Power-law distributions of dynamic cascade failures in power-grid models

摘要: Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here we attempt to describe it using an AC model, with a second-order Kuramoto type equation of motion the power-flow. We have focused on exploration network heterogeneity effects, starting from homogeneous 2D lattices US power-grid, possessing identical nodes and links, realistic electric obtained Hungarian electrical database. The last one exhibits node dependent parameters, topologically marginally verge robust networks. show that too weak quenched heterogeneity, coming solely probabilistic self-frequencies (2D lattice) is not sufficient find power-law cascades. On other hand strong destroys synchronization system. found agreement empirically observed failure size distributions grid, as networks near transition also investigated consequence replacing usual Gaussian exponential ones, describing renewable energy sources. drop steady state averages, but distribution both for systems remained insensitive kept universal tails, characterized exponent $\tau\simeq 1.8$. effect instantaneous feedback mechanism case power-grid.