The need for environmental protection is pushing to a massive introduction of energy production from renewables. Although wind and solar energy present the most mature technologies for energy generation, wave energy has a huge annual energy potential not exploited yet. Indeed, no leading device for wave energy conversion has already been developed. Hence, the future exploitation of wave energy will be strictly related to a specific infrastructure for power distribution and transmission that has to satisfy high requirements to guarantee grid safety and stability, because of the stochastic nature of this source. To this end, an electrical architecture model, based on a common DC bus topology and including a Hybrid Energy Storage System (HESS) composed by Li-ion battery and flywheel coupled to a wave energy converter, is here presented. In detail, this research work wants to investigate the beneficial effects in terms of voltage and current waveforms frequency and transient behavior at the Point of Common Coupling (PCC) introduced by HESS under specific stressful production conditions. Specifically, in the defined simulation scenarios it is demonstrated that the peak value of the voltage wave frequency at the PCC is reduced by 64% to 80% with a faster stabilization in the case of HESS with respect to storage absence, reaching the set value (50 Hz) in a shorter time (by −10% to −42%). Therefore, HESS integration in wave energy converters can strongly reduce safety and stability issues of the main grid relating to intermittent and fluctuating wave production, significantly increasing the tolerance to the expected increasing share of electricity from renewable energy sources.