  The increasing uptake of inverter based resources (IBRs) has resulted in many
new challenges for power system operators around the world. The high level of
complexity of IBR generators makes accurate classical model-based stability
analysis a difficult task. This paper proposes a novel methodology for solving
the problem of estimating the Region of Attraction (ROA) of a nonlinear system
by combining classical model based methods with modern data driven methods. Our
method yields certifiable inner approximations of the ROA, typical to that of
model based methods, but also harnesses trajectory data to yield an improved
accurate ROA estimation. The method is carried out by using analytical Lyapunov
functions, such as energy functions, in combination with data that is used to
fit a converse Lyapunov function. Our methodology is independent of the
function fitting method used. In this work, for implementation purposes, we use
Bernstein polynomials to function fit. Several numerical examples of ROA
estimation are provided, including the Single Machine Infinite Bus (SMIB)
system, a three machine system and the Van-der-Pol system.
