  Potential critical risks of cascading failures in power systems can be
identified by exposing those critical electrical elements on which certain
initial disturbances may cause maximum disruption to power transmission
networks. In this work, we investigate cascading failures in power systems
described by the direct current (DC) power flow equations, while initial
disturbances take the form of altering admittance of elements. The disruption
is quantified with the remaining transmission power at the end of cascading
process. In particular, identifying the critical elements and the corresponding
initial disturbances causing the worst-case cascading blackout is formulated as
a dynamic optimization problem (DOP) in the framework of optimal control
theory, where the entire propagation process of cascading failures is put under
consideration. An Identifying Critical Risk Algorithm (ICRA) based on the
maximum principle is proposed to solve the DOP. Simulation results on the IEEE
9-Bus and the IEEE 14-Bus test systems are presented to demonstrate the
effectiveness of the algorithm.
