Data-driven Estimation for a Region of Attraction for Transient Stability Using the Koopman Operator

This paper presents a novel Koopman Operator based framework to estimate the region of attraction for power system transient stability analysis. The Koopman eigenfunctions are used to numerically construct a Lyapunov function. Then the level set of the function is utilized to estimate the boundary of the region of attraction. The method provides a systematic method to construct the Lyapunov function with data sampled from the state space, which suits any power system models and is easy to use compared to traditional Lyapunov direct methods. In addition, the constructed Lyapunov function can capture the geometric properties of the region of attraction, thus providing useful information about the instability modes. The method has been verified by a simple illustrative example and three power system models, including a voltage source converter interfaced system to analyze the large signal synchronizing instability induced by the phase lock loop dynamics. The proposed method provides an alternative approach to understanding the geometric properties and estimating the boundary of the region of attraction of power systems in a data driven manner.