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

Region of Attraction for Power Systems using Gaussian Process and Converse Lyapunov Function -- Part I: Theoretical Framework and Off-line Study