Derivation and Experimental Validation of a Parameterized Nonlinear Froude-Krylov Force Model for Heaving Point Absorber Wave Energy Converters

Wave energy converters (WECs) have gained significant attention as a promising renewable energy source. Optimal control strategies, crucial for maximizing energy extraction, have traditionally relied on linear models based on small motion assumptions. However, recent studies indicate that these models do not adequately capture the complex dynamics of WECs, especially when large motions are introduced to enhance power absorption. The nonlinear Froude-Krylov (FK) forces, particularly in heaving point absorbers with varying cross-sectional areas, are acknowledged as key contributors to this discrepancy. While high-fidelity computational models are accurate, they are impractical for real-time control applications due to their complexity. This paper presents a parameterized approach for expressing nonlinear FK forces across a wide range of point absorber buoy shapes inspired by implementing real-time, model-based control laws. The model was validated using measured force data for a stationary spherical buoy subjected to regular waves. The FK model was also compared to a closed-form buoyancy model, demonstrating a significant improvement, particularly with high-frequency waves. Incorporating a scattering model further enhanced force prediction, reducing error across the tested conditions. The outcomes of this work contribute to a more comprehensive understanding of FK forces across a broader range of buoy configurations, simplifying the calculation of the excitation force by adopting a parameterized algebraic model and extending this model to accommodate irregular wave conditions.