# Model-Free MLE Estimation for Online Rotor Angle Stability Assessment with PMU Data

## TL;DR

This paper introduces a real-time, model-free method for assessing rotor angle stability using PMU data by estimating the maximal Lyapunov exponent with a recursive least squares approach, enabling timely stability evaluation.

## Contribution

It proposes a novel online stability assessment method that accurately estimates the MLE from real-time measurements without relying on system models, addressing fluctuation issues.

## Key findings

- Effective stability assessment on test systems
- Reliable detection of stability conditions
- Timely evaluation using real-time data

## Abstract

Recent research has demonstrated that the rotor angle stability can be assessed by identifying the sign of the system maximal Lyapunov exponent (MLE). A positive (negative) MLE implies unstable (stable) rotor angle dynamics. However, because the MLE may fluctuate between positive and negative values for a long time after a severe disturbance, it is difficult to determine the system stability when observing a positive or negative MLE without knowing its further fluctuation trend. In this paper, a new approach for online rotor angle stability assessment is proposed to address this problem. The MLE is estimated by a recursive least square (RLS) based method based on real-time rotor angle measurements, and two critical parameters, the Theiler window and the MLE estimation initial time step, are carefully chosen to make sure the calculated MLE curves present distinct features for different stability conditions. By using the proposed stability assessment criteria, the developed approach can provide timely and reliable assessment of the rotor angle stability. Extensive tests on the New-England 39-bus system and the Northeast Power Coordinating Council 140-bus system verify the effectiveness of the proposed approach.