Optimal Power and Semi-dynamic Traffic Flow in Urban Electrified Transportation Networks

The increasing penetration of electric vehicles (EVs) and emerging dynamic wireless charging techniques have strengthened the coupling between traffic networks and power distribution networks. This increased coupling necessitates greater coordination between the two networks. This paper proposes a multi-period optimal traffic and power flow model that considers time-varying electricity and traffic demands. The distribution of traffic flow is represented by a semi-dynamic traffic assignment (SDTA) model, which considers flow propagation between adjacent periods. Combined second-order cone, convex hull, and McCormick envelope relaxations are employed to convexify the power and traffic flow model. Optimization-based bound tightening (OBBT) method combined with a heuristic sequential bound tightening (SBT) method is employed to improve the tightness of the relaxation. The modeling of multi-period scheduling provided by the SDTA model is thoroughly compared with that provided by the conventional static traffic assignment model. In addition, the proposed traffic and power flow model is employed to conduct congestion analysis of the coupled networks. Numerical results on two test systems demonstrate both the spatial and temporal impacts of congestion on each of the coupled networks. Moreover, numerical results verify that the proposed OBBT-SBT-based convex relaxation is sufficiently tight.