Dynamic Modeling And Optimal Planning For The Simultaneous Integration Of Electric Vehicles And Renewable Energy Sources Into The Traffic-Power System

The large-scale adoption of electric vehicles (EVs) is regarded as an effective strategy to reduce greenhouse gas emissions from the transportation sector. Although EVs do not produce tailpipe emissions, their widespread adoption may place significant pressure on the power system - a critical aspect that has often been overlooked in policy and planning. Furthermore, the actual environmental benefits of EVs depend on the source of their electricity; renewable energy sources are more environmentally friendly compared to conventional fossil fuels. Taking into account the power demand induced by EV charging, we develop a continuous-time dynamic model for the optimal planning of the simultaneous adoption of EVs and the integration of renewable energy sources into the power system. The interactions between EVs and the power system (termed the traffic-power system) are explicitly considered within our mathematical model, based on the well-known Lotka-Volterra equations. This model effectively describes the relationship between competing entities, such as EVs versus legacy vehicles (LVs) and renewable versus conventional energy sources. We then formulate a control problem to determine an optimal planning policy aimed at achieving a desired market penetration rate (MPR) of EVs. This policy optimizes EV subsidies, infrastructure investment, and the rates for renewable integration and fossil fuel retirement, while minimizing costs and balancing energy demand and supply. The nonlinear optimization problem is solved using the Pontryagin minimum principle, ensuring optimality. We present a series of numerical results to demonstrate the effectiveness of the proposed approach, including extensive analyses on various aspects of the planning policy, such as different planning horizons and desired MPRs of EVs. Additionally, we conduct a cost-benefit analysis to assess the economic feasibility of selecting one set of planning goals over others. The simulation results provide valuable managerial insights for policymakers involved in the long-term planning of the increasingly interconnected traffic-power system.