Dynamic Modeling and Optimal Planning for Integrating Electric Vehicles and Renewable Energy Into Coupled Traffic-Power Systems

The large-scale adoption of electric vehicles (EVs) is regarded as an effective strategy for reducing greenhouse gas emissions from the transportation sector. Although EVs do not produce tailpipe emissions, their widespread adoption may impose significant pressure on the decarbonization of the power system—a critical aspect often overlooked in planning and policy-making. Moreover, the actual environmental benefits of EVs depend on the source of electricity used for charging. Considering the power demand induced by EV charging, we develop a continuous-time dynamic model for the optimal planning of simultaneous EV adoption and the integration of renewable energy sources into the power system. The interactions between competing entities, such as EVs versus legacy vehicles, and renewable versus conventional energy sources, are incorporated into our mathematical model based on the Lotka-Volterra equations. We formulate an optimal control problem to determine planning policies for EV subsidies, infrastructure investment, and the rates of renewable integration and fossil fuel retirement. The goal is to achieve a desired EV market penetration rate (MPR) while enabling the smooth integration of renewables. The nonlinear optimal control problem is solved using the Pontryagin minimum principle. Comprehensive numerical results are presented to demonstrate the effectiveness of the proposed approach, including sensitivity analyses on MPR targets, planning horizons, and cost-benefit considerations. The results offer useful insights for policymakers in designing long-term strategies for EV adoption within a coupled traffic-power system.