In this paper, the non-linear effects of viscosity on the performance of a Wave Energy Converter (WEC) system are analysed. A standard linear Model Predictive Control (MPC) is used to show the negative effects that the unaccounted non-linear viscosity force in the hydrodynamic system has on the power absorption. A non-linear MPC (NLMPC) is then implemented, where the non-linear viscosity effects are included in the optimisation. A linear drag coefficient estimate of the non-linear viscosity is then included in the linear MPC; creating a Linear Viscous Model Predictive Control. When constraints are incorporated, it is shown that a single choice of the linear viscous drag coefficient for use within the linear MPC can provide comparable results to the non-linear MPC approach, over a wide range of sea states.