  Link failures repeatedly induce large-scale outages in power grids and other
supply networks. Yet, it is still not well understood, which links are
particularly prone to inducing such outages. Here we analyze how the nature and
location of each link impact the network's capability to maintain stable
supply. We propose two criteria to identify critical links on the basis of the
topology and the load distribution of the network prior to link failure. They
are determined via a link's redundant capacity and a renormalized linear
response theory we derive. These criteria outperform critical link prediction
based on local measures such as loads. The results not only further our
understanding of the physics of supply networks in general. As both criteria
are available before any outage from the state of normal operation, they may
also help real-time monitoring of grid operation, employing counter-measures
and support network planning and design.
