Two raft wave energy converters

Abstract

Global warming has caused an increasing demand for renewable energy. Currently, 50% of the renewable energy is provided by wind and solar combined. However, these renewable energy sources are highly volatile. Wave energy converters can provide a stable renewable energy source. Previous research has contributed to understanding various combined effects of length, aspect ratio, hydro-elasticity and PTO damping on the optimisation of peak power absorption for regular waves. However, research on optimising the combined effects on annual energy production and especially power stability is missing. This thesis aims to better understand these effects by answering the following research question: "How can the combined effects of total length, aspect ratio, raft stiffness and PTO damping influence yearly energy conversion and energy stability of a pitching raftWEC"

To do this, a novel formulation for a monolithic finite element model containing Timoshenko beam theory and Linear potential flow is developed. This FEM consists of a two-dimensional domain, where the water is excited by linear irregular waves. The wave energy converter is modelled as two floating Timoshenko beams connected by a damped joint. The model is verified by proving that the solution converges according to the polynomial order +1 for decreasingmesh size. Additionally, it is proven that energy is conserved which shows that there is no wave reflection resulting from the domain boundaries. Finally, the model is validated by comparing the results of the structure with and without joint to previous research.

Two experiments are developed to understand the combined effects. Initially, an eigenmode analysis of the undamped structure is performed. This gives insight into the influence of individual parameters on the eigenfrequencies and shapes. Moreover, the real eigenmodes are used to decompose the real part of the complex resonance shapes of the relative rotation response amplitude operator (RAO). This provides a coupling between the performance according to the relative rotation RAO and the eigenmodes and frequencies. A limitation of this method is that phase differences cannot be considered.
The second experiment maximises the annual energy conversion and energy stability of thewave energy converter with three sets of variable parameters: (total length, aspect ratio, damping parameter), (total length, symmetrical raft stiffness, damping parameter) and (stiffness fore-aft, stiffness aft-raft, damping parameter). This is done in three steps. First, the RAO for the relative rotation at the joint is constructed. This is converted to a power spectrum. Secondly, the power spectrum is scaled by the JONSWAP energy density spectra. These
spectra are constructed using the annual wave conditions, significant wave heights and peak periods from a wave scatter diagram. Subsequently, the results per spectrum are scaled by the number of occurrences of the wave conditions to obtain the annual energy conversion. Third, The optimum damping parameter per configuration is determined by calculating the annual energy conversion for a set of damping parameters. These results are interpolated to select the damping parameter that maximises annual energy conversion.
Finally, the performance of each configuration with their respective optimum damping parameter is assessed on annual energy conversion and capture width per peak wave period to give insight into the energy conversion and stability. The optimisation results are clarified with the results of the eigenmode analysis.
It was found that the optimal total length, considering raft stiffness, aspect ratio and PTO damping can be determined by matching the dimensionless wavelength corresponding to the third mode, and the annual significant wavelength.

Furthermore, It is proven that an aspect ratio of 0.2 to 0.3 increases the performance in high-frequency waves without compromising on low-frequency waves. The capture width is more evenly distributed over peak wave periods, indicating a higher energy stability. This results in an increase of annual energy conversion of 31% with respect to an aspect ratio of 0.5. Besides the aspect ratio, it was found that an asymmetrical raft stiffness, with a moderately flexible fore raft and a rigid aft-raft increase energy stability without compromising annual energy conversion.