Bilevel Planning of Wireless Charging Lanes in Coupled Transportation and Power Distribution Networks

A new bilevel optimization framework is developed for the optimal deployment of wireless charging lanes (WCLs) in coupled transportation and power distribution networks, with explicit incorporation of i) the impact of deployment decisions on the traffic flow and charging demand of electric vehicles (EVs), and ii) the total charging power limit of WCL infrastructure. In the upper level, a distribution company decides the optimal deployment of WCL, subject to power distribution network constraints. With the upper level WCL deployment decisions, in the lower level, each EV makes optimal routing and charging decisions to minimize the sum of its travel and charging costs. The proposed bilevel model is reformulated to a single level mathematical program with equilibrium constraints (MPEC) by replacing the lower level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions. A simplified special ordered set Type 1 (SOS1)-based method is developed to linearize the complementary conditions, avoiding the selection of a proper big constant (as in the big- M method). Numerical simulations on a Hong Kong transportation network and the IEEE 118-node test system demonstrate that the proposed bilevel framework reduces the vehicle owner cost by 8% and 5.3%, compared with the single-level and multi-objective planning frameworks. Ignorance of the WCL total charging power limit can lead to 46% to 107% deviation from the optimal deployed WCL length, when the wireless charging EV adoption rate ranges from 15% to 30%.