Microgrid is a confined energy system that integrates renewable sources, energy storage and advanced control system. This paper discusses about the management of Energy Storage System which is important to ideal use of distributed energy resources in steady, secured, clever and coordinated ways. The Energy storage system is interlinked with the microgrid for performing grid interaction, main aim is to design a Simulink model for a microgrid energy management system and optimize electricity costs through implementation of linear optimization approach. Microgrid Energy Management System (EMS) is used for developing algorithms and control strategies within the Simulink model. Linear Optimization is used to find the optimal operation points for the microgrid components, which results optimizing the electricity costs. MATLAB software is utilized for simulation and analyzed the power outputs like PV system, grid voltage, ESS charge and prize graphs.