Topology and Fragility of European High-Voltage Networks: A Cross-Country Comparative Analysis

Abstract

Reliable electricity supply depends on the seamless operation of high-voltage grid infrastructure spanning both transmission and sub-transmission levels. Beneath this apparent uniformity lies a striking structural diversity, which leaves a clear imprint on system vulnerability. In this paper, we present harmonized topological models of the high-voltage grids of 15 European countries, integrating all elements at voltage levels above 110 kV. Topological analysis of these networks reveals a simple yet robust pattern: node degree distributions consistently follow an exponential decay, but the rate of decay varies significantly across countries. Through a detailed and systematic evaluation of network tolerance to node and edge removals, we show that the decay rate delineates the boundary between systems that are more resilient to failures and those that are prone to large-scale disruptions. Furthermore, we demonstrate that this numerical boundary is highly sensitive to which layers of the infrastructure are included in the models. To our knowledge, this study provides the first quantitative cross-country comparison of 15 European high-voltage networks, linking topological properties with vulnerability characteristics.