the entire national demand, and wave energy also has some attractive features in being relatively uncorrelated with wind, solar and tidal energy, easing the renewable energy dispatch problem. However, wave energy has not yet reached commercial viability, despite the first device designs being proposed in 1898. Control technology can play a major part in the drive for economic viability of wave energy and this paper charts the progress made since the first wave energy control systems were suggested in the 1970s, and examines current outstanding challenges for the control community

Hydrodynamic excitation force estimation and forecasting for wave energy applications

Ocean waves represent a significant energy resource which can complement other renewable energy technologies during the transition to a low-carbon energy mix. Despite the large number of concepts suggested for the conversion of wave energy, none of the technologies has yet demonstrated economic viability. To this end, several solutions have been proposed in the literature, such as deploying Wave Energy Converters (WECs) in large arrays or optimal control of WECs. The majority of WEC optimal control strategies require knowledge of the previous, current, and future excitation force acting on the device. However, for the WEC case, the excitation force is an unmeasurable quantity and, therefore, must first be estimated, based on available measurements, and then predicted in the future. The main objective of this thesis is to analyse the estimation/prediction techniques proposed for wave energy applications and to evaluate whether such techniques are ready to be applied for real WEC control strategies. To this end, a critical comparison of the available excitation force estimators is presented. Additionally, the performance of the autoregressive model as a predictor is analysed, showing that, the obtained prediction accuracy can get close to the theoretically best achievable prediction accuracy. Based on the errors observed from the analysis of excitation force estimation/prediction techniques, a sensitivity analysis of an optimal control strategy to such errors is performed. As a result, this thesis provides an overview of the aspects which should be considered at the stage of tuning estimation/prediction techniques, to not affect the controller performance. Since the estimation/prediction problem becomes more challenging for WEC arrays, due to the hydrodynamic interactions, an important question is whether the extra measurements from the array are sufficient to compensate for the greater complexity of the wave field. Thus, a global estimator/predictor, considering information from all the devices of the array, is developed and compared to a set of independent estimators/predictors. Finally, this thesis introduces an identification strategy to obtain a parametric model of both the force-to-motion dynamics and/or the radiation force convolution term of the device. The strategy allows for the identification of low-order parametric models of WECs, which will simplify the implementation of optimal control strategies in real-time. Additionally, the proposed strategy is compared to the other approaches available in the literature

Moment-based parametric identification of arrays of wave energy converters

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

Optimal control and model reduction for wave energy systems: A moment-based approach

Following the sharp increase in the price of traditional fossil fuels, in combination with issues of security of supply, and pressure to honor greenhouse gas emission limits, much attention has turned to renewable energy sources in recent years. Ocean wave energy is a massive and untapped resource, which can make a valuable contribution towards a sustainable, global, energy mix. Despite the fact that ocean waves constitute a vast resource, wave energy converters (WECs) have yet to make significant progress towards commercialisation. One stepping stone to achieve this objective is the availability of appropriate control technology, suchthatenergyconversionisperformedaseconomicallyaspossible,minimisingthedelivered energy cost, while also maintaining the structural integrity of the device, minimising wear on WEC components, and operating across a wide range of sea conditions. Suitable energy-maximising control technology depends upon the availability of two fundamental ‘pieces’: A control-oriented dynamical model, describing the motion of the WEC, and a model-based optimal control framework, able to efficiently compute the corresponding energy-maximising control law, subject to a set of constraints, defined according to the physical limitations of the device. FollowingtherequirementsforsuccessfulWECcontrol,andbothusingandextendingkeytools arising from the framework of model reduction by moment-matching, this thesis presents two main contributions. Firstly, this monograph proposes a comprehensive moment-based model reduction framework, tailored for WEC systems, addressing linear and nonlinear model reduction cases, providing a systematic method to compute control-oriented models from complex target structures. These approximating models inherit steady-state response characteristics of the target system, via the proposed moment-matching reduction framework. Secondly, by recognising that, besides being a powerful model reduction tool, the parameterisation of the steady-state response of a system in terms of moment-based theory can be explicitly used to transcribe the energy-maximising control problem to a finite-dimensional nonlinear program, a comprehensive moment-based optimal control framework, tailored for WEC systems, is proposed. This framework considers both linear and nonlinear optimal control cases, while also including robust solutions with respect to both system, and input uncertainty, providing an efficient method to compute the energy-maximising control law for WECs, under different modelling assumptions. Throughout this thesis both model reduction, and optimal control frameworks, are presented for a general class of WEC devices, and their performance is analysed via multiple case studies, considering different devices, under different sea state conditions