Searching for small-world and scale-free behaviour in long-term historical data of a real-world power grid

Bálint Hartmann,Viktória Sugár

doi:10.1038/s41598-021-86103-7

Abstract

Since the introduction of small-world and scale-free properties, there is an ongoing discussion on how certain real-world networks fit into these network science categories. While the electrical power grid was among the most discussed examples of these real-word networks, published results are controversial, and studies usually fail to take the aspects of network evolution into consideration. Consequently, while there is a broad agreement that power grids are small-world networks and might show scale-free behaviour; although very few attempts have been made to find how these characteristics of the network are related to grid infrastructure development or other underlying phenomena. In this paper the authors use the 70-year-long historical dataset (1949–2019) of the Hungarian power grid to perform complex network analysis, which is the first attempt to evaluate small-world and scale-free properties on long-term real-world data. The results of the analysis suggest that power grids show small-world behaviour only after the introduction of multiple voltage levels. It is also demonstrated that the node distribution of the examined power grid does not show scale-free behaviour and that the scaling is stabilised around certain values after the initial phase of grid evolution.

Highlights

Since the introduction of small-world and scale-free properties, there is an ongoing discussion on how certain real-world networks fit into these network science categories
A year later Barabási and Albert reported[2] the discovery of a high degree of self-organization in large complex networks based on the nature of the interaction between vertices, an attribute to become known as scale-free behaviour. Both papers demonstrated their concepts on real-world networks, among which a common choice was the electrical power grid of the Western United States
The present paper aims to contribute to all three fields, by examining the 70-year-long historical development of the Hungarian power grid (1949–2019), including all voltage levels (120 kV, 220 kV, 400 kV and 750 kV) that have been constructed for transmission networks in different periods of time

Summary

Introduction

Since the introduction of small-world and scale-free properties, there is an ongoing discussion on how certain real-world networks fit into these network science categories. It is demonstrated that the node distribution of the examined power grid does not show scalefree behaviour and that the scaling is stabilised around certain values after the initial phase of grid evolution It was a little more than 20 years ago when two papers gave impetus to the field of network sciences. A year later Barabási and Albert reported[2] the discovery of a high degree of self-organization in large complex networks based on the nature of the interaction between vertices (nodes), an attribute to become known as scale-free behaviour Both papers demonstrated their concepts on real-world networks, among which a common choice was the electrical power grid of the Western United States (modelled as nodes being generators, transformers and substations and the edges being the power lines between them).

Methods

Results

Conclusion