Alexis Mérigaud

A Nonlinear Extension for Linear Boundary Element Methods in Wave Energy Device Modelling

To date, mathematical models for wave energy devices typically follow Cummins equation, with hydrodynamic parameters determined using boundary element methods. The resulting models are, for the vast majority of cases, linear, which has advantages for ease of computation and a basis for control design to maximise energy capture. While these linear models have attractive properties, the assumptions under which linearity is valid are restrictive. In particular, the assumption of small movements about an equilibrium point, so that higher order terms are not significant, needs some scrutiny. While this assumption is reasonable in many applications, in wave energy the main objective is to exaggerate the movement of the device through resonance, so that energy capture can be maximised. This paper examines the value of adding specific nonlinear terms to hydrodynamic models for wave energy devices, to improve the validity of such models across the full operational spectrum.

Free-Surface Time-Series Generation for Wave Energy Applications

Finite-length, numerical simulations of Gaussian seas are widely used in the wave energy sector. The most common method consists of adding up harmonic sinusoidal components, with random phases and deterministic amplitudes derived from the target wave spectrum [deterministic amplitude scheme (DAS)]. In another approach, the component amplitudes are chosen randomly with a variance depending on the spectrum [random amplitude scheme (RAS)]. It is now generally accepted that only the latter method reproduces the true statistical properties of a Gaussian sea. Compared to previous works, this study clarifies the exact nature of the “statistical properties” that should be represented in the simulation process. Further analysis is carried out to address unanswered questions highlighted in the existing literature, especially with respect to the statistical relationships between discrete successive simulation points, and the probability law governing the average power estimator of a wave energy converter (WEC) simulated with the generated wave time series. It is shown that RAS exactly reflects how the WEC performance, considered over a finite duration, varies with respect to its long-term average, whereas DAS has the advantage of providing accurate estimates of the long-term average values using fewer, or shorter, simulations; in particular, it is demonstrated that only one simulation is sufficient when the WEC model is linear. Furthermore, it is shown why alternative methods, based on nonharmonic superposition of sinusoids, are not recommended. The effects of the simulation method (RAS or DAS) upon the statistics of individual oscillations in the time domain are also explored experimentally. Finally, a table is provided that gives recommendations, depending on the objective of the simulations.

Power production assessment for wave energy converters: Overcoming the perils of the power matrix

Wave energy converter power production assessment, usually carried out using a power matrix, is essential for the appraisal of new wave energy converter technologies and for the planning of specific wave energy projects. Errors in power assessment may arise, both from an inaccurate description of the wave energy converter dynamics and from an excessively simplified representation of wave spectra in the power matrix approach. Ideally, the wave energy converter output should be computed in every individual sea state of the wave dataset considered, without the assumption of any parametric spectral shape. However, computationally efficient methods are necessary to achieve such extensive wave energy converter simulation. The non-linear frequency-domain technique is significantly faster than Runge–Kutta time-domain simulations, without affecting the representation of radiation forces and non-linear dynamics. In this article, the two main sources of errors in wave energy converter power assessment, namely the power matrix representation and wave energy converter modelling inaccuracies, are jointly studied and put into perspective, using four case studies (two wave energy converter systems in two locations). It is found that both types of errors can be of comparable magnitude. The non-linear frequency-domain technique simulation technique is shown to be a computationally efficient tool, retaining a realistic representation of the device dynamics while avoiding the use of a power matrix, thus preserving accurate representation of both the sea states and the wave energy converter, at little computational expense. Aside from those main results, the issue of the length and number of simulations, necessary to achieve average power estimates with sufficient accuracy in every sea state, is addressed in detail.

Ocean forecasting for wave energy production

There are a variety of requirements for future forecasts in relation to optimizing the production of wave energy. Daily forecasts are required to plan maintenance activities and allow power producers to accurately bid on wholesale energy markets, hourly forecasts are needed to warn of impending inclement conditions, possibly placing devices in survival mode, while wave-by-wave forecasts are required to optimize the real-time loading of the device so that maximum power is extracted from the waves over all sea conditions. In addition, related hindcasts over a long time scale may be performed to assess the power production capability of a specific wave site. This paper addresses the full spectrum of the aforementioned wave modeling activities, covering the variety of time scales and detailing modeling methods appropriate to the various time scales, and the causal inputs, where appropriate, which drive these models. Some models are based on a physical description of the system, including bathymetry, for example (e.g., in assessing power production capability), while others simply use measured data to form time series models (e.g., in wave-to-wave forecasting). The paper describes each of the wave forecasting problem domains, details appropriate model structures and how those models are parameterized, and also offers a number of case studies to illustrate each modeling methodology.