  Traditional Lyapunov based transient stability assessment approaches focus on
identifying the stability region (SR) of the equilibrium point under study.
When trying to estimate this region using Lyapunov functions, the shape of the
final estimate is often limited by the degree of the function chosen, a
limitation that results in conservativeness in the estimate of the SR. More
conservative the estimate is in a particular region of state space, smaller is
the estimate of the critical clearing time for disturbances that drive the
system towards that region. In order to reduce this conservativeness, we
propose a methodology that uses the disturbance trajectory data to skew the
shape of the final Lyapunov based SR estimate. We exploit the advances made in
the theory of sum of squares decomposition to algorithmically estimate this
region. The effectiveness of this technique is demonstrated on a power systems
classical model.
