Probabilistic Resilience Distance Measures and Application to Rural Power Distribution System

Rural power distribution systems are evidentially vulnerable to extreme hazards, particularly hurricanes in coastal regions due to low or zero redundancy, low resourcefulness, and aged infrastructure. Some resilience measures exist for quantifying the resilience of infrastructure systems, which can be applied to these rural distribution systems. However, objective decisions based on such measurements are not ready to make due to the lack of framework to assess the change in resilience measure effectively while altering the information of the input parameters. Hence the questions, such as if the infrastructure system is more resilient when subject to some changed input parameters and, if obtained resilience measure is the optimal value for the given infrastructure system considering the available constraints, are not readily answered in terms of existing measures. Thus, this study explores several statistical and information-theoretic distance measures to characterize how a system evolves as a function of system variables from the realm of materials, hazards, or socioeconomic resourcefulness. Numerical evaluation is conducted with stochastically modeled rural distribution systems, which confirms the effectiveness of the proposed framework. Two resilience distance measures, Cramer-Von Mises Distance (CVMD) and Earth Mover's Distance (EMD), are selected and recommended.