On a shipboard electric power system, in steady-state operations, the electric grid disturbances due to powerfull periodic pulsed loads are estimated by the voltage and frequency modulations. Energy Storage System (ESS) with fast discharge ability allows to reduce the stress on the grid components and to meet the design standard requirements. This paper focuses on the sizing and simulation of a supercapacitor ESS (SC ESS). Regarding the chosen topology, the SC bank is directly connected to the grid converter (without DC bus stage) because reliability, efficiency and ability to ensure other functions (as voltage sag mitigations) are expected. Regarding the SC ESS management, the DC voltage is controlled at any time and SC ESS charge and discharge are ordered by stepping the reference DC voltage to minimal value or maximal value. Furthermore SC ESS charge/discharge cycle is synchronized with the pulsed load with a smooth time advance in order to compensate the lower power rise of the ESS in comparison with the one of the pulsed load. The results obtained with the shipgrid simulator are convincing: the frequency modulation is significantly reduced (by more three times) and becomes compliant with the standard requirement. Regarding the generator side, the governor torque variations are strongly mitigated.