Parametric representation of arrays of wave energy converters for motion simulation and unknown input estimation: A moment-based approach

When it comes to parameterisation of dynamical models for arrays of Wave Energy Converters (WECs), the most-used approach, within the wave energy literature, provides a state-space representation whose order (dimension) increases quadratically with the number of devices composing the WEC array. This represents a major drawback for key WEC design elements, such as motion simulation and unknown input estimation, being the latter essential to effectively maximise energy extraction from ocean waves. We present herein a multi-input, multi-output (MIMO) parameterisation strategy based on a system-theoretic interpretation of moments. The state-space representations computed with this moment-based approach exactly match the steady-state behavior of the target WEC system at specific (user-selected) interpolation points, providing efficient low dimensional models that can accurately represent the input-output dynamics of WEC arrays. Moreover, we show that there exists an intrinsic connection between wave excitation force estimation strategies and the moment-based parameterisation method proposed in this paper. We exploit this mathematical correlation to provide low order models that deliver the same degree of wave excitation force estimation accuracy to that obtained by implementing the currently-used parameterisation methods, with mild computational requirements. The performance of the strategy is analysed in terms of a case study, considering a WEC array composed of state-of-the-art CorPower-like devices, for both WEC motion simulation and wave excitation force estimation scenarios.