Lambda-Gaga: Toward a New Metric for the Complex System State of the Electrical Grid

The power transmission grid, as well as many other complex critical infrastructure systems, display characteristics of a critical or near critical complex system with the risk of large cascading failures. Understanding this risk and its relation to the system state as it evolves, could allow for a more realistic risk assessment over time and even for mitigation or at least preparation if in a high risk state. In order to facilitate this type of analysis in the context of the power grid as a complex system, we develop a new measure of the complex system state, the generalized autonomous generational average Lambda-gaga, which correlates with the risk. The Lambda-gaga measure is an extension of the standard cascading propagation measure lambda but avoids the contamination of that measure by small events.