Optimal resource placement for electric grid resilience via network topology

In this paper, we investigate the resilience of alternative electric grid configurations by adopting a stylized approach based on graph theory, probabilistic analysis, and simulation. We consider two alternative classes of electricity network topology: binary trees and rectangular lattices. For each topology, we find the probabilities that customers located at various nodes in the network will continue to have power following a disaster, depending on the locations of resources (e.g., generators, storage units) in the network. Then, these probabilities are incorporated into the problem of optimally placing resources throughout the network. This is a cost–benefit problem that weighs the benefits of placing resources closer to customers – that is, pursuing a distributed resilience strategy – against the higher total cost of deploying a greater number of smaller resource units. Our analytical and numerical results thus shed light on the general circumstances in which centralized or distributed resilience strategies are preferable. While optimal resource placements depend on various assumptions, such as the probability that power lines fail and the strength of economies of scale, we find that distributed resilience strategies are more often preferred in the binary tree topology than in the rectangular lattice topology. Rectangular lattices feature greater redundancy in terms of paths between nodes in the network, enabling the system to be fairly resilient even with centralized resources.