  Dynamic security analysis is an important problem of power systems on
ensuring safe operation and stable power supply even when certain faults occur.
No matter such faults are caused by vulnerabilities of system components,
physical attacks, or cyber-attacks that are more related to cyber-security,
they eventually affect the physical stability of a power system. Examples of
the loss of physical stability include the Northeast blackout of 2003 in North
America and the 2015 system-wide blackout in Ukraine. The nonlinear hybrid
nature, that is, nonlinear continuous dynamics integrated with discrete
switching, and the high degree of freedom property of power system dynamics
make it challenging to conduct the dynamic security analysis. In this paper, we
use the hybrid automaton model to describe the dynamics of a power system and
mainly deal with the index-1 differential-algebraic equation models regarding
the continuous dynamics in different discrete states. The analysis problem is
formulated as a reachability problem of the associated hybrid model. A
sampling-based algorithm is then proposed by integrating modeling and
randomized simulation of the hybrid dynamics to search for a feasible execution
connecting an initial state of the post-fault system and a target set in the
desired operation mode. The proposed method enables the use of existing power
system simulators for the synthesis of discrete switching and control
strategies through randomized simulation. The effectiveness and performance of
the proposed approach are demonstrated with an application to the dynamic
security analysis of the New England 39-bus benchmark power system exhibiting
hybrid dynamics. In addition to evaluating the dynamic security, the proposed
method searches for a feasible strategy to ensure the dynamic security of the
system in face of disruptions.
