Tariff Bounding and Cooperation Stability in Power-Traffic Nexus: A Social Entity Perspective

The growing interdependence between power distribution networks (PDNs) and transportation networks (TNs) has driven recent research on power-transportation coordination. This paper identifies three important gaps in current literature. First, the upper-bounding issue of the tariff-based incentives (road toll, charging service fee, etc) is not well addressed, which might raise drivers’ dissatisfaction or compromise system performance. Second, the TN-PDN cooperation is generally built upon a simple assumption without any guarantee on its existence or stability. Third, the autonomy of network operators in tariff setting, operating goals, and data privacy is overlooked in prevailing bi-level social-cost-minimization frameworks. To bridge the above research gaps, this article proposes a novel tri-level framework where a social entity (SE) at the upper level sets the tariff bound towards the lowest social cost and dispenses subsidies towards a stable TN-PDN cooperation, network operators at the middle level jointly manage TNs and PDNs towards the optimal status, and travelers at the lower level decide charging&route choices to minimize individual travel cost. Cooperative Game Theory is adopted to characterize the cooperation and cost allocation between the middle-level operators, while the Core size is introduced to quantify the coalition stability and to guide the SE’s subsidization. A slope-identification based algorithm is proposed to efficiently solve the tri-level problem in a privacy-preserving manner, and a geometric analysis is conducted to deduce the Core size and the required subsidies. Extensive numerical experiments validate the effectiveness and superiority of the proposed methods.