A simplified model of a redundant power grid is used to study integration of fluctuating renewable generation. The grid consists of large number of generator and consumer nodes. The net power consumption is determined by the difference between the gross consumption and the level of renewable generation. The gross consumption is drawn from a narrow distribution representing the predictability of aggregated loads, and we consider two different distributions representing wind and solar resources. Each generator is connected to D consumers, and redundancy is built in by connecting R ≤ D of these consumers to other generators. The lines are switchable so that at any instance each consumer is connected to a single generator. We explore the capacity of the renewable generation by determining the level of "firm" generation capacity that can be displaced for different levels of redundancy R. We also develop message-passing control algorithm for finding switch settings where no generator is overloaded.