Reliability and computational simplicity are of primary importance in
developing on-line instability detection methods. With regard to these
requirements, this paper has proposed a new method for instability de
tection based on generator angles, angular velocities, and their rates
of change. According to the developed method, system instability or o
ut-of-step condition is detected by identifying the characteristics-co
ncave or convex-of a surface on which the post-fault system trajectory
lies, The variation mode and probabilistic property of the proposed i
ndex are investigated by using the 10 machine 39 bus IEEE test system.