Spectral-Domain Modelling of Wave Energy Converters as an Efficient Tool for Adjustment of PTO Model Parameters

Abstract

The power take-off (PTO) system is a core component in WECs as it plays a critical role in power production. In numerical models the PTO systems are commonly represented and simplified through a combination of linear stiffness and damping terms in the equations of motion. These parameters are influential to the dynamic response and thus affect the power performance of WECs. In the preliminary design and optimization of WECs, proper tuning of the PTO damping and stiffness could reflect better the potential of the concept. In practice, the PTO damping and stiffness are tuned to maximize the absorbed power by achieving the desired velocity amplitude or phase of the velocity with respect to the excitation force. However, recent literature has indicated that the selection of PTO parameters for maximum mechanical power absorption is not necessarily optimal for the maximum production of electrical power when the conversion efficiency of the electrical machine is included. To obtain these parameters which maximize the delivered electrical power, wave-to-wire models are widely used. Nevertheless, wave-to-wire models are predominately established by using time-domain models which can be associated with large computational efforts from the perspective of early-stage design and concept evaluation. To tackle this challenge, a spectral-domain-based wave-to-wire model is proposed to cover both hydrodynamic and electrical responses. In this paper, a spherical heaving point absorber integrated with a linear permanent-magnet generator is used as reference. The relevant nonlinear effects are incorporated by statistical linearization using spectral-domain modelling. In particular, the nonlinear effects considered in this work include the viscous drag force, the electrical current saturation and the partial overlap between the translator and stator components of the linear generator. The model results are then verified against a nonlinear time-domain-based wave-to-wire model. Subsequently, the proposed model is applied to identify the PTO parameters for maximizing the electrical power in various wave states. The computational efficiency and accuracy of the proposed spectral-domain model are compared with the time-domain model, with regard to the identification of the proper PTO damping and stiffness. Based on the results, the advantage of using the spectral-domain-based wave-to-wire modeling in PTO tuning is demonstrated.