This report represents the Master's Thesis on project, "Grid Inertial Response with Lithium-ion Battery Energy Storage Systems". Identification of the issue concerning grid inertia has been discussed along with the proposed solution of using the energy storage system (ESS). Model of the battery energy storage system has been developed on MATLAB/Simulink and the wind turbine generator with full scale converter along with converter for the ESS has been developed in RSCAD. The 12-bus grid model has been implemented to investigate the dynamics of inertial response for different wind power penetration levels. RTDS and dSPACE have been used for real time simulation of power system and ESS, respectivelly. Different approaches of providing inertial response, with ESSs, based on derivative control and combination of derivative - droop control have been investigated. Moreover, the effect of the ESS size on the inertial response has been analyzed. The consequence of variable nature of wind power towards system frequency has also been simulated. The results of the simulations have been present through various study cases.