  Cascading failures are the typical reasons of black- outs in power grids. The
grid topology plays an important role in determining the dynamics of cascading
failures in power grids. Measures for vulnerability analysis are crucial to
assure a higher level of robustness of power grids. Metrics from Complex
Networks are widely used to investigate the grid vulnerability. Yet, these
purely topological metrics fail to capture the real behaviour of power grids.
This paper proposes a metric, the effective graph resistance, as a
vulnerability measure to de- termine the critical components in a power grid.
Differently than the existing purely topological measures, the effective graph
resistance accounts for the electrical properties of power grids such as power
flow allocation according to Kirchoff laws. To demonstrate the applicability of
the effective graph resistance, a quantitative vulnerability assessment of the
IEEE 118 buses power system is performed. The simulation results verify the
effectiveness of the effective graph resistance to identify the critical
transmission lines in a power grid.
