Evolution of the topology of highvoltage electricity network Lubos Buzna, Limor Issacharoff and Dirk

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Evolution of the topology of high-voltage
electricity networkLubos Buzna, Limor
Issacharoff and Dirk Helbing

• ECCS October 5,2007
• Satellite Workshop Critical Infrastructures as
  Complex Systems

IRRIIS EU integrated project (027568)
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Evolution of the topology of high-voltage networks

• Introduction
• Analysed data
• Network growth rate
• Evolution of networks topological properties
• Summary

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Evolution of the topology of high-voltage networks
Electrical power grid
Transmission
Distribution
Generation
Consumption
Main functionalities of transmission system

• Transport of energy across the country
• Transport of energy between the countries over
  long distances
• Backup system for neighbouring countries

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Evolution of the topology of high-voltage networks
Analysed data

• French transmission network (400 kV)
• 220 kV before 1960
• 400 kV introduced in 1960

Data retrieved from the French electricity
network operator RTE (www.rte-france.com).
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Evolution of the topology of high-voltage networks
Network growth rate
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Evolution of the topology of high-voltage networks
Influence of various factors on the networks
growth
Network growth rate
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Evolution of the topology of high-voltage networks
Evolution of topological properties (node
connectivity)
A constant mean node connectivity
in all measured years in spite of significantly
changing degree distribution.
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Evolution of the topology of high-voltage networks
Evolution of topological properties (small-world
property)
Average clustering coefficient
If and the graph is
said to show a small-world property.
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Evolution of the topology of high-voltage networks
Evolution of topological properties (clustering
coefficient)
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Evolution of the topology of high-voltage networks
Evolution of topological properties (betweenness
centrality)
Year 2000
Multiple links
Year 2000 Number of connected node pairs
272 Multiple links 11 double links 3
triple links Edges in the table marked by yellow
represent double links, while green line
represents triple link.
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Evolution of the topology of high-voltage networks
Evolution of topological properties (edge
betweenness centrality)
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Evolution of the topology of high-voltage networks
Evolution of topological properties (node
information centrality)
Graph efficiency
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Evolution of the topology of high-voltage networks

• Summary
• Non-linear network growth (slow growth, intensive
  growth, saturation )
• Constant mean node degree during the power grid
  construction process while the node degree
  distribution changes
• Network grows until it is not small-world
• Information centrality and betweenness centrality
  continuously improving with time
• Clustering coefficients increase only up to the
  year 1996, later on they decrease

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THANK YOU FOR YOUR ATTENTION!

• FURTHER INFORMATION buzna_at_vwi.tu-dresden.de

IRRIIS EU integrated project (027568)
Fakultät Verkehrswissenschaften Friedrich
List Dresden