Future power grid systems are envisioned to be integrated with many distributed renewable energy sources (DRES). Energy storage is the key technology to enable reliable and cost-effective renewable energy. Given the fact that large-scale energy storage devices are typically costly to install and operate, we are naturally led to the following question: How much storage is necessary to guarantee the stability of a power grid network with DRESs? In this paper, we study the tradeoff between capacity of energy storage devices and outage probability, i.e., the probability of the occurrence of imbalance between the supply and demand. We first propose a secure scheduling and dispatch (SSD) algorithm that is capable of maintaining the grid stability in the presence of volatility in the power generation. We then derive a closed-form expression that quantifoes the tradeoff between the storage capacity and the outage probability. Under mild assumptions, we show that the outage probability decreases exponentially with respect to the square of the storage capacity. This finding implies that energy storage is an effective and economically viable solution to maintain the stability of a smart grid network, even in the presence of many volatile and intermittent renewable energy sources.