Clustering-based Two-stage Probabilistic Small-signal Stability Analysis of Power Systems with Uncertainties

This paper proposes a clustering-based two-stage framework for evaluating the small-signal stability risk caused by the uncertainties of power systems. In the first stage, through a fast K-medoids clustering (FKMC) algorithm, representative samples (RSs) can be selected from massive uncertainty samples. The risk levels of RSs are determined by eigenvalue analysis, and then the convex hull of each risk level can be established. Through iteration, the convex hull-based risk regions can continuously extend to be more accurate. In the second stage, the established risk regions are updated when the uncertainty distributions and correlations change. Based on the risk regions established in the first stage, the risk levels of most new samples can be labeled. Then, a density-based spatial clustering of application with noises (DBSCAN) algorithm is introduced to detect outliers from the unlabeled samples. RSs are selected from the remaining non-outlier samples by the FKMC. Finally, the risk regions are updated based on the outlier and new RSs. Through the proposed framework, the probability of different risk levels can be evaluated, and the risk regions can be visualized. The effectiveness of the proposed framework is verified in a modified IEEE 68-bus power system with 3 wind power generators.