Optimal pricing for wireless charging under competition and price uncertainty from charging stations in coupled power-transportation networks

Abstract

Unlike traditional charging stations (TCSs), wireless charging lanes (WCLs) enable electric vehicles (EVs) to charge while in motion, thereby substantially reducing EV owners’ time costs. However, this advantage also intensifies competition with TCS, where uncertain and fluctuating charging prices further complicate pricing decisions for the WCL manager (WCLM). These challenges highlight the necessity of a competitive and robust pricing strategy that not only ensures the profitability of WCLM but also supports efficient EV charging and routing. This article presents a novel bilevel distributionally robust optimization (DRO) model for determining optimal wireless charging prices in the integrated power and transportation networks (TNs). The model introduces a bilevel Stackelberg game framework to capture the competitive relationship between WCLM and TCS. Additionally, a DRO method is employed to account for intraday charging price uncertainties at TCS. In the upper level (UL), the wireless charging prices are optimized to maximize the profit of the WCLM. In the lower level (LL), responding to the wireless charging prices released by the UL and uncertain charging prices at TCS, the EV manager determines the optimal charging and routing strategy to minimize the worst-case charging cost and time cost while satisfying the power network and TN constraints. To effectively solve the proposed model, we first employ duality theory to transform the distributionally robust objective function into a tractable form. Next, we propose a value-function-based method to convert the bilevel problem into a single-level problem. Subsequently, a decomposition and sample-based algorithm is developed to solve the single-level problem. Finally, a set of methods are proposed to linearize and convexify the subproblem within the algorithm. Simulation results demonstrate that the proposed pricing scheme leads to an average profit increase of 86.16% compared to the traditional pricing scheme.