The rapid proliferation of electric vehicles (EVs) and the large-scale deployment of charging facilities have considerably increased the electrification of transportation road networks. However, road networks exhibit vulnerability to failure at several critical sections, which in turn may trigger a cascade of failures, ultimately leading to widespread road network disruptions. In the context of mixed electric and nonelectric vehicular flows, such adverse impacts may further spread and cascade due to EV-specific characteristics, such as limited EV range and required charging time. Protective measures for vulnerable road sections of electrified road networks against hazards could mitigate the risk of cascading failures and the further spread of disruptive events. Therefore, assessing the vulnerability of electrified transportation road networks and identifying critical road sections have become paramount. Given that the vulnerability of electrified transportation road networks has been scarcely explored in existing literature, this paper proposes a two-layered attacker-defender model to study the vulnerability of electrified transportation road networks.

The outer layer model aims to minimize system performance by targeting roads within the system for disruption, i.e., maximizing the total system travel time. The inner layer model serves as a defender, minimizing the total system travel time by dynamically and optimally distributing traffic flows containing both electric and nonelectric vehicles. The inner layer model is formulated based on an enhanced link transmission model, taking into consideration the critical characteristics of the electrified transportation road networks. This two-layered model can describe the temporal and spatial evolution of the mixed electric and nonelectric vehicular flows. Additionally, this paper provides a detailed solution method and theoretical analysis of this model. A mixed-integer quadratic programming problem is obtained by considering the dual of the inner problem and combining the inner problem with the outer problem. This problem is subsequently converted into a mixed-integer linear programming problem using the big M method.

The proposed model is applied to a segment of the highway network in North Carolina, U.S. The experimental results reveal that (1) critical road sections as determined with and without EVs differ considerably. Therefore, it is necessary to incorporate EVs when analyzing the vulnerability of an electrified transportation road network. (2) The set of critical road sections varies depending on the level of attack resources. In particular, the set of critical road sections in the low attack resource level scenarios is not necessarily a subset of the critical road sections in the high attack resource level scenarios. (3) The experimental results confirm the existence of a critical point in the attack resource level. When this critical point is reached, the system performance displays a phase change phenomenon, marked by a notable decline.

The results verify that the proposed model can identify the set of critical road sections in the system and provide theoretical support to improve the vulnerability of the electrified transportation road networks.