## 2 Knowledge and Tools of Model Preparation
For proposed model, the coverage probability of forecasting interval (FICP) is 98.96% in one-step, 79.06% in two-step and 78.95% in three-step. The average width of the interval is 356.9044, 333.2484 and 355.3731 in three steps according to MPI. Compared with the absolute value of power load, the interval width obtained is relatively accurate. AWD is 0.0002, 0.0587 and 0.0554 for three steps, shows the deviation degree of the constructed interval is small. All indexes reflect that the predicted interval of proposed model is qualified. In contrast, for the FICP of single prediction model, none of the predictions is better than proposed model. Although the ICEEMDAN-ELM has the same value of FICP as proposed model in one-step, it is largely lower than two and three-step. (2) By combining FINAW with FICP, for the proposed model, when the FICP value is very high, FINAW is relatively small, which also shows the superiority of the developed model. In the one and two step forecast, the AWD of most other benchmark models is more than ten times of the developed model in one-step, and they are much larger in two and three step. This reflects the less deviation of the developed model. These four indexes fully reflect the superior forecasting ability of the developed model. The same conclusion can be drawn for site 3 in Table 7.

Figure 5: The multi-step forecast ability in Experiment II for site 2. The picture is divided into three parts: one to three steps time series forecasting chart, three steps error comparison bar chart and one-step forecasting error point chart. (3) At the same time, in order to intuitive show the comparison results, the results of the designed model and comparison models are pictured in Figure 6. The conclusions are consistent with Table 7, providing intuitive evidence for verifying the superior ability of the proposed system in the load interval forecasting. As shown in Figure 6, compared with other models, the proposed model has more accuracy interval forecast results. Obviously, the prediction range not only covers most of the load values, but also is narrowest among all models. This shows that the designed model is more stable than others. As a result, the designed model has greater advantages for three experimental datasets. **Remark 1. **_The same as the comparison model used in point forecast, 13 different competition models based on four datasets and multi-step interval forecast are compared. The results show the designed interval model is better than all the comparison models. Due to the excellent ability of the designed interval prediction module based on fuzzy clustering, it is a very promising interval prediction method of power load._

## 5 Discussions

For the sake of discussing the experiment conclusions in detail and reduce the error of power load forecasting, the validity of the established model, the combination mechanism of combination model and the practical application in the power system are discussed. \[\mathrm{H}_{0}:\mathbf{E}[\mathbf{L}(\mathbf{err}_{i}^{1})]=\mathbf{E}[\mathbf{L}(\mathbf{err}_{i}^{2 })] \tag{20}\]0 The final interval results of some models in multi-step forecasting in Experiment III for site 3. The figure shows the interval forecast results of the proposed model, singular spectrum analysis (SSA)-based model, Improved Complete Ensemble Empirical Mode Decomposition (ICEEMDAN)-Autoregressive Integrated Moving Average (ARIMA) model and Generalized Regression Neural Network (GRNN) single model, respectively. In addition, the figure shows the relationship between the interval forecasting band and the real value. ### DM Test

The validity of the model is verified by DM test by all other models comparing with the proposed hybrid forecasting model. Based on DM test theory, the zero hypothesis is that the prediction results of both models is no significant difference, while the alternative hypothesis is contrast. We chose two scales with alpha of 0.1 and 0.05 as the criteria to judge the significance of the results, among which \(Z_{0.05/2}=1.96\) and \(Z_{0.1/2}=1.645\).