Effect of a nonlinear power take off on a wave energy converter
Bailey, Helen Louise
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This thesis is titled The influence of a nonlinear Power Take Off on a Wave Energy Converter. It looks at the effect that having a nonlinear Power Take Off (PTO) has on an inertial referenced, slack moored, point absorber, Wave Energy Converter (WEC). The generic device studied utilizes relative heave motion between an axi-symmetric cylinder and an internal mass, for the PTO to operate between. The PTO is the part of the WEC that transforms the relative motion into electricity. In this work, three different types of nonlinear PTO and a linear PTO are presented, tested, analysed and compared. The three nonlinear PTO types are: • A PTO that extracts energy in only one direction, either in relative compression or expansion. • A linear PTO and an additional endstop or peripheral PTO, that can only extract energy when the relative position of the internal mass has reached a pre-determined position. • A PTO that has damping forces that are quadratically proportional to the relative velocity. A numerical simulation has been built based upon a Runge-Kutta time series progression. The model uses the summation of the excitation force from the waves, the radiation force from the movement of the cylinder, the buoyancy force and the PTO forces. These combine to cause acceleration of the mass of the external cylinder, with an equal and opposite PTO force acting on the internal mass. The excitation force and added mass values are obtained from the boundary element method software, WAMIT. Prony’s method is used to obtain an approximate radiation force, based upon the radiation time force history. This numerical model operates on both a 1:40 scale and a full sized model. The numerical model finds the optimal PTO parameters, for different PTO setups, in irregular sea states. This optimum is based on the power extracted as well as indications of the reliability and lifetime of the system. The numerical simulation presents results showing how the nonlinearity of the PTO influences the motions of the WEC, resulting in dissimilarities between the Response Amplitude Operator (RAO) results, obtained from regular seas, and the Linear Transfer Function (LTF), found from irregular sea testing. The experimental model has been tested in the Curved Wave Tank facility at the University of Edinburgh, with a 1:40 scaled model. It used a central rod both as a support structure and to limit the movement of the cylinder and internal mass to heave. Between the cylinder and internal mass a spring and pneumatic damper operate in parallel, in various setups. It was tested in regular and irregular sea states and the position of the internal mass and cylinder was monitored. The experimental model was tested to ascertain the time series motions, RAO, LTF, the relative phase between the bodies and the power extracted for different wave climates. The numerical and experimental work were compared to allow confidence in both models. They showed relatively good agreement for the RAOs, LTFs and predictions of the relative phase but there was discrepancies in the predicted power for both regular and irregular seas. This difference is due to the difficulties in obtaining the relative velocities in the experimental model, resulting in a significant error in power prediction, since the power is proportional to the square of the relative velocities. The conclusions show that having a mono-directional PTO as opposed to a bi-directional PTO results in an approximately equal or greater power extraction in a variety of different sea states. An additional endstop or peripheral damper can increase the total power that a WEC extracts, in some situations, and may be advantageous depending upon the other potential benefits it brings to the WEC.