A three-tier stackelberg game-based hierarchical optimization framework for integrated electric vehicle battery swapping and charging systems

This paper proposes a three-tier Stackelberg game-based hierarchical optimization framework for integrated electric vehicle (EV) battery swapping stations (BSS) and charging point operator (CPO) systems. The framework models the strategic interactions among three decision-making layers comprising grid operators, integrated CPO-BSS operators, and EV users within a multi-stakeholder energy management environment. A bi-level mixed-integer linear programming (MILP) formulation combined with backward-induction-based Subgame Perfect Nash Equilibrium (SPNE) analysis is developed to optimize dynamic electricity pricing, battery charging and swapping schedules, grid power utilization, and user service decisions under operational and grid constraints. The upper layer determines time-varying tariffs, demand-response incentives, and capacity charges to improve grid stability and social welfare, while the middle layer optimizes integrated charging-swapping operations and battery inventory management in response to grid signals and user behavior. The lower layer models EV users as rational followers responding to dynamic pricing through charging or swapping decisions. The proposed framework is validated using EV charging sessions from the publicly available ACN-Data corpus from which BSS swapping demand inputs were synthetically derived via a principled data-mapping procedure and Italian GME day-ahead electricity market price data. The results show that the proposed hierarchical framework reduces the operational cost of the system by 14.2-26.5% when compared with the unoptimized baseline system over the five-year simulation period (2020-2024), while reducing the peak grid demand by 26-28% (192-204 kW) compared with the unoptimized system and maintaining 96.8% service reliability. The coordinated strategy further enables effective load shifting toward low-price periods, enhances battery utilization efficiency, and improves demand elasticity through dynamic pricing mechanisms. Comparative analysis shows that the proposed framework captures 15-22% additional value over decentralized Nash equilibrium strategies while achieving near-optimal centralized social welfare performance under realistic institutional and operational constraints. Sensitivity and benchmarking studies confirm the robustness, computational tractability, and scalability of the proposed approach across varying tariff structures, battery inventories, and demand scenarios. The framework provides practical insights for EV infrastructure planning, grid-aware energy management, and regulatory policy design for future integrated charging and battery swapping ecosystems.