针对多阶段灾害冲击下, 电力系统韧性评估中传统Monte Carlo方法计算效率低和不确定性传播分析复杂等问题, 该文提出一种基于解析推演的电力网络概率韧性高效评估方法。首先, 建立了考虑多阶段灾害演化的电力网络韧性指标评估模型, 并基于电力单元划分构建了用于生成供电路径的混合整数规划模型, 以确定各负荷节点的供电路径; 其次, 结合输电杆塔损伤概率预测结果, 推导了灾中和灾后负荷节点供电中断持续时间的概率分布, 进而通过解析方式计算了电力网络韧性指标; 最后, 以改进IEEE-123节点电力网络为例进行了验证。结果表明: 该文所提方法在与传统Monte Carlo方法评估精度相同的条件下, 显著提高了计算效率, 适用于多阶段灾害场景下电力网络的快速韧性评估。该文研究结果可为电力系统韧性优化和关键基础设施灾害风险评估提供参考。

Objective: With the growing complexity of modern power networks, coupled with the increasing frequency and intensity of natural hazards, there is an urgent need to develop advanced resilience assessment methods. Unlike conventional single-stage disaster events, multi-stage hazards such as earthquake-landslide-debris flow chains have successive and compounding impacts on electrical infrastructure. Such cascading events introduce severe uncertainty into the damage mechanisms and recovery processes of power systems, thereby threatening the continuity of electricity supply in disaster-affected regions. Traditional simulation-based approaches, especially those relying heavily on Monte Carlo techniques, often fail to capture the full dynamics of multi-stage shocks because of limited sampling or become computationally prohibitive when scaled to larger networks. To overcome these challenges, this study developed a probabilistic resilience assessment model that combines analytical probability calculations with optimization-based network analysis. The aim was to develop an accurate and efficient method for evaluating resilience in power systems under multi-stage disaster shocks. Methods: The proposed framework incorporates several method ological innovations. First, the entire power network is partitioned into smaller units through a community detection strategy, ensuring computational tractability while retaining the integrity of network interdependencies. Within these units, a mixed-integer programming model generates feasible power supply paths for each load node under normal operating constraints. This optimization-based representation identifies not only primary supply routes but also redundant paths that become critical in the event of failures. Second, the model incorporates probabilistic damage forecasting of transmission towers, which are among the most vulnerable components during seismic and secondary hazards. Instead of relying on scenario sampling, the model derives closed-form probability distributions of interruption durations during disasters and post-disaster recovery times. These distributions are obtained by analytically linking tower damage probabilities with repair processes, assuming realistic restoration practices. Finally, the resilience indicator is defined as the expected cumulative load-serving capability over the entire disaster cycle. By integrating the temporal evolution of service continuity, the framework captures both the degradation during hazard propagation and the recovery trajectory once repair efforts commence. This analytic approach eliminates the need for extensive sampling and significantly accelerates resilience estimation. Results: The proposed framework was validated using a modified IEEE 123-bus power network as the research object. This grid comprised one generation unit, 123 load centers, and 125 transmission lines. The application of the proposed method to this grid yielded several key research findings: First, the resilience of the power network exhibited an overall downward trend with increasing mainshock magnitude. It declined slowly under low-magnitude earthquakes with favorable disaster resistance. As the mainshock magnitude intensified and more chain-disasters occurred, the failure probability of transmission towers and lines increased, power supply redundancy was gradually weakened, and the network resilience dropped rapidly. Second, the established probabilistic resilience assessment model achieved markedly higher computational efficiency while guaranteeing satisfactory accuracy. By adopting analytical calculations, it realized accurate and efficient evaluation under the spatiotemporal evolution of earthquake disasters, effectively overcoming the excessive computational burden of Monte Carlo simulation. The resilience assessment results also revealed important system-level patterns: The resilience index of the studied grid was approximately 88.644 7% under a magnitude 7.0 earthquake, decreased to 76.854 9% under a magnitude 7.5, and further decreased to 58.413 4% under a magnitude 8.0. Although the resilience index declined significantly with increasing earthquake magnitude, the grid's supply path redundancy capability ensured that most electricity demand could still be met even under severe seismic events. These findings confirmed the crucial role of supply path redundancy and transmission tower reliability in maintaining stable electricity supply under cascading hazards. Conclusions: This study develops a novel probabilistic resilience assessment framework tailored for power networks exposed to multi-stage disaster shocks. By combining power unit partitioning, supply path optimization, and analytical probability modeling, the method addresses the limitations of simulation-heavy approaches and ensures the accuracy and efficiency of resilience estimation. The case study demonstrates the capability of the proposed method to quantify the interplay between disaster evolution, infrastructure vulnerabilities, and system recovery, offering highly relevant insights for planning resilient electricity infrastructure. This approach is particularly valuable for decision-makers and emergency planners, as it supports rapid assessment without sacrificing precision. In conclusion, the proposed method represents a significant advancement in resilience modeling for power systems. This study not only validates the feasibility of analytical probability-based approaches but also sets the stage for further research on integrating adaptive recovery strategies and resource-constrained repair models. In future work, the approach may be extended to consider real-time data integration, simultaneous restoration during hazard evolution, and multi-resource coordination, thereby enhancing the practical applicability of resilience assessment in real-world emergency contexts.