Non-linear simulation of a wave energy converter with multiple degrees of freedom using a harmonic balance method

Computationally efficient simulation methods for wave en-ergy converters (WECs) are useful in a variety of applica-tions. The simulation task is particularly challenging when non-linearities are present in the WEC model. Using a Fourierprojection of the system inputs and variables, harmonic bal-ance (HB) is a computationally-efficient method to solve for thesteady-state motion of a non-linear system, preserving an accu-rate representation of the non-linear effects. In previous work,HB has been used for the simulation of WECs with one degreeof freedom (DoF). Here, HB is presented for WEC systems withan arbitrary number of DoFs. A non-linear, 2-DoF model of theISWEC wave energy device is used as an example of application.The HB implementation of the ISWEC model is described in de-tail. Through numerical applications, chosen in both regular andirregular waves, general features of the HB method are exempli-fied, in particular the exponential convergence rate to the actualmathematical solution, and the sensitivity, in some cases, to thestarting point of the HB algoritm.