A modified spectral-domain model for nonlinear hydrostatic restoring force of heaving wave energy converters

Abstract

A modified spectral-domain (SD) model is introduced in this study to address the nonlinear hydrostatic restoring force for heaving wave energy converters (WECs) with non-uniform cross-sectional areas. Distinguished from previous SD models, the modified SD model collectively includes the effects of incident wave elevation and buoy displacement, through the utilization of the multi-variate stochastic linearization method. The proposed SD model is verified against results obtained from a corresponding nonlinear time-domain (TD) model. Subsequently, a comprehensive comparison is carried out between the modified SD model, the other two existing SD models and the linear frequency-domain (FD) model. The nonlinear TD model is considered as the accuracy reference in this comparison. Various environmental and operational inputs, such as sea states, Power Take-Off (PTO) parameters, and buoy drafts, are systematically taken into account in the comparison. Additionally, the computational efficiency of each model is evaluated.

The results suggest that the modified SD model demonstrates significantly enhanced accuracy in cases where hydrostatic force nonlinearity intensifies, compared to the existing SD models and the FD model. Throughout the entire domain of the simulation cases, the maximum relative error of the modified SD model to the nonlinear TD model is below 5 %, while it is 20 % for the FD model and approximately 15 % for the two existing SD models. Moreover, the modeling accuracy of the FD model and existing SD models could be strongly disturbed by the variation of the environmental and operational inputs. Comparatively, the modified SD model is associated with much more stable accuracy. Nevertheless, the modified SD model only requires a modest increase in computational load compared to the FD model and existing SD models and it is still thousands of times faster than the nonlinear TD model.