Correlating empirical data and extended topological measures in power grid networks

Abstract

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.

Optimizing the Structure of Distribution Smart Grids with Renewable Generation against Abnormal Conditions: A Complex Networks Approach with Evolutionary Algorithms

“…In this respect, as mentioned, hybrid approaches include concepts from EE [82][83][84]96,[98][99][100][101][102]. Nonetheless, the CN approach with purely topological analysis (or even with extended ones to take into account minimal electrical information [34]) has been found to be useful to detect critical elements and to assess topological robustness [35,97,103]. Specifically, Luo and Rosas-Casals have recently reported studies [97,103] that aim at correlating electric-based vulnerability metrics (based on the extended topological approach) with real malfunction data corresponding to some European power transmission grids (Germany, Italy, France and Spain).…”

“…Nonetheless, the CN approach with purely topological analysis (or even with extended ones to take into account minimal electrical information [34]) has been found to be useful to detect critical elements and to assess topological robustness [35,97,103]. Specifically, Luo and Rosas-Casals have recently reported studies [97,103] that aim at correlating electric-based vulnerability metrics (based on the extended topological approach) with real malfunction data corresponding to some European power transmission grids (Germany, Italy, France and Spain). The results, validated and proven by empirical reliability data, are statistically significant (Kolmogorov-Smirnov test) and suggest the existence of a relationship between structure (described by extended topological metrics) and dynamical empirical data.…”

“…Although much research must be carried out, the evidence in [97,103] opens a research line to find a more meaningful link between CN-based metrics and the real empirical data of power grids. The CN approach could be useful to make vulnerability assessment and to design specific actions to reduce topological fragility [34].…”

“…The CN approach could be useful to make vulnerability assessment and to design specific actions to reduce topological fragility [34]. The analyses of [33,35,97,103] suggest that there is a connection between the topological structure and operation performance in a power grid because the structural change could disturb its operational condition and, as a consequence, degrade its operation performance. As a result, there is an increasing interest in analyzing structural vulnerability of power grids by means of the CN methodology.…”

“…In fact, the low level, detailed design must be carried out using electrical engineering techniques. In this respect, a deep discussion about the controversy still unresolved between the complex network and electrical engineering communities can be found in [33,35,97,103], reference [35] being a clear introduction to complexity science in the context of power grids.…”