Frequency waves, grid friendly appliances and geographic limits in a smart grid

Grid Friendly Appliances (GFAs) are water heaters, refrigerators, and other domestic electrical appliances that sense and respond to frequency problems in the electric power grid. The controller in a GFA monitors the power signal at its plug and turns the device off when the frequency drops below 59.95 Hz. When the frequency recovers its nominal value of 60 Hz, the device is turned back on. Large numbers of these devices can act as a distributed control system that improves the resilience of the power system as a whole to sudden, large, and unexpected mismatches in supply and demand. Recently, it has been shown that the frequency signal acted on by GFAs moves at a relatively slow pace of about 500 miles per second, thereby introducing a previously unaccounted for delay into this distributed control system. In this paper, we use a simple, linear model to demonstrate that this propagation delay imposes a limit on the geographic extent of the distributed control system: if this limit is violated, then the controllers can cause instability and, potentially, precipitate a blackout.