In their recent work, Bálint Hartmann and Viktória Sugár, researchers at the ELKH Centre for Energy Research assembled a 70-year-long historical dataset (1949–2019) of the Hungarian power grid to perform complex network analysis. It is the first attempt to evaluate small-world and scale-free properties on long-term real-world data. These properties strongly correlate with the robustness of the infrastructure against attacks such as cyber-physical attacks or malicious activities. The results were published in Nature’s Scientific Reports.
Though the study of complex networks representing real-world systems has been an active field of network science, surprisingly, evolving power grids have not received significant attention. In an earlier paper Watts and Strogatz presented the concept of small-world networks, describing systems that are highly clustered but have small characteristic path lengths, thus showing similarity in certain aspects to both lattices and random graphs. Such networks include the internet, mapping of international flights and neural connections of the brain. A year later, Barabási and Albert reported the discovery of a high degree of self-organization in large complex networks based on the nature of the interaction between nodes, an attribute that became known as scale-free behavior. Both papers demonstrated their concepts on the electrical power grid of the Western United States, but it was done using a ‘snapshot’ of the evolution of the grid.
It was observed that most complex network properties of the grid stabilized at practically constant values after the initial phase of evolution. This initial phase took approximately 20 years and was closed by the introduction and deployment of the 220 kV voltage level, which connected distant nodes of the network and formed a meshed topology. Four periods of grid development were identified, during which the clustering coefficient (and thus the small-world coefficient) of the network increased significantly. All of these periods were related to the introduction of new voltage levels and the creation of meshed/looped topological formations, which is atypical in single voltage level subnetworks of the power grid. The results imply that power grids show small-world behavior more prominently if they consist of multiple voltage levels.
Because ‘small-worldness’ is a good metric of the strength of the topology (i.e. robustness against failures and targeted attacks), these results are valuable contributions for future grid development planning, an area which is responsible for generating an increase in socio-economic welfare by EUR 7.3 to EUR 13.2 billion per year, ensuring 1.7 million jobs in Europe.
Figure: Four periods of network development activities, which have significantly increased the clustering coefficient of the network. A vast majority of the newly commissioned connections were 220 and 400 kV lines, creating a meshed topology with the underlying 120 kV network.