On the difficulty (and success) of correlating empirical data and (extended) topological measures in power grid networks

Abstract

Power grids have entered the complex networks realm for quite a long time now. Their structure (i.e., topology) and dynamics have been thoroughly studied and many topological measures have been used in order to classify them, evaluate their behavior in terms of robustness or model their dynamic response to malfunctions. Generally speaking, results have been mainly theoretical and sound correlations between real grid’s dynamical behavior (i.e., malfunctions and major events) and any of the mentioned before measures have not yet been found. In recent years, though, new extended topological measures have been used to quantify the ability of a network in sustaining its basic functions. In this paper we present a first attempt to correlate these new measures with real malfunction data for some major European power transmission grids. Similar behavior is found, in terms of robustness to selected attacks to buses, between different networks. This is measured by means of extended topological indexes electrically better defined. These behaviors can be (weakly) correlated with similar probability distributions of major events, identifying similar dynamical response among topologically similar grids. This would raise hopes in finding a more meaningful and significant linkage between structural measures and the real dynamical output (i.e., major events) of a grid.