Coupled Macroscopic Modelling of Electric Vehicle Traffic and Energy Flows for Electromobility Control

The simultaneous proliferation of electric vehicles and intermittent renewable energy sources promises to expedite decarbonization of two sectors with highest emissions. However, both these developments threaten to endanger power system stability, which may hinder their widespread adoption. To tackle these challenges, there is a need for joint modelling of electric vehicle traffic flows, together with their battery dynamics. We propose a macroscopic electromobility model, augmenting the LWR model, describing the traffic dynamics, with an inhomogeneous advection equation, describing the evolution of vehicles’ State of Charge (SoC). The Riemann problem for the joint model is solved for the case of triangular fundamental diagram, and the solutions are used to formulate a Godunov-like scheme for model discretization. Additionally, we propose an advection-based charging station model, discretize it, and link it with the rest of the traffic and SoC model. We demonstrate the capabilities and use of the full coupled model by proposing a pedagogic example where a simple control law regulates the average SoC of all vehicles on a ring road by controlling the traffic flow entering the charging station.