## 7 Conclusions  
This paper proposes a spatiotemporal evolution-based risk assessment method, considering the time-varying abnormal states of source-grid equipment under the spatiotemporal trajectory of typhoons. Building on the spatiotemporal characteristics of grid faults, this study further explores the spatiotemporal evolution mechanism of grid anomalies, driven by the coupling of extreme weather factors and power flow, identifying the propagation paths of grid anomalies. This study reveals the inherent patterns of grid fault evolution under extreme weather conditions, addressing gaps in current research. The study identifies evaluation metrics that effectively reflect the grid fault evolution process and system vulnerability. Through a systematic risk assessment process, it provides a new theoretical framework and practical tools for assessing the safety of power grids during extreme weather disasters. The proposed method outperforms traditional cascade fault models that consider only meteorological factors (e.g., the OPA model). Traditional models typically overlook the impact of power flow redistribution on grid fault evolution. In extreme weather events, the interaction between meteorological factors and power flow redistribution affects the stability of grid lines. By considering the coupling effects of meteorological factors and power flow, this study more accurately predicts the spatiotemporal evolution of grid faults, enhancing both the accuracy and timeliness of fault prediction. The proposed method is validated through case studies of the modified IEEE 14 and IEEE 118 systems, effectively capturing the dynamic changes in grid equipment during tropical cyclone passage, particularly regarding fault characteristics under varying meteorological conditions and power flow loads. This evaluation method simulates the alternating processes of equipment failures and power flow redistribution, enabling more accurate predictions of fault chain formation and propagation. Furthermore, the method accounts for uncertainties in meteorological factors and grid parameters, enhancing the accuracy of the overall system risk assessment. In conclusion, the method presented in this paper not only provides a scientific basis for power grid risk management under extreme weather conditions but also offers valuable insights for future disaster prevention and mitigation strategies in power grids. Future research will focus on larger-scale real-world power systems, simulating typhoons that have occurred within these systems and comparing the simulation results with actual operational data. The study will also explore fault recovery strategies during disasters, integrating recovery measures into the fault evolution scheduling process based on real grid operational patterns. Additionally, the research will extend to more tropical cyclone scenarios, including the impact of extreme weather events, such as thunderstorms, on source-grid equipment. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Fault Chain Path** & \(\mathbf{R_{E}}\) \\ \hline
1 & 167, 164, 154–104–110–169–170–30–54–44–26–24–27, 145–128–127–123–124–122 & 1.1344 \\
2 & 167, 159, 145–169–170, 164–128–158–150–147–149, 157, 156–104–110–30–54–44 & 2.3695 \\
3 & 169–104–110–30–106–105–26–24–27, 172–152–153–128–151–148 & 5.1445 \\
4 & 167–104–110–152–153–128–151, 148–30–54–44–26–24–27 & 6.8375 \\
5 & 159, 167–26–48–21–17–18, 168–104–30–102–106–65–63, 172–95–94–60–57–58\(\_\)49 & 19.0674 \\
6 & 167, 159, 169–152–153–155–151–148–149–128, 150–104–30–102–106, 147–155–160 & 8.2863 \\
7 & 159, 167–46–45–60–97–57, 158–104–30–102–106–65–64–62–50, 154–58–178–179 & 1.6215 \\
8 & 167, 159, 172–107–111–109–127–65–106–63–43, 164–180–403–57–58–66–67 & 5.5062 \\
9 & 164, 159, 158, 154, 167–107–127–112–65–109–106–63–96–60–57–58 & 4.1999 \\
10 & 167, 163–164, 145–150–156–158–159–129, 149, 146–160–129–154 & 1.3580 \\ \hline \hline \end{tabular}
\end{table}