Proactive dispatch strategy under spatiotemporal market volatility and EV-operator integration in multi-energy microgrids based on a multi-level game-theoretic robust optimization

• Robust model handles EV, load, and price uncertainty in multi-energy microgrids. • Stackelberg game optimizes EV–grid interactions for decentralized energy scheduling. • Clustering reduces EV uncertainty, improving realism and limiting conservatism. • C&CG algorithm ensures fast convergence for real-time scheduling. • Model outperforms others in cost-efficiency and uncertainty resilience. This study proposes a novel three-stage robust optimization framework that addresses the operational uncertainties in multi-energy microgrids by integrating electricity pricing volatility, renewable generation fluctuations, and electric vehicle (EV) behavioral variability. Existing models often fail to reflect the sequential revelation of uncertainties and overlook the heterogeneous nature of EV users. To fill this gap, we introduce a data-driven uncertainty set derived from over 16,000 real-world EV charging records, enabling the construction of realistic behavioral clusters. A hierarchical Stackelberg game is formulated to represent the strategic interaction between microgrid operators and EV aggregators, balancing system-wide cost objectives with individual user preferences. The proposed model is solved using a Column-and-Constraint Generation (C&CG) algorithm, achieving convergence in 28.03 s across 13 iterations. Comparative case studies demonstrate that while the deterministic model yields the lowest operational cost (21,816.34 yuan), it lacks robustness. In contrast, the fully robust model incurs a higher cost (23,855.70 yuan) but significantly enhances resilience to uncertainty. The findings underscore the effectiveness of integrating behavioral clustering with multi-stage robust optimization, offering both economic efficiency and operational reliability. Future extensions will explore dynamic user interaction modeling and broader resource integration to further enrich urban energy system adaptability.