Linearisation-based nonlinearity measures for wave-to-wire models in wave energy

Abstract

It is important to consider nonlinear effects when designing controllers to maximise generated energy in wave energy converters (WECs). Due to the substantial extra computation and complexity added when considering nonlinearities in the controller calculations, quantifying the extent of nonlinearity in WECs’ behaviour is crucial to avoid designing overcomplicated control strategies. This paper suggests two nonlinearity measures to quantify the nonlinearity degree of wave-to-wire (W2W) models in steady-state, using the best linear approximation identified through a minimisation problem as a benchmark. The first measure, referred to as the original nonlinearity measure, evaluates the nonlinear effects of the wave-absorber hydrodynamic interaction. The second measure, referred to as the power nonlinearity measure, quantifies the nonlinear effects in power take-off (PTO) systems, considering the quadratic response of the power signal. The degree of nonlinearity of two WEC models, a partially-nonlinear hydrodynamic model with an ideal PTO model and a complete nonlinear W2W model, is evaluated using monochromatic and polychromatic waves over a wide range of wave periods and heights, covering the whole operational space of a WEC.