An Inverse Optimization Method for Electric Vehicle Charging and Road Toll Pricing in Coupled Urban Transportation and Power Distribution Systems

This is the sequel to our earlier paper on A Decentralized Bi-level Decomposition Method for Optimal Operation of Electric Vehicles in Coupled Urban Transportation and Power Distribution Systems. After presenting the pricing framework, coordinated operation model and bi-level decomposition algorithm to obtain the optimal operation state in the previous work, this paper presents the pricing approach to adjust EVs' behavior and achieve that expected state. First, the network equilibrium (NE) and social optimum (SO) operation states are defined, based on which the traditional marginal social cost pricing is developed as benchmark. Second, in light of inverse optimization approach, the minimum charge pricing is proposed which adopts road tolls, charging prices and plug-in fees to coordinate the system operation. Different from the traditional pricing approach, the proposed one can align coupled power-transportation network (CPTN) flows from the spontaneously-formed NE with the least-cost SO state, while minimizing extra user charges. Third, various partial pricing schemes are developed to approximate the expected SO state for practical applications. Finally, case studies on a modified real-world urban network verify the effectiveness and performance of the pricing method. It is proven to significantly reduce the extra user charges while attaining the same optimum state.