Direct computation of critical clearing time using trajectory sensitivities

The transient energy function (TEE) and single machine equivalent (SIME) techniques have been used successfully over the years to compute the critical clearing time for faults in the system. Sensitivity of the energy margin has also been used to find critical generators for rescheduling of generation. This procedure involves using trajectory sensitivities explicitly and the computation of the critical energy V _cr depends on the system parameters. The need to compute V _cr makes it computationally intensive. In this paper, the authors compute the sensitivity of the energy function to the fault clearing time t_cl directly. By computing this sensitivity for two values of t_cl, the results can be extrapolated to obtain a good estimate of t_cl. The method is illustrated for a structure-preserving model of a 3-machine, 9-bus power system with nonlinear voltage dependent loads