Traffic Toll Design for Dynamic Wireless Charging in Coupled Power-Transportation Networks: A Tri-Level Optimization Approach

This article proposes a novel tri-level mixed-integer nonlinear programming (MINLP) framework to investigate the design of time-based tolls for hybrid traffic flows in coupled power-transportation networks with dynamic wireless charging (DWC) infrastructures. To minimize the total travel time over the transportation network, we propose time-based tolls in the upper level, which impact the routing decisions made by hybrid traffic flows in the middle level. The aggregate charging demands from the middle level are then integrated into the lower level problem for power distribution network market clearing. The proposed framework is the first that explores the design of optimal tolls for the efficient operation of coupled power-transportation networks with DWC infrastructures. We convert the formulated tri-level MINLP to an equivalent single level MINLP through a series of techniques, including the Karush-Kuhn-Tucker (KKT) optimality conditions, the value-function method, and a decomposition and constraint generation algorithm. Numerical simulations on a widely adopted testing transportation network and the IEEE 118-node test system demonstrate that the proposed toll scheme leads to significant savings in the social and vehicle owners' costs, by reducing the travel time on transportation links with DWC.