On Dynamic Network Equilibrium of a Coupled Power and Transportation Network

Abstract

The increasing prevalence of electric vehicles (EVs) has intensified the coupling between power distribution networks (PDNs) and transportation networks (TNs) in both temporal and spatial dimensions. In order to accurately model the coupled network, this paper studies the dynamic network equilibrium to capture the temporally-dynamic interactions between PDNs and TNs. This equilibrium encapsulates the driver’s choices of route, departure time, and charging location, and the electricity price. In the TN, a dynamic traffic model with point queues is proposed to describe the spatial and temporal evolution of traffic flows that is congruent with established user equilibrium choices. In particular, the queues formed at charging stations are, for the first time, modeled by a point queue. In the PDN, the electricity prices are accurately determined from a second-order conic program with a guarantee of strong duality. After theoretically proving the existence of an equilibrium solution, an improved fixed-point algorithm based on extrapolation is also proposed to solve the equilibrium problem efficiently. Numerical results show that the dynamic network equilibrium can be efficiently solved to capture the temporally variant nature of traffic flows, queues, and electricity prices.