## 6 Case Study Analysis
### Comparison of Grid Abnormal Evolution Under Coupled Power Flow and Weather vs. OPA Model  
The traditional OPA(ORNL-PSERC-Alaska) model neglects the influence of post-fault power flow dynamics on cascading failure chains and oversimplifies the temporal arrangement of critical events. This limitation is demonstrated through simulations performed on a modified IEEE 14-bus system.Using the abnormal conditions of power grid equipment calculated in Section 5.1, fault sampling is performed to extract fault lines from all periods during the typhoon, resulting in a grid fault line set considering only meteorological effects. Based on these fault lines, power flow calculations are conducted to identify system overloads caused by the typhoon. Overloaded lines are removed to obtain cascading fault chains considering only meteorological effects. Through extensive sampling simulations, the 10 most frequently occurring fault chains are identified, and their risk indices are calculated, as summarized in Table 3.  
A comparative analysis of the prediction results between the proposed method, which accounts for the coupling effects of power flow and meteorological factors (Method 1), and the OPA model (Method 2), reveals that Method 1 can more accurately capture the risks of power insufficiency. Method 2 neglects the influence of power flow factors on system stability during incident development, leading to considerable deviations in expected values of power insufficiency. In scenarios with substantial wind speed fluctuations, variations in power flow can greatly impact the stability of the power system. Method 1 effectively captures these intricate dynamic changes, while Method 2 does not respond adequately, leading to an incomplete assessment of the actual risks to the power system. Method 1 more accurately represents the complexities present in real power systems, especially under conditions of strong interaction between power flow and meteorological factors, enhancing \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Fault Chain Path** & \(R_{\text{E}}\) \\ \hline
1 & 14, 15, 8, 3–10–9–11–13–12 & 2.7782 \\
2 & 14, 15, 8, 6, 2–5–4–11–13–12–10 & 29.5626 \\
3 & 14, 15, 8, 6–1–2–10–11–20, 5, 4 & 21.1386 \\
4 & 14, 15, 5, 1–2–10–11–20, 3–4–6 & 13.0584 \\
5 & 14, 6, 15, 3, 8, 4–5–2–11–13–12–10 & 21.6176 \\
6 & 14, 15, 8, 6, 5, 1–2–10–11–20 & 1.1137 \\
7 & 14, 8, 15, 6–1–2–10–11–20, 4 & 7.7995 \\
8 & 14, 8, 15, 6–1–2–10–11–20, 5, 3–4 & 19.0836 \\
9 & 8, 14, 15, 4–5–2–3–6 & 0.7352 \\
10 & 15, 14, 6–1–2–10–11–20, 4, 5 & 21.3830 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Risk assessment results of IEEE 14 system considering the coupling effects of power flow and meteorological factors. its value in power system planning and risk management. During extreme weather events, power systems may face challenges due to changes in power flow factors, which Method 2 fails to identify promptly. Scalability Analysis of Spatiotemporal Risk Assessment Methodology for Power Grid Anomalies in Large-Scale Networks Under Extreme Disasters  
The IEEE 118 system, comprising 118 buses and 186 transmission branches, is configured with topological parameters and typhoon trajectory, as depicted in Figure A1. Conventional generators at buses 87, 89, and 100 are retrofitted with equivalently rated wind farms, while new wind installations (50 MW, 50 MW, and 20 MW capacities) are deployed at buses 90, 92, and 104, respectively. Component parameters (including wind turbines, transmission towers, and line characteristics) maintain consistency with the IEEE 14 system, with detailed specifications provided in Table 1. Temporal load profiles with normalized hourly variations are illustrated in Figure A2. The computational results reveal wind power generation profiles (Figure A3 and transmission line failure probabilities (Figure A4) under typhoon conditions. Based on the anomaly propagation pathways in Section 4.2 and cascading failure simulation methodology in Section 5.1, the cascading fault chains are predicted under tropical cyclone.