  Due to the evolving nature of power grids and model uncertainty, the online
stability assessment of electrical power systems is always a challenging
problem. This paper aims to provide a theoretical framework for estimating the
region of attraction for power systems in real time. By analyzing and learning
the measurement data in a given time duration, a windowed online Gaussian
process (GP) approach is developed to provide the real-time security assessment
and quantify the uncertainty caused by measurement errors and dynamic evolution
of power systems. In addition, the theoretical analysis is conducted to ensure
the conference level of the estimated region of attraction. Finally, numerical
simulations are implemented on a microgrid model with $9$ buses and $3$
generators to validate the proposed approach. The proposed online assessment
approach contributes to improving the situational awareness of human operators,
thereby taking remedial actions before the emergency.
