Line Failure Localization of Power Networks Part I: Non-Cut Outages

Transmission line failures in power systems propagate non-locally, making the control of resulting outages extremely difficult. In this work, we establish a mathematical theory that characterizes patterns failure propagation and localization terms network graph structure. It provides novel perspective on distribution factors precisely captures Kirchhoff's Law topological structures. Our results show specific collections subtrees transmission plays critical role redistribution, motivates block decomposition as structure to understand long-distance disturbances. Part I paper, present case when post-contingency remains connected after an initial set lines are disconnected simultaneously. II, outage separates into multiple islands.