Topological Vulnerability of the European Power Grid Under Errors and Attacks

Electronic version of an article published as "International journal of bifurcation and chaos", vol. 17, no. 7, July 2007, p. 2465-2475. DOI No: 10.1142/S0218127407018531. © Copyright World Scientific Publishing Company We present an analysis of the topological structure and static tolerance to errors and attacks of the September 2003 actualization of the Union for the Coordination of Transport of Electricity (UCTE) power grid, involving thirty-three different networks. Though every power grid studied has exponential degree distribution and most of them lack typical small-world topology, they display patterns of reaction to node loss similar to those observed in scale-free networks. We have found that the node removal behaviour can be logarithmically related to the power grid size. This logarithmic behaviour would suggest that, though size favours fragility, growth can reduce it. We conclude that, with the ever-growing demand for power and reliability, actual planning strategies to increase transmission systems would have to take into account this relative increase in vulnerability with size, in order facilitate and improve the power grid design and functioningPeer ReviewedPostprint (author’s final draft

A simple spatiotemporal evolution model of a transmission power grid

In this paper, we present a model for the spatial and temporal evolution of a particularly large human-made network: the 400-kV French transmission power grid. This is based on 1) an attachment procedure that diminishes the connection probability between two nodes as the network grows and 2) a coupled cost function characterizing the available budget at every time step. Two differentiated and consecutive processes can be distinguished: a first global space-filling process and a secondary local meshing process that increases connectivity at a local level. Results show that even without power system engineering design constraints (i.e., population and energy demand), the evolution of a transmission network can be remarkably explained by means of a simple attachment procedure. Given a distribution of resources and a time span, the model can also be used to generate the probability distribution of cable lengths at every time step, thus facilitating network planning. Implications for network's fragility are suggested as a starting point for new design perspectives in this kind of infrastructures.Peer ReviewedPostprint (author's final draft

Interdependence of Transmission Branch Parameters on the Voltage Levels

Transformers and transmission lines are critical components of a grid network. This paper analyzes the statistical properties of the electrical parameters of transmission branches and especially examines their interdependence on the voltage levels. Some interesting findings include: (a) with appropriate conversion of MVA rating, a transformer’s per unit reactance exhibits consistent statistical pattern independent of voltage levels and capacity; (b) the distributed reactance (ohms/km) of transmission lines also has some consistent patterns regardless of voltage levels; (c) other parameters such as the branch resistance, the MVA ratings, the transmission line length, etc, manifest strong interdependence on the voltage levels which can be approximated by a power function with different power constants. The results will be useful in both creation of synthetic power grid test cases and validation of existing grid models