  This paper introduces a novel framework to construct the region of attraction
(ROA) of a power system centered around a stable equilibrium by using stable
state trajectories of system dynamics. Most existing works on estimating ROA
rely on analytical Lyapunov functions, which are subject to two limitations:
the analytic Lyapunov functions may not be always readily available, and the
resulting ROA may be overly conservative. This work overcomes these two
limitations by leveraging the converse Lyapunov theorem in control theory to
eliminate the need of an analytic Lyapunov function and learning the unknown
Lyapunov function with the Gaussian Process (GP) approach. In addition, a
Gaussian Process Upper Confidence Bound (GP-UCB) based sampling algorithm is
designed to reconcile the trade-off between the exploitation for enlarging the
ROA and the exploration for reducing the uncertainty of sampling region. Within
the constructed ROA, it is guaranteed in probability that the system state will
converge to the stable equilibrium with a confidence level. Numerical
simulations are also conducted to validate the assessment approach for the ROA
of the single machine infinite bus system and the New England $39$-bus system.
Numerical results demonstrate that our approach can significantly enlarge the
estimated ROA compared to that of the analytic Lyapunov counterpart.
