Optimization analysis of a heaving point absorber wave energy converter in wave focusing conditions near a parabolic vertical wall

Optimization analysis was conducted to maximize the power generation of a cylindrical heaving point-absorber wave energy converter (HPA-WEC) positioned in front of a bottom-mounted parabolic vertical wall, using the wave energy focusing effect. Hydrodynamic analyses were performed using a three-dimensional linear frequency-domain boundary element method (FD-BEM) developed and validated independently in previous studies. The FD-BEM was integrated into an automated optimization framework with metaheuristic algorithms. The optimization analysis assumed regular waves propagating perpendicular to the wall and considered four design variables: the position of the parabolic wall vertex, the distance between the WEC and the wall vertex, the draft of the WEC, and the power take-off damping coefficient. Various metaheuristic algorithms were used to calculate the maximum power generation of the HPA-WEC and compare the performance of each algorithm. The optimization results showed that the parabolic wall significantly improved power generation compared to a straight wall, with power increases of 34 %, 112 %, and 208 % at widths of the parabolic wall of 10 m, 20 m, and 40 m, respectively. Maximum power was achieved when the WEC was positioned near the vertex of the parabolic wall or approximately half a wavelength away. Influenced by wave interactions, the center of the WEC is located near but slightly outside the focal point of the parabolic wall. Optimization results indicate that positioning near the focal point significantly enhances power generation efficiency, emphasizing the importance of the shape of the parabolic wall and the strategic placement of the WEC.