Optimization of pendulum-based wave energy converter through mathematical approximation

This study analyzes a pendulum-based wave energy converter with multiple degrees of freedom and a rigid hull encapsulation design that enhances robustness and extends lifespan. The kinetic equation of the vertical axis parametric pendulum is proposed alongside the concept of the Prescribed Excitation Model. This model can be applied to evaluate the pendulum's performance in the early design stage at an extremely low cost. A mathematical approximation of this model is derived using the Perturbation Technique. The maximum linear damping obtained from the approximation provides a reference value for the numerical model, reducing the simulation quantity required for optimization. The power assessment of the pendulum through both mathematical approximation and numerical simulation is compared, indicating that the mathematical approximation is reliable for comparing the performance of different pendulums. Finally, a case study reveals that mounting the pendulum upon the mass center of the hull enhances performance. Additionally, the mass of the pendulum and its moment of inertia have less influence on the optimization of the mounting position, suggesting that the optimization process can be divided into two separate parts. The numerical modeling shows that the pendulum under optimal mounting position has the potential to product energy of 6.79 $\mathrm{MW}\bullet h$ (annually).