Combining Trajectory Data with Analytical Lyapunov Functions for Improved Region of Attraction Estimation

TL;DR

This paper introduces a hybrid approach combining classical Lyapunov functions with data-driven methods to improve the estimation of the Region of Attraction in nonlinear power systems, enhancing accuracy and certifiability.

Contribution

It presents a novel methodology that integrates analytical Lyapunov functions with trajectory data to produce more accurate and certifiable ROA estimates, independent of the data fitting technique.

Findings

Improved ROA estimation accuracy demonstrated on multiple systems.

Method provides certifiable inner approximations of the ROA.

Flexible approach applicable with different function fitting methods.

Abstract

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.