The objective of this article is to analyze the system benefits of distributed storage at different locations on a grid that has a high penetration of renewable generation. The chosen type of distributed storage modeled is deferrable demand (e.g., thermal storage) because it is relatively inexpensive to install compared to batteries and could potentially form a large component of the peak system load. The advantage of owning deferrable demand is that the purchase of energy from the grid can be decoupled from the delivery of an energy service to customers. Consequently, these customers can reduce costs by shifting their purchases from expensive peak periods to off-peak periods when electricity prices are low. In addition, deferrable demand can provide ramping services to the grid to mitigate the uncertainty of renewable generation. The primary economic issue addressed in this paper is to determine how the storage capacity is allocated between shifting load and providing ramping services. The basic economic tradeoff is between the benefit from shifting more load from peak periods to less expensive periods, and reserving some storage capacity for ramping to reduce the amount of conventional reserve capacity purchased. Our approach uses a new form of stochastic, multi-period Security Constrained Optimal Power Flow (SCOPF) that minimizes the expected system costs for energy and ancillary services over a 24-hour horizon. For each hour, five different levels of wind generation may be realized and these are treated as different system states with known probabilities of occurring. This model is applied to a reduction of the grid in New York State and New England and simulates the hourly load on a hot summer day, treating potential wind generation at different sites as stochastic inputs. The results determine the expected amount and location of conventional generating capacity dispatched, the reserve capacity committed to maintain operating reliability, the charging/discharging of storage capacity, and the amount of potential wind generation spilled. The results show there are major differences in how the deferrable demand at two large load centers, Boston and New York City, is managed, and we provide an explanation for these differences.