Geometric Modelling and Energy Optimisation in a Heaving-Point Absorber Wave Energy Converter

Dhananjay Tiwari, Ravi N. Banavar, D. H. S. Maithripala

Abstract: This paper describes a model for a heaving-point absorber wave energy converter (WEC). A semi-submerged, spherical buoy with an internally suspended pendulum is used to study the constrained motion of the WEC. The initial aim is to derive the mathematical model for the motion of the WEC. In the current study, translation motion of the spherical buoy is constrained at the bottom-most point, and the link of the pendulum is attached internally at a diametrically opposite end. The rotational dynamics of the two-body system is derived on a configurational manifold using geometric techniques and validated using MATLAB simulations. Later on, the attempt is to maximize the total oscillation energy stored in the pendulum for the periodic forces acting at specific points on the sphere. The optimization is achieved by using the local coordinates of the configurational manifold on which the system moves. It is observed that the current method is computationally inefficient. Hence this work will be extended at later stages in designing a more efficient geometric-structure preserving optimal control technique. Our study is a first attempt to mimic the impact of waves on these spheres coupled with a pendulum and arrive at preliminary results on optimal energy extraction before proceeding to more realistic and complex scenarios.