Sustainability SI: Optimal Prices of Electricity at Public Charging Stations for Plug-in Electric Vehicles

With an increasing deployment of plug-in electric vehicles, evaluating and mitigating the impacts of additional electrical loads created by these vehicles on power distribution grids become more important. This paper explores the use of prices of electricity at public charging stations as an instrument, in couple of road pricing, to better manage both power distribution and urban transportation networks. More specifically, a multi-class combined distribution and assignment model is formulated to capture the spatial distribution of plug-in electric vehicles across the transportation network and estimate the electrical loads they impose on the power distribution network. Power flow equations are subsequently solved to estimate real power losses. Prices of electricity at public charging stations and road tolls are then optimized to minimize both real power losses in the distribution grid and total travel time in the urban transportation network. The pricing model is formulated as a mathematical program with complementarity constraints and solved by a manifold suboptimization algorithm and a pattern search method. Numerical examples are presented to demonstrate the proposed model and solution algorithms.