Analytical solutions for instantaneous power of heaving-buoy wave energy converters in irregular waves

Abstract

Evaluating instantaneous power output of heaving-buoy wave energy converters (WECs) with power take-off (PTO) damping in irregular waves has commonly been conducted in the time domain by numerically solving the Cummins equation. Not only is the time domain-method computationally time-consuming, but also no explicit closed-form solution has been available. This paper develops a novel and efficient pole-residue approach, operated in the frequency domain, for estimating instantaneous power of heaving-buoy WECs in arbitrary irregular waves. A closed-form solution for the instantaneous power, which is an explicit function of PTO damping coefficient, is derived. The proposed pole-residue approach formulates the system frequency response function in its analytical form, from which “artificial” poles located along the imaginary axis of complex plane are designated. The correctness of the proposed method is verified by using a time-domain method through numerical examples of a heaving-buoy WEC in regular and irregular waves, respectively. The proposed method would be useful for the practical design and optimization of the PTO system for heaving-buoy WECs.