# Optimization of Buoy Shape for Wave Energy Converter Based on Particle Swarm Algorithm
###### Abstract
In the field of secondary energy conversion, the processes are mainly hydraulic, electromagnetic direct-drive, mechanical direct-drive [29], etc. Due to the general low frequency of waves, direct-driven wave energy conversion is not efficient for power generation. [PERSON] et al. [30] proposed a dual-stack coaxial magnetic gear to improve the energy output efficiency of a generator and [PERSON] et al. [31] proposed a permanent magnet-induction magnetic screw with high thrust density and high energy conversion efficiency to improve the energy conversion efficiency of direct-drive electromagnetic processes. [PERSON] et al. [32] proposed a technique to match the geometric and control parameters of a power take-off (PTO) system for a WEC using a genetic algorithm to increase the excitation torque of the buoy and improve the conversion efficiency of the PTO system. [PERSON] et al. [33] proposed a hydraulic WEC combined with an offshore wind turbine, and a fuzzy controller was designed to regulate the displacement of the hydraulic motor and control the output power. [PERSON] et al. [34] proposed a new hydraulic PTO power regulation module structure to improve the power output stability of the hydraulic PTO under irregular wave conditions. In the field of power plant array arrangement, [PERSON] et al. [35] proposed a cost function to optimize the array arrangement of a WEC, with the aim of minimizing power variation and energy storage while maximizing the energy delivered to onshore points co-coupled with the grid. [PERSON] et al. [36] studied the coefficients influencing the layout of wave energy field arrays, such as the number of WECs and wave directionality. [PERSON] et al. [37] conducted experimental studies by means of design trials for a range of geometric layout configurations and wave conditions. Through an analysis of the current research status at home and abroad, it has been found that although defining the geometric shape of buoys using methods such as Bezier curves or B-spline surfaces can achieve optimal energy harvesting efficiency, it sacrificesthe manufacturability of the buoys. This is because buoy shapes that are symmetric and regular are more suitable for engineering applications. Defining specific shapes to describe buoy shapes and optimizing buoy shapes using computational fluid dynamics methods presents challenges such as high computational complexity and scalability issues. Similarly, using metaheuristic algorithms for buoy optimization also has limitations. For example, optimizing buoy shapes typically involves a large number of design variables, leading to a large search space. Some algorithms may also exhibit slow convergence rates, especially when dealing with complex problems, requiring long search times to achieve satisfactory solutions. The proposed method defines the geometric shape of the buoy through a 5-dimensional shape vector based on B-spline curves, while enforcing constraints on the coordinate parameters' upper and lower limits, ensuring that the buoy's shape remains regular throughout the optimization process. In terms of model development, compared to conventional computational fluid dynamics buoy shape optimization methods, the unique modeling tool of WEC-Sim empowers this method with the capability to develop multi-degree-of-freedom WECs. Due to the introduced PSO's capability to search for the global optimal solution within the population, it does not require the computation of gradients or derivatives. Therefore, it can effectively handle problems without explicit expressions or continuity. Compared to traditional optimization methods such as gradient descent, the implementation of PSO is relatively simple. It does not require a complex problem framework; rather, it only necessitates the definition of appropriate fitness functions and parameter settings. Additionally, PSO is less sensitive to the choice of initial conditions and parameter settings, typically exhibiting good robustness.