Dynamic Flow Equilibrium of Urban Power and Transportation Networks Considering the Coupling in Time and Space

With the development of smart cities, the increasing penetration of electric vehicles has intensified the deep coupling of power grid and transportation networks in time and space. Against this background, this paper studied the mechanism of the temporal and spatial coupling of power-transportation network, and proposed a proper mathematical framework to describe the dynamic equilibrium state achieved by the interaction of the two networks. In the transportation network, a bi-directional wave dynamic model was applied to characterize the spatial and temporal variations in traffic flows. On this basis, a dynamic charging station model was proposed to capture the charging and queuing of electric vehicles. Then, finite-dimensional variational inequality was introduced to define the mixed dynamic user equilibrium, which included different decisions of electric vehicles and other vehicles. In the power distribution network, a second-order cone relaxation-based AC optimal power flow model was employed. To ensure the accuracy of nodal local marginal price, the strong duality condition was derived in the presence of electric vehicle's charging load. Finally, based on the fixed-point mapping theory, the dynamic flow equilibrium mechanism of the coupled networks was analyzed, and a fixed-point iteration algorithm was developed to solve the problem. Simulation results verify the effectiveness of the proposed model, framework and algorithm. © 2021 Chin. Soc. for Elec. Eng.