Measures of robustness for networked critical infrastructure: An empirical comparison on four electrical grids

Evaluating the robustness of critical infrastructure is important for good decisions and for communicating progress toward greater robustness. Nonetheless there is no widely accepted measure analogous to readily available measures of cost-efficiency; our aim here is to examine the usefulness of some candidate robustness measures. A number of possible choices can be computed based on different principles including network topology, entropy and direct estimation of cumulative maximum capacity loss, and measures based on the latter principles are suggested here. To judge their usefulness we introduce the required-capacity survival function and compute this function on representations of four electrical grids, together with a set of scalar robustness measures, conditional on publicly available information. We then evaluate the degree to which the scalar measures provide adequate summary indicators of the more comprehensive capacity-loss information revealed in the survival functions. The measures produce substantially different results, and we find in particular that topological measures correspond only weakly with cumulative capacity loss from destructive events.