Stability guarantees for primary frequency control with randomized flexible loads

There has recently been interest in diversifying the technologies that provide primary frequency control of the power grid beyond generation. One method of interest to obtain frequency control by turning on or off flexible loads in response to local measurements of line frequency. Because of the large number of loads involved, it is desirable to implement this control without communication among the loads or to a centralized controller. One proposal that does not require communication is to have each load choose the frequency at which it switches on or off randomly. In this paper we use tail bounds and absolute stability to obtain stability guarantees that are satisfied with high probability. This stability result considers not only grid inertia and damping but local measurement delays.