Study on the nonlinear synergistic characteristics of V2G and electricity-hydrogen chains based on the Stackelberg game framework

To address the flexible regulation requirements of integrated energy systems with high renewable penetration, this study investigates the nonlinear coordination between Vehicle-to-Grid (V2G) and the electricity–hydrogen chain. A Stackelberg-game-based bi-level optimization model is developed, in which the upper level optimizes electricity pricing and incentive signals, while the lower level performs coordinated charging/discharging and multi-energy conversion scheduling. The objective function incorporates electricity trading cost, battery degradation cost, hydrogen-related operating cost, and carbon cost. To quantify whether the joint deployment of the two flexibility resources creates additional value beyond their standalone effects, a synergistic gain index, Δ, is introduced. A nested GA-MILP framework is adopted to solve the resulting problem, providing a tractable and practically implementable strategy for the nonlinear upper-level decisions and the lower-level dispatch problem. Based on 2019 load and electricity-price data together with representative renewable-generation scenarios, the model is evaluated through operational analysis, parameter sensitivity experiments, multi-season robustness tests, and an additional renewable-generation forecast-error stress test. The results show that, within the examined case-study settings, the coordinated use of V2G and the electricity–hydrogen chain achieves the most favorable synergistic outcome when the renewable penetration coefficient is 2.0 and the carbon-cost weight is 1.0, with the best joint capacity configuration occurring at an EV capacity multiplier of 3.0 and a hydrogen-chain capacity multiplier of 1.5. The study provides a quantitative framework for evaluating and scheduling multiple flexibility resources in integrated energy systems.