Potential field-guided dynamic hierarchical Stackelberg game for MESS-DV synergistic power restoration under storm tide

Extreme storm tides often cause scheduling strategies for critical recovery resources to fail due to coupled deadlocks: flood-induced transportation paralysis limits power restoration. Thus, drainage resource scheduling must be considered when developing optimal grid restoration schedules. To address this issue, this paper proposes a potential field-guided dynamic hierarchical Stackelberg game (DHSG) approach. By endogenizing the physical causal chain of “drainage-transportation-power” into a leader-follower framework, drainage vehicles (DV, Leaders) can proactively reshape transportation network topology, thereby unlocking feasible regions for mobile energy storage systems (MESS, Followers). We introduce fidelity non-linear drainage dynamics model at the leader level to correct operational efficiency deviations, and integrate an action-dependent dynamic horizon mechanism, enabling DV to anticipate future road network topology evolution and avoid myopic behaviors that prioritize localized water removal over global power restoration value. Theoretically, we prove DHSG possesses an exact potential game (EPG) property, guaranteeing algorithm convergence to an asymptotically socially optimal pure-strategy Nash equilibrium within finite steps. To ensure computational feasibility, we develop an oracle-based stochastic reshuffling asynchronous best-response dynamics (RS-ABRD) algorithm. For “zero-gradient plateaus” caused by feedback loop disruptions during post-disaster initial stages, we employ an artificial potential field-based accessibility gradient reward mechanism to provide continuous guidance for blind searches, effectively resolving system cold-start problems. Case studies on the real-world Macau Peninsula system demonstrate this framework reduces cold-start delay by 66.7% and achieves single-step sub-second decision speed, validating its effectiveness in real-time emergency scheduling.