Equivalent Circuit Model based Electric Vehicle Evacuation with Mobile Charging Stations

The increasing penetration of electric vehicles (EVs) introduces new challenges for emergency evacuation planning due to limited driving range, long charging times, and constrained charging infrastructure, particularly under disaster induced disruptions. This paper proposes a novel optimization based evacuation framework for EVs using Equivalent Circuit Models (ECMs) to jointly address routing, charging, and congestion management. By leveraging electrical analogies, traffic flow is modeled as electrical current, travel time as resistance, and driving range as voltage, enabling the use of Kirchhoff laws to enforce flow balance and energy feasibility constraints. The proposed controllable ECM incorporates binary switches to regulate route selection and explicitly models charging delays and range replenishment at both Fixed Charging Stations (FCSs) and Mobile Charging Stations (MCSs). The resulting formulation leads to an integer programming problem that determines optimal evacuation routes, charging durations, and the placement and number of MCSs to minimize evacuation time. The framework is extended to multiple origin destination pairs using the principle of superposition and supports fairness aware performance metrics, including worst case, average, and variance based evacuation times. Simulation studies on large scale transportation networks in California demonstrate that the proposed approach significantly improves evacuation efficiency and robustness, particularly in scenarios with limited charging access, highlighting the critical role of MCSs in EV based emergency evacuations.