Large scale renewable energy source (RES) integration planned for multiple power grids around the world will require additional resources/reserves to achieve secure and stable grid operations to mitigate the inherent intermittency of RES. In this paper, we present formulations to understand the effect of fast storage reserves in improving grid reliability under different cost functions. Our formulations not only aim to minimize imbalance but also maintain state-of-charge (SoC) of storage. The proposed approaches rely on a macroscopic supply-demand model of the grid with total power output of energy storage as the control variable. We show that accounting for system response due to inertia and local governor response enables a more realistic quantification of storage requirements for damping net load fluctuations. Simulation case studies are embedded in the paper by using datasets from the Elia TSO in Belgium and BPA in the USA. The numerical results benchmark the marginal effect on reliability due to increasing storage size under different system responses and associated cost functions. Further we observe myopic control of batteries proposed approximates deterministic control of batteries for faster time scale reserve operation.