Critical synchronization dynamics on power-grids

Power-grids are among the largest man-made complex systems, staying in the synchronization state of billions of nodes. Formerly power-law tailed cascade size distributions have been found by outage statistics and DC models. The spread of renewable resources poses unprecedented pressure on system stability. Here we show how this can be modeled by Kuramoto-like synchronization models, which describe the real power flow in AC systems. The combination of swing equations with line threshold failures allows us to describe the dynamical avalanche-like blackout failures in different HV power-grid networks. In particular, we compare the stability and blackout statistics for the US and the EU HV networks, taking into account the feedback effects. We show that nonuniversal power-law size and duration distributions emerge below the first-order transitions of the Kuramoto model, thus we see an example for hybrid transition known in other branches of physics.