Risk Metrics for Dynamic Complex Infrastructure Systems Such as the Power Transmission Grid

Complex critical infrastructures such as power transmission networks, communication systems, transportation network and others display many of the characteristic properties of complex systems. They exhibit infrequent large cascading failures that often obey a characteristic power law distribution in their probability versus size. This power law behavior suggests that conventional risk analysis does not apply to these systems. They also often display correlations between events suggesting that the system memory is important in its evolution. It is thought that much of this behavior comes from the dynamical evolution of the system as it is upgraded, ages, is repaired, and as the operational rules evolve. Metrics for the "system state", i.e. quantifying how likely and risky large failures are is discussed in the context of the power transmission grid. How these metrics change, implying changed risk, with different upgrade and operational strategies is initially explored.