## 4 Results
### Evaluation Criteria and Result  
Validating the proposed model with load data of station 1, the forecasting results are formed from load values with CIs that are determined by the total uncertainty. The former and latter 200 h of forecasting results are respectively shown in Figures 9 and 10. The palettes attached to the right of the figures indicate that the confidence level ranges from 0% to 100%, which corresponds to the color changes from dark green to light green. It can be recognized that the results are credible most of the time. Table 1 presents the accuracy of the forecasting results under various confidence levels. The confidence level can be obtained by setting the value of \(z\) according to the standard normal (\(z\)) distribution table. Then, the accuracy is represented by the coverage of CIs ranging from \(\mu-z\sigma\) to \(\mu+z\sigma\). It is evident that the larger interval size can improve the forecasting accuracy, though the additional uncertainty is undesirable. For the purpose of a pertinent contrast between different classifications in PLF methods, three criteria are designed here to reach a fair comparison among the particular ones:  
_(1) Accuracy under the same confidence level_ (A/CL): A/CL is obtained by calculating the accuracy under an exact quantile or confidence level. This criterion is suitable for the comparison of quantile regression and CI methods, both of which aim at variable interval size. The graphical results of Model 1 and proposed model under quantile and confidence level of 50% are displayed in Figure 11. As shown in Table 1, the Model 1 performs better than the proposed model only when  
Figure 10: The latter 200 h of results predicted by the proposed model. Figure 9: The former 200 h of results predicted by the proposed model. the quantile/confidence-level is set to be low, i.e., 10% and 20%. As the quantile/confidence-level increases, the proposed model is more accurate than Model 1 and it better adapts to the given quantile/confidence-level. _(2) Uncertainty under equal accuracy_ (U/A): U/A is obtained by summing the total interval size under the same accuracy. It provides a feasible way to deal with the variable interval size, which is a barrier in comparing the PI and CI methods. Lower uncertainty also means fewer risks of predicting load within a required accuracy level. Comparing Model 2 and proposed model under accuracy of 90%, the results in Figure 12 show that the proposed model can forecast the load with a smaller interval size. _(3) Accuracy under equal uncertainty_ (A/U): A/U is obtained by calculating the accuracy under equal uncertainty (\(2z\sigma\)). It is designed especially for concise access to distinguish the CI methods, of which the total uncertainty can be easily calculated. As seen in Figure 13, CI methods of Model 3 and proposed model are traced in A/U form. It is clear that the proposed model is more efficient for all given levels of uncertainty. All of the statistical characteristics are described Figure 14 for an intuitive comparison. Influenced by the environmental noise, the raw load data may contain some extreme \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Quantile/Confidence-Level** & **10\%** & **20\%** & **30\%** & **40\%** & **50\%** & **60\%** & **70\%** & **80\%** & **90\%** & **99\%** \\ \hline Model 1 & **20\%** & **28\%** & 30\% & 35\% & 38\% & 43\% & 51\% & 56\% & 60\% & 72\% \\ proposed model & 12\% & 21\% & **31\%** & **38\%** & **46\%** & **53\%** & **68\%** & **74\%** & **88\%** & **94\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Accuracy comparison between Model 1 and the proposed model. Figure 11: Accuracy under the same confidence level (A/CL) comparison between Model 1 and the proposed model under confidence level 50%. Figure 12: Uncertainty under equal accuracy (U/A) comparison between Model 2 and the proposed model under accuracy 90%. values. There is no need to cover all these outliers while forecasting.