## 1 Introduction
Considering both the short-term emergency and long-term operating limit, a robust preventive-corrective security-constrained optimal power flow is presented under \(N-k\) outages [23]. Emergency dispatch during extreme weather events is a crucial element in the three-stage dispatch process. Preventive and restorative dispatches mainly serve as preparatory and backup plans for emergency dispatch, enhancing its effectiveness and preventing the escalation of incidents. Emergency dispatch directly determines whether the system can operate normally under extreme weather conditions. Although researchers have extensively studied emergency dispatch from aspects such as resource types, dispatch objectives, and uncertainties in emergency conditions, few studies have considered the spatiotemporal characteristics of system failures caused by typhoons and their impact on emergency dispatch. Typhoons have distinct spatiotemporal trajectories, causing power grid equipment to experience varying extreme weather factors at different times, leading to continuously changing equipment failure characteristics. Consequently, the distribution of system failures varies across both temporal and spatial dimensions. The spatiotemporal variation in system failure distribution adds complexity to uncertain emergency conditions, necessitating an accurate depiction of emergency conditions that account for the spatiotemporal changes in anomaly distribution during the passage of typhoon. This will enhance the adaptability and robustness of emergency dispatch plans. This paper first analyzes the mechanisms by which typhoons cause failures or abnormal states in typical source-grid equipment (wind power plants, poles and conductors) to provide the time-varying abnormal states of wind power and transmission lines, including abnormal wind power output and line fault probability. Based on the spatiotemporal characteristics of grid failures, the fault probability threshold-based emergency scenarios are constructed. A novel robust emergency dispatch strategy is developed using the emergency scenarios under a defender-attacker framework (DAF). Eventually, by recasting the DAF as a two-stage robust optimization model, the robust emergency dispatch of thermal units and energy storage systems is obtained using the C&CG algorithm. The main contributions of the paper include:  
* Considering time-varying abnormal states of typhoon-susceptible grid-source equipment under the spatiotemporal trajectory of typhoons, spatiotemporal characteristics of grid failures are studied. Based on the spatiotemporal grid failures, fault probability threshold-based emergency scenarios during typhoons are developed, thus laying foundations for subsequent emergency dispatch. * A novel robust emergency dispatch strategy is developed, considering spatiotemporal grid failures during typhoons. Based on the defender-attacker framework, a two-stage robust optimization (TSRO) model is developed, considering the fault probability threshold-based emergency scenarios. The C&CG algorithm is employed to solve the developed TSRO model to obtain the optimal dispatch of various emergency sources such as thermal units and energy storage systems. The remainder of the paper is organized as follows: Section 2 addresses the spatiotemporal grid failures during typhoons and fault probability-based emergency scenarios; Section 3 studies the robust emergency strategy for the constructed emergency scenarios; Section 4 verifies the developed emergency strategy using the benchmark IEEE 14-bus system. Finally, the last section details the concluding remarks.