# Novel Data-Driven Models Applied to Short-Term Electric Load Forecasting
## 4 Results and Discussion
In Figure A1 (Appendix A), a complete table is provided, integrating the results from Figures 6-8 into a single one. The Table in the Appendix A contains additional results that are not shown in Figures 6-8, with the intention to simplify them by not showing the worst performing models. Another interesting result is that including additional features (date/time, weather) should provide an improvement in the results due to the strong correlation between weather and electricity consumption. Nevertheless, this influence turned out to be less significant than anticipated, with most models performing better simply by using the past load values. An explanation could be obtained from the results presented in previous works showing that the influence of weather data is more noticeable as the forecast period increases [36; 37], and their influence is small for a forecast horizon of a few hours [37]. It is interesting to analyze the evolution of the forecast metrics for the different time-ahead time-slots. This evolution depends mainly on the forecasting model, and it can range from a monotonous decreasing line to a decreasing exponential, and it can have intermediate plateaus where the performance is almost constant regardless of the prediction time distance. In all cases, the performance metrics experience a decline when the forecast is for a longer time interval, as intuitively expected. Figure 9 presents the evolution of the forecast metrics for different k-ahead forecasts for two of the best models for average forecasting (Table 1) and Figure 10 for another two of the best models for near-term forecasting (Table 1). It is interesting to analyze the impact of the rolling window length (parameter \(p\)) on the forecast performance metrics. Figure 11 presents the impact on the performance metrics with a rolling window length between 24 (1 day) and 1440 h (60 days). In Figure 11, a vertical red line marks an interval of one week (168 h). A performance improvement is obtained by increasing the value of \(p\) up to a value of 168 (1 week of rolling window length); from this point, the improvement is much smaller, and even decreases with a  
Figure 10: Forecast metrics for successive predicted time-slots for models: classic ML, (linear regression) (\(f=1\), \(p=168\), \(k=24\)) (**left**) and Seq2 seq + attention (2 LSTM + 1 FC) (\(f=45\), \(p=24\), \(k=24\)) (**right**). Figure 9: Forecast metrics for successive predicted time-slots for models: ensemble Type II ((1 LSTM + 2 FC) * 2 + (4 FC) * 2) (\(f=1\), \(p=168\), \(k=24\)) (**left**) and DL architecture (2 1D-CNN + 1 LSTM + 1 FC) (\(f=1\), \(p=720\), \(k=24\)) (**right**). \(p\) value greater than 720 (4 weeks). This behavior explains why the best results were obtained with a \(p\) value between 168 and 720. The Seq2 seq models are an exception in this case due to their difficulties in handling large input vectors. It may also be of interest to investigate the evolution of the loss function during training. Figure 12 provides this evolution for one of the deep learning architectures ((1 LSTM + 1 FC) (\(f\) = 1, \(p\) = 168, \(k\) = 24)), using the mean squared error (MSE) loss. In general, we observed that after 20-30 epochs, most of the models converged smoothly, with the Seq2 seq and ensemble models experiencing the most difficulties in their convergence. To provide a visual indication of the quality of the 24 h forecast, Figure 13 shows a comparison between real (ground-truth) load signals and their forecasts as we increase the forecast time horizon. The different diagrams are 24 h time windows taken at random points in the test set. The forecast follows the real signal almost perf  
Figure 11: Influence of the rolling window length (\(p\)) on different forecast metrics (MSE, MAE, MAD, \(R^{2}\), SMAPE and RRMSE), obtained with the DMD model. The range of values for \(p\) is between 24 (1 day) and 1440 h (60 days).