PMU Visibility Graphs

Laith Shalalfeh, Paul Bogdan, Edmond A. Jonckheere

Abstract: In this paper, we map the PMU data to a graph via the visibility algorithm to generate the PMU visibility graph. Applying complex network analysis to this graph unravels several hidden features in the PMU data. The applications of the PMU visibility graphs in the real power grid include anomaly detection, topology identification, and state estimation. We show that the PMU visibility graph is not random and could not be modeled by the cc. On the contrary, the graph represents a scale-free network with a heavy-tailed degree distribution. So, we fit its degree distribution to a power-law distribution to find the best model and we perform goodness-of-fit analysis on the estimated distribution. Lastly, it is argued that power-law degree distribution of the PMU visibility graph reveals the nonstationarity and fractality in the PMU data.