Hysteretic transition of coarse-grained power grid model on small-world network

We study synchronous phenomena of a coarse-grained power grid model, the swing equation, on small-world networks. We show that its steady state, which stands for the normal operation of the power systems, can be realized even if the phases are disordered. In addition, we prove the linear stability of steady state with small-different phases between the adjacent oscillators. On the other hand, a trigger of instantaneous power failure, which is described by the hysteretic transition, might disappear on an appropriate small-world network. This result suggests that the small-world connection would potentially prevent the massive blackouts.