As the increasing utilization of wind resources and lightweight gas turbine units, the power grid is shifting towards a situation with declining system inertia, which causes a larger frequency deviation after disturbances and threatens the reliability of the grid. Thus, we devote this work to develop an appropriate tool to determine the economic value of the inertia to the systems. To do so, we discretize and integrate the system dynamic equations into a modified version of the linear security-constrained unit commitment framework. Since the fast-acting storage devices are able to respond in a very short time, we also develop a storage control scheme to mimic the inertia and to provide primary frequency responses. We perform extensive studies on the IEEE 24-bus reliability test system and present some illustrative simulation results to demonstrate the effectiveness of the proposed method to assess the economic value of the power system inertia.