Recovery of Infrastructure Networks via Importance-based Multicentric Percolation Processes

Abstract

Recovery processes across infrastructure systems after disasters are critical to improve their resilience, yet poorly understood. The common assumption of prioritizing the size of the reconnected network as the goal for recovery in many algorithms today is impractical, given that satisfaction of demands is more important for the functional recovery of infrastructure systems such as power grids. Mixed-integer programming formulations that guarantee optimality under practical resource and time constraints continue advancing, but become computationally intractable even for systems with only hundreds of elements. Algorithms approximating the optimal solution with lower computational cost are in need, including competitive percolation or surrogate models. We propose a method based on statistical mechanics that exhibits phase transitions, as when restoring networked systems. Our importance-based multicentric percolation recovery strategy for spatially distributed engineered networks, approximates optimal restoration solutions with a substantially lower computational cost. Small tree-like clusters form first in the network, which then interconnect into bigger components gradually mirroring optimal restoration and aligning with field practices. A key observation is that the formation of large connected components is suppressed during the recovery process, which enables balancing computational efficiency and accuracy. The proposed strategy is very close to optimization-based methods and methods based on competitive percolation, particularly when load is homogeneous and the fraction of generators is small

illustrative examples showcase the adequate trade-off between computation cost and accuracy relative to competing alternatives.