Future power grid systems are envisioned to be integrated with many distributed renewable energy sources (DRES). Energy storage is a key technology to enable reliable and cost-effective renewable energy. Given the fact that a large-scale energy storage device is usually 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? This paper represents a first step in systematically exploring the tradeoff between the capacity of energy storage devices and the 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 bound to quantify 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. The impact of correlation in energy generation on the stability of a smart grid network is also investigated .