## 4 Case Study
### Effectiveness Analysis of QGCT-BiLSTM for Load Forecasting  
The comparative analysis is used in this study to analyze the superiority of the load forecasting model. The first stage is constructed to incorporate all influential factors not analyzed by causal correlation into the input feature set for load forecasting. The training set fitting load curve and test set prediction load curve are shown in Figure 2a,b. The basic fitting properties is presented during the training stage, but the test set scatter point  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Quantile** & \begin{tabular}{c} **Maximum** \\ **Temper-** \\ **ature** \\ \end{tabular}  & \begin{tabular}{c} **Minimum** \\ **Temper-** \\ **ature** \\ \end{tabular}  & \begin{tabular}{c} **Average** \\ **Temperature-** \\ **ature** \\ \end{tabular}  & \begin{tabular}{c} **Maximum** \\ **Humid-** \\ **ity** \\ \end{tabular}  & \begin{tabular}{c} **Minimum** \\ **Humid-** \\ **ity** \\ \end{tabular}  & \begin{tabular}{c} **Average** \\ **Humid-** \\ **Speed** \\ \end{tabular}  & \begin{tabular}{c} **Maximum** \\ **Wind** \\ **Speed** \\ \end{tabular}  & \ \begin{tabular}{c} **Minimum** \\ **Wind** \\ **Speed** \\ \end{tabular}  & \begin{tabular}{c} **Average** \\ **Wind** \\ **Speed** \\ \end{tabular}  \\ \hline
0.05 & 0.0071 & 0.0071 & **0.0355** & 0.0071 & 0.0071 & **0.4610** & 0.0071 & 0.0071 & **0.0326** & 0.0071 \\
0.10  
distribution reveals that there are abnormal deviations in the results as shown in Figure 2c,d, and about 37.97% of the test samples show a relative error of more than \(\pm 15\%\). The second stage was implemented as a causality-based feature screening mechanism that retained only those influences that had significant association with load changes. The key factors affecting the load variations are screened out including: maximum temperature, minimum temperature, maximum relative humidity, minimum relative humidity, maximum wind speed, minimum wind speed and rainfall. These key influencing factors are used as input features to realize the forecasting of load. The fitted load curve of the training set and test set with the improved model are shown in Figure 3a,b. The scatter distributions show tighter linear aggregation characteristics as shown in Figure 3c,d. The comparative analysis shows that the curve shape of the model after feature screening agrees significantly with the measured load trend, and the percentage of samples exceeding \(\pm 15\%\) relative error decreases by 11.39%. To evaluate the differences further quantitatively in prediction performance, a four-dimensional assessment system containing root mean square error (RMSE), mean absolute error (MAE), mean bias error (MBE) and mean absolute percentage error (MAPE) is established. As shown in Table 5, the test set prediction errors of the model after feature screening show a systematic decrease: the relative decrease of RMSE, MAE and MAPE are 29.19%, 30.06% and 45.63%. The directional correction of MBE is 35.53%. The improved consistency of the indicators confirms that causal feature screening effectively reduces the noise interference of spurious-correlated variables, enabling the model to capture the essential driving mechanisms of load changes more accurately. Moreover, the key factors screened by the Granger causality test significantly reduced the forecast errors. The decreases in RMSE and MAE indicate that the exclusion of low-correlation variables reduces the risk of overfitting the model to noise. The large decrease in MAPE further suggests that the screened feature set is more attuned to the driving mechanisms of load changes. For example, maximum temperature as a key factor is directly associated with the peak demand of air conditioning loads in summer, while the inclusion of rainfall may reflect the short-term dampening effect of stormy weather on  
Figure 2: Load forecasting results for unfiltered key factors: (**a**) training set load curve; (**b**) test set load curve; (**c**) scatterplot of training set; (**d**) scatterplot of test set.