Estimating the Region of Attraction for Power Systems Using Gaussian Process and Converse Lyapunov Function

Abstract

The significant penetration of renewable energy resources into power systems introduces intermittent disturbances that drive the system away from its stable operating point (i.e., equilibrium). Nevertheless, as long as the system states are still contained inside a region of attraction (ROA), the system will finally return to the normal operating equilibrium. Thus, the ROA plays a crucial role in the stability assessment of dynamical power systems under uncertainties. This brief introduces a novel framework to construct the ROA of a power system centered around a stable equilibrium by using stable state trajectories of system dynamics. Most existing works on estimating ROA rely on analytic Lyapunov functions, which are subject to two limitations: the analytic Lyapunov functions may not be always readily available and the resulting ROA may be overly conservative. This work overcomes these two limitations by leveraging the converse Lyapunov theorem in control theory to eliminate the need for an analytic Lyapunov function and learning unknown Lyapunov functions with the Gaussian process (GP) approach. In addition, a GP upper confidence bound (GP-UCB)-based sampling algorithm is designed to reconcile the tradeoff between the exploitation for enlarging the ROA and the exploration for enhancing the confidence level of the sample region. Within the constructed ROA, it is guaranteed in the probability that the system state will converge to the stable equilibrium with a confidence level. Extensive simulations and experimental validations are conducted to substantiate the assessment approach for the ROA of IEEE test systems and a real smartgrid using phasor measurement unit (PMU) data. It is demonstrated that the proposed approach can significantly enlarge the estimated ROA compared to that of the analytic Lyapunov counterpart.