Spectral-domain modelling of a non-linear wave energy converter: Analytical derivation and computational experiments

Harvesting energy from waves is gaining popularity in the last decades, due to growing technological maturity and reduction of manufacturing costs of Wave Energy Converter (WEC) devices. However, the optimal design of WECs represents a challenge to its large-scale commercialisation. Behind this multi-objective optimisation, a significant number of simulations are necessary to identify the optimal configuration of the device that minimise certain technoeconomic parameter. Frequency-domain models are suggested in an early stage since they provide a simple and fast simulation tool. On the other hand, non linear time-domain numerical models are more suitable during an advanced design phase where it is essential to assess performance and acting loads with greater reliability. The aim of this work is the development of a spectral-domain model of a WEC device that combines the computational speed of frequencydomain models with the accuracy of non-linear models to improve the design in early stage. Three different models of the ISWEC, a WEC developed by the MOREnergy Lab of Politecnico di Torino (Italy), are derived and compared: a fully non-linear time-domain model, a frequencydomain model, and a spectral-domain model. The spectral-domain modelling of the ISWEC system represents an important novelty for the technological development of the system and an example framework for similar technologies. Moreover, in the energy harvesting field, no previous work addressed the analytical representation of a realistic electro-mechanical converter with both torque and power saturation, and the representation of a gyro-pendulum system in spectral-domain remains untreated. The numerical experiments demonstrate that the spectraldomain model shows an improved accuracy compared with the frequency-domain model, with a reduction of percentage error of the computed gross power in the order of two times. Despite a not perfect accuracy of the spectral-domain model against the time-domain one, the spectraldomain framework is considered as a valid solution due to its computational efficiency, that is demonstrated to be, at least, three order of magnitude higher than the time-domain one